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value | tactic stringlengths 3 2.13k | text_state stringlengths 7 2.31k | text_target_state stringlengths 0 4.07k | raw_goal_sexp stringlengths 10 11.8M | raw_hyp_sexps stringlengths 2 15.6M | model_goal_sexp stringlengths 10 2.68M | model_hyp_sexps stringlengths 2 3.62M | source_syntax stringlengths 179 164k | syntax_args stringclasses 256
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classes | raw_schema_version int64 4 4 | raw_extractor_version stringclasses 1
value | model_schema_version int64 2 2 | model_normalization stringclasses 1
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value | raw_record_sha256 stringlengths 64 64 | state_sha256 stringlengths 64 64 | tactic_sha256 stringlengths 64 64 | target_state_sha256 stringlengths 64 64 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
cat-searcher/leandojo-benchmark-4-random | test | 407 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>isClosed_of_mem_irreducibleComponents</a> _ hz.1 | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
r : U = ∅
z : Set α
hz : z ∈ ι
⊢ IsClosed z | ((:c IsClosed) (:fv _uniq.25970) (:fv _uniq.25976) (:fv _uniq.26729)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:app (:c IsClosed) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV13))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"exact","sourceEnd":12365,"sourceStart":12360,"tag":"atom"},{"children":[{"name":"isClosed_of_mem_irreducibleComponents","semanticRole":"global","source":"isClosed_of_mem_irreducibleComponents","sourceEnd":12403,"sourceStart":12366,"tag":"identifier"},{"children":[{"children":[{"source":"_","sour... | [] | [{"source":"isClosed_of_mem_irreducibleComponents _ hz.1","source_end":12410,"source_start":12366,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 26 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | db7d776250a97501bf21910c1b920f5cd6758cded05d40811893d945524d3842 | 9915551c83f3b21c95fe9232a123855af4309ba8c356e92f669bfcc97bbe9a7e | 67f552b68c569e1b4d88f5929369e2478ec5ebd298f65053e9d9397a48e7396a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 408 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.Finite.coe_toFinset</a>, <a>Set.sUnion_eq_iUnion</a>] | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
r : U = ∅
⊢ Z ⊆ ⋃₀ ↑hι.toFinset | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
r : U = ∅
⊢ Z ⊆ ⋃ i, ↑i | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.25970)) ((:c Set.instHasSubset) (:fv _uniq.25970)) (:fv _uniq.26112) ((:c Set.sUnion) (:fv _uniq.25970) ((:c Finset.toSet) ((:c Set) (:fv _uniq.25970)) ((:c Set.Finite.toFinset) ((:c Set) (:fv _uniq.25970)) (:fv _uniq.26195) (:fv _uniq.26277))))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:fv FV6)) (:arg :explicit 3 (:app (:c Set.sUnion) (:arg :implicit-type 0 (:fv FV0)) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":12432,"sourceStart":12430,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12434,"sourceStart":12433,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.Finite.coe_t... | [] | [{"source":"Set.Finite.coe_toFinset","source_end":12457,"source_start":12434,"syntax_kind":"ident"},{"source":"Set.sUnion_eq_iUnion","source_end":12479,"source_start":12459,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 31 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 94d9d7aa7d14339e80588509a6d7a2e3ab841f2c544caf97e11ccf407d718f1a | 2a8aa97bdcbb340c746a5e612bcb246c36749739a028f2ffce3ca9b0b06a8335 | aa0319f2b1b9f2ac9290181432383e2039c7b4645e95246da4edce6f0a5a75a9 | 64df5bf9dedcdeb9530cf5f4fb5058e65787b87c7f6196242757086cfbbed80b |
cat-searcher/leandojo-benchmark-4-random | test | 409 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.diff_eq_empty</a>] at r | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
r : U = ∅
⊢ Z ⊆ ⋃ i, ↑i | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
r : Z ⊆ ⋃ x, ↑x
⊢ Z ⊆ ⋃ i, ↑i | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.25970)) ((:c Set.instHasSubset) (:fv _uniq.25970)) (:fv _uniq.26112) ((:c Set.iUnion) (:fv _uniq.25970) ((:c Set.Elem) ((:c Set) (:fv _uniq.25970)) (:fv _uniq.26195)) (:lambda i ((:c Set.Elem) ((:c Set) (:fv _uniq.25970)) (:fv _uniq.26195)) ((:c Subtype.val) ((:c Set) (:fv _u... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:fv FV6)) (:arg :explicit 3 (:app (:c Set.iUnion) (:arg :implicit-type 0 (:fv FV0)) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":12491,"sourceStart":12489,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12493,"sourceStart":12492,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.diff_eq_empt... | [] | [{"source":"Set.diff_eq_empty","source_end":12510,"source_start":12493,"syntax_kind":"ident"},{"source":"r","source_end":12516,"source_start":12515,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 35 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 57c5c7a7ad283850aa0887527bbe855e14b1dfc835deca2d082f100231d414c3 | 64df5bf9dedcdeb9530cf5f4fb5058e65787b87c7f6196242757086cfbbed80b | 764772fe95d3e14d996b0c30d14f3670269f9d9fae327d9ab782340d72173f37 | edc9aad94dbb28d64688c63ba2e7dcd4a893d9cfc2923c272210a69038a30de4 |
cat-searcher/leandojo-benchmark-4-random | test | 410 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact r | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
r : Z ⊆ ⋃ x, ↑x
⊢ Z ⊆ ⋃ i, ↑i | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.25970)) ((:c Set.instHasSubset) (:fv _uniq.25970)) (:fv _uniq.26112) ((:c Set.iUnion) (:fv _uniq.25970) ((:c Set.Elem) ((:c Set) (:fv _uniq.25970)) (:fv _uniq.26195)) (:lambda i ((:c Set.Elem) ((:c Set) (:fv _uniq.25970)) (:fv _uniq.26195)) ((:c Subtype.val) ((:c Set) (:fv _u... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:fv FV6)) (:arg :explicit 3 (:app (:c Set.iUnion) (:arg :implicit-type 0 (:fv FV0)) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"exact","sourceEnd":12530,"sourceStart":12525,"tag":"atom"},{"contextIndex":12,"semanticRole":"local","source":"r","sourceEnd":12532,"sourceStart":12531,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact r","sourceEnd":12532,"sourceStart":12525,"tag":"node"} | [] | [{"source":"r","source_end":12532,"source_start":12531,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 38 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fec1ef63c0f1c8890704e39a3b84b737950b5a4e47b2630d36040f9b49931c94 | edc9aad94dbb28d64688c63ba2e7dcd4a893d9cfc2923c272210a69038a30de4 | d8f1aeff34cff9e02f5c1537f031608f00e2d44830f096780f990f728dfa2cf5 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 411 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.compl_eq_univ_diff</a>] | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
⊢ U = (⋃ x, ↑x)ᶜ | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
⊢ U = Set.univ \ ⋃ x, ↑x | ((:c Eq) ((:c Set) (:fv _uniq.25970)) (:fv _uniq.26601) ((:c HasCompl.compl) ((:c Set) (:fv _uniq.25970)) ((:c Set.instHasCompl) (:fv _uniq.25970)) ((:c Set.iUnion) (:fv _uniq.25970) ((:c Set.Elem) ((:c Set) (:fv _uniq.25970)) (:fv _uniq.26195)) (:lambda x ((:c Set.Elem) ((:c Set) (:fv _uniq.25970)) (:fv _uniq.26195)) ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:fv FV11)) (:arg :explicit 2 (:app (:c HasCompl.compl) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c HasCompl) (:arg :explicit 0 (:app (:c Set) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":12733,"sourceStart":12731,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12735,"sourceStart":12734,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.compl_eq_uni... | [] | [{"source":"Set.compl_eq_univ_diff","source_end":12757,"source_start":12735,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 43 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6f1fbd7abf77190d80ea9997968f5ef34b2edf130aa6b95cc33c6f19ad0e3e94 | 09bd558e425c1bc9f1db85c96846814ba120bef35df864778d96e6b7a462e550 | 86439758f04e4952a97ace6235581a2807f85c4d2e404024f0da9e5b443b8cf3 | 6f423ba21822815d798d221d71cce9a7480a4b0b2fc602f3854c23ef77866e62 |
cat-searcher/leandojo-benchmark-4-random | test | 412 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>le_antisymm</a> (<a>Set.diff_subset_diff</a> <a>le_top</a> <| <a>subset_refl</a> _) ?_ | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
⊢ U = Set.univ \ ⋃ x, ↑x | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
⊢ Set.univ \ ⋃ x, ↑x ≤ U | ((:c Eq) ((:c Set) (:fv _uniq.25970)) (:fv _uniq.26601) ((:c SDiff.sdiff) ((:c Set) (:fv _uniq.25970)) ((:c Set.instSDiff) (:fv _uniq.25970)) ((:c Set.univ) (:fv _uniq.25970)) ((:c Set.iUnion) (:fv _uniq.25970) ((:c Set.Elem) ((:c Set) (:fv _uniq.25970)) (:fv _uniq.26195)) (:lambda x ((:c Set.Elem) ((:c Set) (:fv _uniq... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:fv FV11)) (:arg :explicit 2 (:app (:c SDiff.sdiff) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c SDiff) (:arg :explicit 0 (:app (:c Set) (:arg :explicit... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"refine","sourceEnd":12769,"sourceStart":12763,"tag":"atom"},{"children":[{"name":"le_antisymm","semanticRole":"global","source":"le_antisymm","sourceEnd":12781,"sourceStart":12770,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":12783,"sourceStart":12782,"tag":"atom"},{"ch... | [] | [{"source":"le_antisymm (Set.diff_subset_diff le_top <| subset_refl _) ?_","source_end":12831,"source_start":12770,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 46 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0c01e836c68ce9748da24b87be91c08a764003e525e2dbfb5d068ef092de1d11 | 6f423ba21822815d798d221d71cce9a7480a4b0b2fc602f3854c23ef77866e62 | 0cc95423a3a0d0cf4e6f53b7daab350b3c70d1619f9af282e79e062f073bf41d | bc900e8ad3a85bd1038290e4317979dd2f057a6a7c976c2b49f15601fd1c9aab |
cat-searcher/leandojo-benchmark-4-random | test | 413 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Set.compl_eq_univ_diff</a>] | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
⊢ Set.univ \ ⋃ x, ↑x ≤ U | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
⊢ (⋃ x, ↑x)ᶜ ≤ U | ((:c LE.le) ((:c Set) (:fv _uniq.25970)) ((:c Preorder.toLE) ((:c Set) (:fv _uniq.25970)) ((:c PartialOrder.toPreorder) ((:c Set) (:fv _uniq.25970)) ((:c CompleteSemilatticeInf.toPartialOrder) ((:c Set) (:fv _uniq.25970)) ((:c CompleteLattice.toCompleteSemilatticeInf) ((:c Set) (:fv _uniq.25970)) ((:c CompletelyDistrib... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:app (:c SDiff.sdiff) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":12838,"sourceStart":12836,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12840,"sourceStart":12839,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":12843,"sourceSt... | [] | [{"source":"Set.compl_eq_univ_diff","source_end":12866,"source_start":12844,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 47 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6c8d4cda3ce4a307f2aa9c84f7f108bbe900c1eb8453c4e04970c73f502f5ca4 | bc900e8ad3a85bd1038290e4317979dd2f057a6a7c976c2b49f15601fd1c9aab | 201117ed70c23a929d1b553f3246ab8b7a7b5e2125fe6b3693dcf94c1b30c761 | ad9373f86c740a6a9e314248cb862a144c833abb5696639f8948c24974bb351c |
cat-searcher/leandojo-benchmark-4-random | test | 414 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine Set.compl_subset_iff_union.mpr (<a>le_antisymm</a> <a>le_top</a> ?_) | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
⊢ (⋃ x, ↑x)ᶜ ≤ U | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
⊢ Set.univ ≤ (⋃ x, ↑x) ∪ U | ((:c LE.le) ((:c Set) (:fv _uniq.25970)) ((:c Preorder.toLE) ((:c Set) (:fv _uniq.25970)) ((:c PartialOrder.toPreorder) ((:c Set) (:fv _uniq.25970)) ((:c CompleteSemilatticeInf.toPartialOrder) ((:c Set) (:fv _uniq.25970)) ((:c CompleteLattice.toCompleteSemilatticeInf) ((:c Set) (:fv _uniq.25970)) ((:c CompletelyDistrib... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:app (:c HasCompl.compl) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"refine","sourceEnd":12878,"sourceStart":12872,"tag":"atom"},{"children":[{"source":"Set.compl_subset_iff_union.mpr","sourceEnd":12909,"sourceStart":12879,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":12911,"sourceStart":12910,"tag":"atom"},{"children":[{"name":"le_antis... | [] | [{"source":"Set.compl_subset_iff_union.mpr (le_antisymm le_top ?_)","source_end":12933,"source_start":12879,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 50 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | df78467416c4370da9bd89d366fbee24ddac6d52c220199d6249a2c635f894e5 | ad9373f86c740a6a9e314248cb862a144c833abb5696639f8948c24974bb351c | e10df7c2312829a62063a0699cebb9bc61a2cd8cd21c09232b2049533623caa2 | e62be8fc85cb3752c60b05e49258f3862e65ed89703518e4f28499fef66f31b5 |
cat-searcher/leandojo-benchmark-4-random | test | 415 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.union_comm</a>, ← <a>Set.sUnion_eq_iUnion</a>, ← <a>Set.sUnion_insert</a>] | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
⊢ Set.univ ≤ (⋃ x, ↑x) ∪ U | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
⊢ Set.univ ≤ ⋃₀ insert U ι | ((:c LE.le) ((:c Set) (:fv _uniq.25970)) ((:c Preorder.toLE) ((:c Set) (:fv _uniq.25970)) ((:c PartialOrder.toPreorder) ((:c Set) (:fv _uniq.25970)) ((:c CompleteSemilatticeInf.toPartialOrder) ((:c Set) (:fv _uniq.25970)) ((:c CompleteLattice.toCompleteSemilatticeInf) ((:c Set) (:fv _uniq.25970)) ((:c CompletelyDistrib... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:app (:c Set.univ) (:arg :implicit-type 0 (:fv FV0)))) (:arg :explicit 3 (:app (:c Union.union) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":12940,"sourceStart":12938,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12942,"sourceStart":12941,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.union_comm",... | [] | [{"source":"Set.union_comm","source_end":12956,"source_start":12942,"syntax_kind":"ident"},{"source":"Set.sUnion_eq_iUnion","source_end":12982,"source_start":12962,"syntax_kind":"ident"},{"source":"Set.sUnion_insert","source_end":13005,"source_start":12988,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 51 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a85d426cf777f5875c57b61e92af6c9d5f9847a9f4d29d35344f514d27a5dece | e62be8fc85cb3752c60b05e49258f3862e65ed89703518e4f28499fef66f31b5 | 0977924eea4bba2d993e48724099b10dc5012c35ed01b9fb312137db1e622368 | 76b2fb0872c7f749bd7ad6fc2be447417c7047fe4e28093146b7e9e58c1ccf77 |
cat-searcher/leandojo-benchmark-4-random | test | 416 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro a - | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
⊢ Set.univ ≤ ⋃₀ insert U ι | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
a : α
⊢ a ∈ ⋃₀ insert U ι | ((:c LE.le) ((:c Set) (:fv _uniq.25970)) ((:c Preorder.toLE) ((:c Set) (:fv _uniq.25970)) ((:c PartialOrder.toPreorder) ((:c Set) (:fv _uniq.25970)) ((:c CompleteSemilatticeInf.toPartialOrder) ((:c Set) (:fv _uniq.25970)) ((:c CompleteLattice.toCompleteSemilatticeInf) ((:c Set) (:fv _uniq.25970)) ((:c CompletelyDistrib... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:app (:c Set.univ) (:arg :implicit-type 0 (:fv FV0)))) (:arg :explicit 3 (:app (:c Set.sUnion) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rintro","sourceEnd":13017,"sourceStart":13011,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"a","sourceEnd":13019,"sourceStart":13018,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"a","sourceEnd":13019,"sourceStart":13018,"... | [{"role":"fresh_name","source":"a","source_end":13019,"source_start":13018,"syntax_kind":"ident"}] | [{"source":"-","source_end":13021,"source_start":13020,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.clear"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 56 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7bb94742a8834fe74d7f2023ac9fdaa76479d32d32f8b4d404cca5f19ab0dae8 | 76b2fb0872c7f749bd7ad6fc2be447417c7047fe4e28093146b7e9e58c1ccf77 | ffd8e8f586ebe5556eff011ebc500db1d3576ffa504159a343d497ae2eeb4108 | 011e1372eca0d45d4ae10080dd7e55956d4df1941979ca2c2838bdb801639b00 |
cat-searcher/leandojo-benchmark-4-random | test | 417 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases h : a ∈ U | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
a : α
⊢ a ∈ ⋃₀ insert U ι | case pos
α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
a : α
h : a ∈ U
⊢ a ∈ ⋃₀ insert U ι
case neg
... | ((:c Membership.mem) (:fv _uniq.25970) ((:c Set) (:fv _uniq.25970)) ((:c Set.instMembership) (:fv _uniq.25970)) (:fv _uniq.28790) ((:c Set.sUnion) (:fv _uniq.25970) ((:c Insert.insert) ((:c Set) (:fv _uniq.25970)) ((:c Set) ((:c Set) (:fv _uniq.25970))) ((:c Set.instInsert) ((:c Set) (:fv _uniq.25970))) (:fv _uniq.2660... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV13)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"by_cases","sourceEnd":13034,"sourceStart":13026,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":13036,"sourceStart":13035,"tag":"identifier"},{"source":":","sourceEnd":13038,"sourceStart":13037,"tag":"atom"}],"kind":"null","source":"h :","sourceEnd":13038,"sour... | [] | [{"source":"a ∈ U","source_end":13046,"source_start":13039,"syntax_kind":"«term_∈_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 57 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 913b989e7572dbe4ad1bd3a68f9e0456f64f1d659fa8c15d6d81f731999625b2 | 011e1372eca0d45d4ae10080dd7e55956d4df1941979ca2c2838bdb801639b00 | 7058ac2f2a6cd009909572d07473d9c589ba1e8cdb261eb11ecfb3f6d7ac9282 | bf9e1a52094b06ad0699c73bbd8f204510c97bbf20ad4785ca321409cb8596b7 |
cat-searcher/leandojo-benchmark-4-random | test | 418 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨U, <a>Set.mem_insert</a> _ _, h⟩ | case pos
α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
a : α
h : a ∈ U
⊢ a ∈ ⋃₀ insert U ι | ((:c Membership.mem) (:fv _uniq.25970) ((:c Set) (:fv _uniq.25970)) ((:c Set.instMembership) (:fv _uniq.25970)) (:fv _uniq.28790) ((:c Set.sUnion) (:fv _uniq.25970) ((:c Insert.insert) ((:c Set) (:fv _uniq.25970)) ((:c Set) ((:c Set) (:fv _uniq.25970))) ((:c Set.instInsert) ((:c Set) (:fv _uniq.25970))) (:fv _uniq.2660... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV13)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":13059,"sourceStart":13054,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":13063,"sourceStart":13060,"tag":"atom"},{"children":[{"contextIndex":11,"semanticRole":"local","source":"U","sourceEnd":13064,"sourceStart":13063,"tag":"identi... | [] | [{"source":"⟨U, Set.mem_insert _ _, h⟩","source_end":13090,"source_start":13060,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 60 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | be6ca552a29638cb66441cfd7d8bb0ba98cf66d347d7068c394fba3fdde43d97 | 0392ad0a8635299a77f179cfdf103c9a63bfa68ec0de0b65cbbdb48f2fd9022b | 0c530471ff74c366422a7d465689f22ceb1ea8dee7502501f4fc659feb841c71 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 419 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.mem_diff</a>, <a>Decidable.not_and_iff_or_not_not</a>, <a>Classical.not_not</a>, <a>Set.mem_iUnion</a>] at h | case neg
α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
a : α
h : a ∉ U
⊢ a ∈ ⋃₀ insert U ι | case neg
α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
a : α
h : a ∉ Z ∨ ∃ i, a ∈ ↑i
⊢ a ∈ ⋃₀ insert... | ((:c Membership.mem) (:fv _uniq.25970) ((:c Set) (:fv _uniq.25970)) ((:c Set.instMembership) (:fv _uniq.25970)) (:fv _uniq.28790) ((:c Set.sUnion) (:fv _uniq.25970) ((:c Insert.insert) ((:c Set) (:fv _uniq.25970)) ((:c Set) ((:c Set) (:fv _uniq.25970))) ((:c Set.instInsert) ((:c Set) (:fv _uniq.25970))) (:fv _uniq.2660... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV13)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":13100,"sourceStart":13098,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":13102,"sourceStart":13101,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.mem_diff","s... | [] | [{"source":"Set.mem_diff","source_end":13114,"source_start":13102,"syntax_kind":"ident"},{"source":"h","source_end":13179,"source_start":13178,"syntax_kind":"ident"},{"source":"Decidable.not_and_iff_or_not_not","source_end":13148,"source_start":13116,"syntax_kind":"ident"},{"source":"not_not","source_end":13157,"source... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 67 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f81a122042561d2d0455da223bdeafbf25c88370d64b4344a4fd7b8ee73c5f8b | e102d80eeb441e3199c8679ae75fbf8d59248a532f5a2460c1fbe734af1fcfe9 | 07fa4c879ace3f16826710dd29322c6e01c797642b0e5748895a9906ff520e2e | 0ed84c007c9817dcda555f85abe167a1272c928f4f7a1f95ddf125e04f946375 |
cat-searcher/leandojo-benchmark-4-random | test | 420 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases h with (h|⟨i, hi⟩) | case neg
α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
a : α
h : a ∉ Z ∨ ∃ i, a ∈ ↑i
⊢ a ∈ ⋃₀ insert... | case neg.inl
α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
a : α
h : a ∉ Z
⊢ a ∈ ⋃₀ insert U ι
case ... | ((:c Membership.mem) (:fv _uniq.25970) ((:c Set) (:fv _uniq.25970)) ((:c Set.instMembership) (:fv _uniq.25970)) (:fv _uniq.28790) ((:c Set.sUnion) (:fv _uniq.25970) ((:c Insert.insert) ((:c Set) (:fv _uniq.25970)) ((:c Set) ((:c Set) (:fv _uniq.25970))) ((:c Set.instInsert) ((:c Set) (:fv _uniq.25970))) (:fv _uniq.2660... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV13)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rcases","sourceEnd":13192,"sourceStart":13186,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":14,"semanticRole":"local","source":"h","sourceEnd":13194,"sourceStart":13193,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","... | [] | [{"source":"h","source_end":13194,"source_start":13193,"syntax_kind":"ident"},{"source":"(h|⟨i, hi⟩)","source_end":13215,"source_start":13200,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.paren"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 73 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ea717a0c1c12ad963fa36be41288551f6126a3b9be50c6a809a749cdc0710924 | 0ed84c007c9817dcda555f85abe167a1272c928f4f7a1f95ddf125e04f946375 | 3daab5419744a9f8e147a0b8cbe2d38816439ca6bf5add26a9862dc6267963c0 | 6f58f2c69fcea7b2bb4fd083ef0f02d8779e84532390c20543e876cb5c548677 |
cat-searcher/leandojo-benchmark-4-random | test | 421 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨<a>irreducibleComponent</a> a, <a>Or.inr</a> ?_, <a>mem_irreducibleComponent</a>⟩ | case neg.inl
α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
a : α
h : a ∉ Z
⊢ a ∈ ⋃₀ insert U ι | case neg.inl
α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
a : α
h : a ∉ Z
⊢ irreducibleComponent a ... | ((:c Membership.mem) (:fv _uniq.25970) ((:c Set) (:fv _uniq.25970)) ((:c Set.instMembership) (:fv _uniq.25970)) (:fv _uniq.28790) ((:c Set.sUnion) (:fv _uniq.25970) ((:c Insert.insert) ((:c Set) (:fv _uniq.25970)) ((:c Set) ((:c Set) (:fv _uniq.25970))) ((:c Set.instInsert) ((:c Set) (:fv _uniq.25970))) (:fv _uniq.2660... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV13)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"refine","sourceEnd":13231,"sourceStart":13225,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":13235,"sourceStart":13232,"tag":"atom"},{"children":[{"children":[{"name":"irreducibleComponent","semanticRole":"global","source":"irreducibleComponent","sourceEnd":13255,"sourceStart":13235,"tag":... | [] | [{"source":"⟨irreducibleComponent a, Or.inr ?_, mem_irreducibleComponent⟩","source_end":13297,"source_start":13232,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 78 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d3b8ad976fb04a16db15830ac30c15c104eaa45b7f7fbcac879a5cf95bff9f73 | 9c5860001768f9637fd1dbc1a2ab1da9ecf8ac90cda5e2e552780b6ab8ee46f1 | 38f2280c3d21af3582f05cf115d05335f1fdd77bd074cddb6adeac9961934296 | 9aeac240b8e1b4025e1d686b6306ecfda8c07ca6e82018568675b9d2dce2fe1f |
cat-searcher/leandojo-benchmark-4-random | test | 422 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [ι, <a>Set.mem_diff</a>, <a>Set.mem_singleton_iff</a>] | case neg.inl
α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
a : α
h : a ∉ Z
⊢ irreducibleComponent a ... | case neg.inl
α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
a : α
h : a ∉ Z
⊢ irreducibleComponent a ... | ((:c Membership.mem) ((:c Set) (:fv _uniq.25970)) ((:c Set) ((:c Set) (:fv _uniq.25970))) ((:c Set.instMembership) ((:c Set) (:fv _uniq.25970))) ((:c irreducibleComponent) (:fv _uniq.25970) (:fv _uniq.25976) (:fv _uniq.28790)) (:fv _uniq.26195)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"simp","sourceEnd":13310,"sourceStart":13306,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":13315,"sourceStart":13311,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":133... | [] | [{"source":"ι","source_end":13319,"source_start":13317,"syntax_kind":"ident"},{"source":"Set.mem_diff","source_end":13333,"source_start":13321,"syntax_kind":"ident"},{"source":"Set.mem_singleton_iff","source_end":13356,"source_start":13335,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 79 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1bbe7156bc1c5c03245179b08557b7744a9e7eb120a8e51913f7d95f761f08f2 | 9aeac240b8e1b4025e1d686b6306ecfda8c07ca6e82018568675b9d2dce2fe1f | a59a3e412f445824329c07b3513b250d0f0f866e358631e41ed777dd21abb591 | 9c986d7e908f4b0a8418dc95756c9e97e7723c6de15262d32d566bf7a3f70cd2 |
cat-searcher/leandojo-benchmark-4-random | test | 423 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨<a>irreducibleComponent_mem_irreducibleComponents</a> _, ?_⟩ | case neg.inl
α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
a : α
h : a ∉ Z
⊢ irreducibleComponent a ... | case neg.inl
α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
a : α
h : a ∉ Z
⊢ ¬irreducibleComponent a... | ((:c And) ((:c Membership.mem) ((:c Set) (:fv _uniq.25970)) ((:c Set) ((:c Set) (:fv _uniq.25970))) ((:c Set.instMembership) ((:c Set) (:fv _uniq.25970))) ((:c irreducibleComponent) (:fv _uniq.25970) (:fv _uniq.25976) (:fv _uniq.28790)) ((:c irreducibleComponents) (:fv _uniq.25970) (:fv _uniq.25976))) ((:c Not) ((:c Eq... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:app (:c Set) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"refine","sourceEnd":13372,"sourceStart":13366,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":13376,"sourceStart":13373,"tag":"atom"},{"children":[{"children":[{"name":"irreducibleComponent_mem_irreducibleComponents","semanticRole":"global","source":"irreducibleComponent_mem_irreducibleComp... | [] | [{"source":"⟨irreducibleComponent_mem_irreducibleComponents _, ?_⟩","source_end":13431,"source_start":13373,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 80 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6aa750364ced21c112d05e509fd95fa8185535408c375d2b54516e490d97cf37 | 9c986d7e908f4b0a8418dc95756c9e97e7723c6de15262d32d566bf7a3f70cd2 | e579bf395eab171ac93a25b9267fbbf1fa564accf54888cebef9a120798fd634 | acd6f7dfa8da8cebd070bf179eadea81e269174d340648d87ad2c630f411efd4 |
cat-searcher/leandojo-benchmark-4-random | test | 424 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro rfl | case neg.inl
α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
a : α
h : a ∉ Z
⊢ ¬irreducibleComponent a... | case neg.inl
α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
a : α
H : irreducibleComponent a ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {irreducibleComponent a}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := irreducibleComponent a \ ⋃ ... | ((:c Not) ((:c Eq) ((:c Set) (:fv _uniq.25970)) ((:c irreducibleComponent) (:fv _uniq.25970) (:fv _uniq.25976) (:fv _uniq.28790)) (:fv _uniq.26112))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:app (:c Not) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c irreducibleComponent) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV13)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rintro","sourceEnd":13446,"sourceStart":13440,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"rfl","sourceEnd":13450,"sourceStart":13447,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"rfl","sourceEnd":13450,"sourceStart":134... | [] | [{"source":"rfl","source_end":13450,"source_start":13447,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 81 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 43f1cea12f505b52ae1dd49f85a6d8fdb3c309d8b07ed88999dc56b1298e440c | acd6f7dfa8da8cebd070bf179eadea81e269174d340648d87ad2c630f411efd4 | 09e128cd6787f35d3c063b643315aff1382388dafa4e55b6546fbf9dcecb02da | d6c55cb843de2e00da210c3f4bb29ecf5985dec7536079a4ef9e04e429cfe1da |
cat-searcher/leandojo-benchmark-4-random | test | 425 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact h <a>mem_irreducibleComponent</a> | case neg.inl
α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
a : α
H : irreducibleComponent a ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {irreducibleComponent a}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := irreducibleComponent a \ ⋃ ... | (:c False) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"exact","sourceEnd":13464,"sourceStart":13459,"tag":"atom"},{"children":[{"contextIndex":13,"semanticRole":"local","source":"h","sourceEnd":13466,"sourceStart":13465,"tag":"identifier"},{"children":[{"name":"mem_irreducibleComponent","semanticRole":"global","source":"mem_irreducibleComponent","so... | [] | [{"source":"h mem_irreducibleComponent","source_end":13491,"source_start":13465,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 82 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b86cf5f783c717a40957e6687e5ebadec557324cfae405a743d27b774902011f | d6c55cb843de2e00da210c3f4bb29ecf5985dec7536079a4ef9e04e429cfe1da | b15956bbd7ed8ede3dd2ae075c2cda1c116a6d936dc8ae7270838b7a4b275457 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 426 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨i, <a>Or.inr</a> i.2, hi⟩ | case neg.inr.intro
α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
a : α
i : ↑ι
hi : a ∈ ↑i
⊢ a ∈ ⋃₀ i... | ((:c Membership.mem) (:fv _uniq.25970) ((:c Set) (:fv _uniq.25970)) ((:c Set.instMembership) (:fv _uniq.25970)) (:fv _uniq.28790) ((:c Set.sUnion) (:fv _uniq.25970) ((:c Insert.insert) ((:c Set) (:fv _uniq.25970)) ((:c Set) ((:c Set) (:fv _uniq.25970))) ((:c Set.instInsert) ((:c Set) (:fv _uniq.25970))) (:fv _uniq.2660... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV13)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":13506,"sourceStart":13501,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":13510,"sourceStart":13507,"tag":"atom"},{"children":[{"contextIndex":14,"semanticRole":"local","source":"i","sourceEnd":13511,"sourceStart":13510,"tag":"identi... | [] | [{"source":"⟨i, Or.inr i.2, hi⟩","source_end":13530,"source_start":13507,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 85 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | def8ef643c6d7ad7e8a4c5a640e2fb686589c43a2146e711f3a8f9f7f1f2232c | 01f25f131d81a2c33819b4bcef417c2ce6611652d46ecd7abd9db6ae7036eedb | 3008fd45c4b38c6c68ee752c9148ae05a8575fa8e672e01995960800a6f5b90a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 427 | List.Ico.filter_le_of_top_le | Mathlib/Data/List/Intervals.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>decide_eq_true_eq</a>] | n m l : ℕ
hml : m ≤ l
k : ℕ
hk : k ∈ Ico n m
⊢ ¬decide (l ≤ k) = true | n m l : ℕ
hml : m ≤ l
k : ℕ
hk : k ∈ Ico n m
⊢ ¬l ≤ k | ((:c Not) ((:c Eq) (:c Bool) ((:c Decidable.decide) ((:c LE.le) (:c Nat) (:c instLENat) (:fv _uniq.9665) (:fv _uniq.9689)) ((:c Nat.decLe) (:fv _uniq.9665) (:fv _uniq.9689))) (:c Bool.true))) | [{"name":"n","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"l","sexp":"(:c Nat)"},{"name":"hml","sexp":"((:c LE.le) (:c Nat) (:c instLENat) (:fv _uniq.9664) (:fv _uniq.9665))"},{"name":"k","sexp":"(:c Nat)"},{"name":"hk","sexp":"((:c Membership.mem) (:c Nat) ((:c List) (:c Nat)) ((:c List.instMembership) (:... | (:app (:c Not) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Bool)) (:arg :explicit 1 (:app (:c Decidable.decide) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.9663","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.9664","is_instance":false,"is_let":false,"name":"m","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index... | {"children":[{"source":"rw","sourceEnd":7110,"sourceStart":7108,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7112,"sourceStart":7111,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"decide_eq_true_eq","... | [] | [{"source":"decide_eq_true_eq","source_end":7129,"source_start":7112,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.9663","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.9664","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":3,"internal_name":"_uniq... | 55 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | faf14b84c57afb589a59f2b334d40174bf9f11f551d8080df6b2da8b04f60ac2 | 58b8559615cac145ea25b97d4970a7c231af16157bfa865ba8362276e1d08c53 | a729c866619df97d0b128a7ac04d363a753ed663648807ed8f6580e8a76fa510 | 584126d41825cb301156979a6d12181fa062be607b78d67aaddfc91e2f413239 |
cat-searcher/leandojo-benchmark-4-random | test | 428 | List.Ico.filter_le_of_top_le | Mathlib/Data/List/Intervals.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>not_le_of_gt</a> (<a>lt_of_lt_of_le</a> (<a>List.Ico.mem</a>.1 hk).2 hml) | n m l : ℕ
hml : m ≤ l
k : ℕ
hk : k ∈ Ico n m
⊢ ¬l ≤ k | ((:c Not) ((:c LE.le) (:c Nat) (:c instLENat) (:fv _uniq.9665) (:fv _uniq.9689))) | [{"name":"n","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"l","sexp":"(:c Nat)"},{"name":"hml","sexp":"((:c LE.le) (:c Nat) (:c instLENat) (:fv _uniq.9664) (:fv _uniq.9665))"},{"name":"k","sexp":"(:c Nat)"},{"name":"hk","sexp":"((:c Membership.mem) (:c Nat) ((:c List) (:c Nat)) ((:c List.instMembership) (:... | (:app (:c Not) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:fv FV5))))) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.9663","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.9664","is_instance":false,"is_let":false,"name":"m","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index... | {"children":[{"source":"exact","sourceEnd":7140,"sourceStart":7135,"tag":"atom"},{"children":[{"name":"not_le_of_gt","semanticRole":"global","source":"not_le_of_gt","sourceEnd":7153,"sourceStart":7141,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":7155,"sourceStart":7154,"tag":"atom"},{"childre... | [] | [{"source":"not_le_of_gt (lt_of_lt_of_le (mem.1 hk).2 hml)","source_end":7187,"source_start":7141,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.9663","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.9664","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":3,"internal_name":"_uniq... | 55 | 7 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 98884639f19eb863f1985992dde41b1f31f89387fbd4f6a18dae52105fb343ba | 584126d41825cb301156979a6d12181fa062be607b78d67aaddfc91e2f413239 | 87dcb79bdf74f750e820129240256244ff1dbfdfdb12f0a09c545aa1b18ed9ad | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 429 | Submodule.map_unop_mul | Mathlib/Algebra/Algebra/Operations.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Submodule.map_comp</a>, <a>Submodule.map_op_mul</a>, ← <a>Submodule.map_comp</a>, ← <a>Submodule.map_comp</a>, <a>LinearEquiv.comp_coe</a>, <a>LinearEquiv.symm_trans_self</a>, <a>LinearEquiv.refl_toLinearMap</a>, <a>Submodule.map_id</a>, <a>Submodule.map_id</a>, <a>Submodule.map_id</a>] | ι : Sort uι
R : Type u
inst✝² : CommSemiring R
A : Type v
inst✝¹ : Semiring A
inst✝ : Algebra R A
S T : Set A
M✝ N✝ P Q : Submodule R A
m n : A
M N : Submodule R Aᵐᵒᵖ
this : Function.Injective ⇑↑(opLinearEquiv R)
⊢ map (↑(opLinearEquiv R)) (map (↑(opLinearEquiv R).symm) (M * N)) =
map (↑(opLinearEquiv R)) (map (↑(o... | ((:c Eq) ((:c Submodule) (:fv _uniq.128238) ((:c MulOpposite) (:fv _uniq.128243)) ((:c CommSemiring.toSemiring) (:fv _uniq.128238) (:fv _uniq.128241)) ((:c MulOpposite.instAddCommMonoid) (:fv _uniq.128243) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.128243) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiri... | [{"name":"ι","sexp":"(:sort uι)"},{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝²","sexp":"((:c CommSemiring) (:fv _uniq.128238))"},{"name":"A","sexp":"(:sort (+ v 1))"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.128243))"},{"name":"inst✝","sexp":"((:c Algebra) (:fv _uniq.128238) (:fv _uniq.128243) (:fv _... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c MulOpposite) (:arg :explicit 0 (:fv FV3)))) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.128236","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.128238","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":11731,"sourceStart":11729,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":11733,"sourceStart":11732,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"... | [] | [{"source":"map_comp","source_end":11745,"source_start":11737,"syntax_kind":"ident"},{"source":"map_op_mul","source_end":11757,"source_start":11747,"syntax_kind":"ident"},{"source":"map_comp","source_end":11771,"source_start":11763,"syntax_kind":"ident"},{"source":"map_comp","source_end":11785,"source_start":11777,"syn... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.128236","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.128238","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal... | 91 | 2 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2c510c52e55afc4ae39932311a8de3d0e0f0e6d557a7153e96b9a811c71740a5 | 47fb3e3da5f89237b56f7f5f7fd4732f2528c7783c4f6af83a9eeb30f39a18e3 | f2a1c8a24a7004386f72af0e8cd586ca5b2a3b174ebdf47073b8397f0b47f23d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 430 | MeasureTheory.measure_union_add_inter₀' | Mathlib/MeasureTheory/Measure/NullMeasurable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.union_comm</a>, <a>Set.inter_comm</a>, <a>MeasureTheory.measure_union_add_inter₀</a> t hs, <a>add_comm</a>] | ι : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
m0 : MeasurableSpace α
μ : Measure α
s t✝ : Set α
hs : NullMeasurableSet s μ
t : Set α
⊢ μ (s ∪ t) + μ (s ∩ t) = μ s + μ t | ((:c Eq) (:c ENNReal) ((:c HAdd.hAdd) (:c ENNReal) (:c ENNReal) (:c ENNReal) ((:c instHAdd) (:c ENNReal) ((:c Distrib.toAdd) (:c ENNReal) ((:c NonUnitalNonAssocSemiring.toDistrib) (:c ENNReal) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:c ENNReal) ((:c Semiring.toNonAssocSemiring) (:c ENNReal) ((:c OrderedSemi... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.31102))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.31102) (:fv _uniq.31111))"},{"name":... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :implicit-type 2 (:c ENNReal)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c ENNReal)) (:arg :explicit 1 (:c ENNReal)) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31099","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31102","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":15534,"sourceStart":15532,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":15536,"sourceStart":15535,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"union_comm","source_end":15546,"source_start":15536,"syntax_kind":"ident"},{"source":"inter_comm","source_end":15558,"source_start":15548,"syntax_kind":"ident"},{"source":"measure_union_add_inter₀ t hs","source_end":15591,"source_start":15560,"syntax_kind":"Lean.Parser.Term.app"},{"source":"add_comm","sourc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.31099","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.31102","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 86 | 2 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8b50f43576bce6158cf1436f20ea2932a00234129a79db63b0a73a325eb6c708 | 56507903c772d1aa56603584d71de937b12b0b1b69bb8dc1652be12dc5c05954 | 1c7525c94d1b78016f67c5af0920ea04d7d01b4a3830baea48e0d58387453b4d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 431 | Complex.abs_cpow_inv_nat | Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Complex.abs_cpow_real</a>] | x : ℂ
n : ℕ
⊢ abs (x ^ (↑n)⁻¹) = abs x ^ (↑n)⁻¹ | x : ℂ
n : ℕ
⊢ abs (x ^ (↑n)⁻¹) = abs (x ^ ↑(↑n)⁻¹) | ((:c Eq) (:c Real) ((:c DFunLike.coe) ((:c AbsoluteValue) (:c Complex) (:c Real) (:c Complex.instSemiring) (:c Real.orderedSemiring)) (:c Complex) (:lambda _ (:c Complex) (:c Real)) ((:c AbsoluteValue.funLike) (:c Complex) (:c Real) (:c Complex.instSemiring) (:c Real.orderedSemiring)) (:c Complex.abs) ((:c HPow.hPow) (... | [{"name":"x","sexp":"(:c Complex)"},{"name":"n","sexp":"(:c Nat)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c AbsoluteValue) (:arg :explicit 0 (:c Complex)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:c Complex))))) (:arg :instance 3 (:instance-of (:... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.60370","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Complex)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.60371","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"}] | {"children":[{"source":"rw","sourceEnd":14366,"sourceStart":14364,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":14368,"sourceStart":14367,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":14371,"sourceSt... | [] | [{"source":"abs_cpow_real","source_end":14385,"source_start":14372,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.60370","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.60371","is_instance":false,"is_let":false,"user_name":"n"}] | 107 | 4 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3513a3f7b0ad670e2af5a6649fdbe360fabfc7b66dab7249b3690643ef1fd458 | c037a2c6272329c580734f02b5ad7623aa27c9c14cfb88132ffb04d0cc810fbc | 3031b4f51782de19574bf4af3959a36381836cfff64a234b0d16641f412bc233 | a396de78d10ab361d389caf2dc84189a809b55bea8a38d7554e55897deac7ce1 |
cat-searcher/leandojo-benchmark-4-random | test | 432 | Complex.abs_cpow_inv_nat | Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [-<a>Complex.abs_cpow_real</a>] | x : ℂ
n : ℕ
⊢ abs (x ^ (↑n)⁻¹) = abs (x ^ ↑(↑n)⁻¹) | ((:c Eq) (:c Real) ((:c DFunLike.coe) ((:c AbsoluteValue) (:c Complex) (:c Real) (:c Complex.instSemiring) (:c Real.orderedSemiring)) (:c Complex) (:lambda _ (:c Complex) (:c Real)) ((:c AbsoluteValue.funLike) (:c Complex) (:c Real) (:c Complex.instSemiring) (:c Real.orderedSemiring)) (:c Complex.abs) ((:c HPow.hPow) (... | [{"name":"x","sexp":"(:c Complex)"},{"name":"n","sexp":"(:c Nat)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c AbsoluteValue) (:arg :explicit 0 (:c Complex)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:c Complex))))) (:arg :instance 3 (:instance-of (:... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.60370","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Complex)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.60371","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"}] | {"children":[{"source":"simp","sourceEnd":14392,"sourceStart":14388,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":14394,"sourceStart":14393,"tag":"a... | [] | [{"source":"abs_cpow_real","source_end":14408,"source_start":14395,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.60370","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.60371","is_instance":false,"is_let":false,"user_name":"n"}] | 107 | 8 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 02b27b4a62d9819fb17d0f471c6c66347a4019e1759865eb46a26258b94ebcee | a396de78d10ab361d389caf2dc84189a809b55bea8a38d7554e55897deac7ce1 | c2b94f468f6b7a078f24a3195cb2eff7e18020d6d62f0c711109134bb91cc7f0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 433 | Nat.add_pos_iff_pos_or_pos | Mathlib/Data/Nat/Defs.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | omega | a b c d m n k : ℕ
p q : ℕ → Prop
⊢ 0 < m + n ↔ 0 < m ∨ 0 < n | ((:c Iff) ((:c LT.lt) (:c Nat) (:c instLTNat) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.15109) (:fv _uniq.15111))) ((:c Or) ((:c LT.lt) (:c Nat) (:c instLTNat) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c ... | [{"name":"a","sexp":"(:c Nat)"},{"name":"b","sexp":"(:c Nat)"},{"name":"c","sexp":"(:c Nat)"},{"name":"d","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"k","sexp":"(:c Nat)"},{"name":"p","sexp":"(:forall _ (:c Nat) (:sort 0))"},{"name":"q","sexp":"(:forall _ (:c Nat) (:sort 0)... | (:app (:c Iff) (:arg :explicit 0 (:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15101","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15103","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Nat)"},{"binder_role":":implicit","context_ind... | {"children":[{"children":[{"children":[{"children":[{"source":"omega","sourceEnd":12418,"sourceStart":12413,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.omega","source":"omega","sourceEnd":12418,"sourceStart":12413,"tag":"node"}],"kind":"null","source":"omega","source... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15101","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15103","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 129 | 2 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8226349581997ad8cc3df9c09848e1ba4d876f416af7e8859deacb9833471617 | bafdd0ec9437969fe048944ab1d7ad8a5ecb14c747a622a647fad3074b713787 | 304b4a90a76a1cbe4c112e074b30e75181f54df43d60f883597457844293b341 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 434 | Finset.nonempty_Ico | Mathlib/Order/Interval/Finset/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Finset.coe_nonempty</a>, <a>Finset.coe_Ico</a>, <a>Set.nonempty_Ico</a>] | ι : Type u_1
α : Type u_2
inst✝¹ : Preorder α
inst✝ : LocallyFiniteOrder α
a a₁ a₂ b b₁ b₂ c x : α
⊢ (Ico a b).Nonempty ↔ a < b | ((:c Iff) ((:c Finset.Nonempty) (:fv _uniq.305) ((:c Finset.Ico) (:fv _uniq.305) (:fv _uniq.308) (:fv _uniq.316) (:fv _uniq.318) (:fv _uniq.324))) ((:c LT.lt) (:fv _uniq.305) ((:c Preorder.toLT) (:fv _uniq.305) (:fv _uniq.308)) (:fv _uniq.318) (:fv _uniq.324))) | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c Preorder) (:fv _uniq.305))"},{"name":"inst✝","sexp":"((:c LocallyFiniteOrder) (:fv _uniq.305) (:fv _uniq.308))"},{"name":"a","sexp":"(:fv _uniq.305)"},{"name":"a₁","sexp":"(:fv _uniq.305)"},{"name":"a₂","sexp"... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Finset.Nonempty) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Finset.Ico) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 2 (:instance-of (:app (:c LocallyFiniteOrder) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.302","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.305","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit"... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":2131,"sourceStart":2129,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2133,"sourceStart":2132,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"sour... | [] | [{"source":"coe_nonempty","source_end":2149,"source_start":2137,"syntax_kind":"ident"},{"source":"coe_Ico","source_end":2158,"source_start":2151,"syntax_kind":"ident"},{"source":"Set.nonempty_Ico","source_end":2176,"source_start":2160,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.302","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.305","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_name"... | 14 | 2 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cba47c4a867026ee4401e9eeed46b78d305697045c6de09a4e5a7a4073955507 | 4343de71a47719b381e9f72e567af981c5e08e5909f7d08b826b508de30af7bf | 60447e5f45d688fc62047d5dbf4fe66aa4a465469ba594b76fcdcec8f031e6df | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 435 | not_summable_of_ratio_norm_eventually_ge | Mathlib/Analysis/SpecificLimits/Normed.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Filter.eventually_atTop</a>] at h | α✝ : Type u_1
β : Type u_2
ι : Type u_3
α : Type u_4
inst✝ : SeminormedAddCommGroup α
f : ℕ → α
r : ℝ
hr : 1 < r
hf : ∃ᶠ (n : ℕ) in atTop, ‖f n‖ ≠ 0
h : ∀ᶠ (n : ℕ) in atTop, r * ‖f n‖ ≤ ‖f (n + 1)‖
⊢ ¬Summable f | α✝ : Type u_1
β : Type u_2
ι : Type u_3
α : Type u_4
inst✝ : SeminormedAddCommGroup α
f : ℕ → α
r : ℝ
hr : 1 < r
hf : ∃ᶠ (n : ℕ) in atTop, ‖f n‖ ≠ 0
h : ∃ a, ∀ b ≥ a, r * ‖f b‖ ≤ ‖f (b + 1)‖
⊢ ¬Summable f | ((:c Not) ((:c Summable) (:fv _uniq.191350) (:c Nat) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.191350) ((:c SeminormedAddCommGroup.toAddCommGroup) (:fv _uniq.191350) (:fv _uniq.191351))) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.191350) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.191350) ((:c Seminorme... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.191350))"},{"name":"f","sexp":"(:forall _ (:c Nat) (:fv _uniq.191350))"},{"name":"r","sexp":"(... | (:app (:c Not) (:arg :explicit 0 (:app (:c Summable) (:arg :implicit-type 0 (:fv FV4)) (:arg :implicit-type 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV4))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 4 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"rw","sourceEnd":32024,"sourceStart":32022,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":32026,"sourceStart":32025,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Filter.eventuall... | [] | [{"source":"eventually_atTop","source_end":32042,"source_start":32026,"syntax_kind":"ident"},{"source":"h","source_end":32048,"source_start":32047,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 140 | 4 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a9ace3c376c5ae12d6533d2815d546893107fe3c49da62167ec158904dabb22e | ccede5bef4d30264c06ebe7255483fc274713667dbccd764dcb5ca715ed6b9c4 | 50080ffe00226139f15de3b57490673bc85038c1c5fbcb8a559220b1ac2c6979 | 62a94141e26cbeb8a2c355ae80f32b404b4aecc29c00dacbddcec922cbb0febc |
cat-searcher/leandojo-benchmark-4-random | test | 436 | not_summable_of_ratio_norm_eventually_ge | Mathlib/Analysis/SpecificLimits/Normed.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases h with ⟨N₀, hN₀⟩ | α✝ : Type u_1
β : Type u_2
ι : Type u_3
α : Type u_4
inst✝ : SeminormedAddCommGroup α
f : ℕ → α
r : ℝ
hr : 1 < r
hf : ∃ᶠ (n : ℕ) in atTop, ‖f n‖ ≠ 0
h : ∃ a, ∀ b ≥ a, r * ‖f b‖ ≤ ‖f (b + 1)‖
⊢ ¬Summable f | case intro
α✝ : Type u_1
β : Type u_2
ι : Type u_3
α : Type u_4
inst✝ : SeminormedAddCommGroup α
f : ℕ → α
r : ℝ
hr : 1 < r
hf : ∃ᶠ (n : ℕ) in atTop, ‖f n‖ ≠ 0
N₀ : ℕ
hN₀ : ∀ b ≥ N₀, r * ‖f b‖ ≤ ‖f (b + 1)‖
⊢ ¬Summable f | ((:c Not) ((:c Summable) (:fv _uniq.191350) (:c Nat) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.191350) ((:c SeminormedAddCommGroup.toAddCommGroup) (:fv _uniq.191350) (:fv _uniq.191351))) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.191350) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.191350) ((:c Seminorme... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.191350))"},{"name":"f","sexp":"(:forall _ (:c Nat) (:fv _uniq.191350))"},{"name":"r","sexp":"(... | (:app (:c Not) (:arg :explicit 0 (:app (:c Summable) (:arg :implicit-type 0 (:fv FV4)) (:arg :implicit-type 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV4))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 4 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"rcases","sourceEnd":32057,"sourceStart":32051,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":10,"semanticRole":"local","source":"h","sourceEnd":32059,"sourceStart":32058,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","... | [] | [{"source":"h","source_end":32059,"source_start":32058,"syntax_kind":"ident"},{"source":"⟨N₀, hN₀⟩","source_end":32082,"source_start":32065,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 140 | 7 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8115b365bb91bfc1c84772aebaca41031bc33ef334bb2f61e10949abe482b756 | 62a94141e26cbeb8a2c355ae80f32b404b4aecc29c00dacbddcec922cbb0febc | 54c0a8d45c0e3d5da92cf171148928b79a99fdb7dbe0f343a5e0d3c0532cf8af | 52263229097d51838dc372d45f10a1bc4a679f4caaa1f313a647d371836bff78 |
cat-searcher/leandojo-benchmark-4-random | test | 437 | not_summable_of_ratio_norm_eventually_ge | Mathlib/Analysis/SpecificLimits/Normed.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Filter.frequently_atTop</a>] at hf | case intro
α✝ : Type u_1
β : Type u_2
ι : Type u_3
α : Type u_4
inst✝ : SeminormedAddCommGroup α
f : ℕ → α
r : ℝ
hr : 1 < r
hf : ∃ᶠ (n : ℕ) in atTop, ‖f n‖ ≠ 0
N₀ : ℕ
hN₀ : ∀ b ≥ N₀, r * ‖f b‖ ≤ ‖f (b + 1)‖
⊢ ¬Summable f | case intro
α✝ : Type u_1
β : Type u_2
ι : Type u_3
α : Type u_4
inst✝ : SeminormedAddCommGroup α
f : ℕ → α
r : ℝ
hr : 1 < r
hf : ∀ (a : ℕ), ∃ b ≥ a, ‖f b‖ ≠ 0
N₀ : ℕ
hN₀ : ∀ b ≥ N₀, r * ‖f b‖ ≤ ‖f (b + 1)‖
⊢ ¬Summable f | ((:c Not) ((:c Summable) (:fv _uniq.191350) (:c Nat) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.191350) ((:c SeminormedAddCommGroup.toAddCommGroup) (:fv _uniq.191350) (:fv _uniq.191351))) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.191350) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.191350) ((:c Seminorme... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.191350))"},{"name":"f","sexp":"(:forall _ (:c Nat) (:fv _uniq.191350))"},{"name":"r","sexp":"(... | (:app (:c Not) (:arg :explicit 0 (:app (:c Summable) (:arg :implicit-type 0 (:fv FV4)) (:arg :implicit-type 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV4))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 4 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"rw","sourceEnd":32087,"sourceStart":32085,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":32089,"sourceStart":32088,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Filter.frequentl... | [] | [{"source":"frequently_atTop","source_end":32105,"source_start":32089,"syntax_kind":"ident"},{"source":"hf","source_end":32112,"source_start":32110,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 140 | 8 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3a608db8498bcdb5525ab811a22e3f3a8122e5135cc8e3728cc6efef629e7762 | 52263229097d51838dc372d45f10a1bc4a679f4caaa1f313a647d371836bff78 | 23069b960070b9cea26e1061ee1f5dc49c9667029674d71a98e36e3a6dcee66c | 283e6784fbbcca7df58e35c13d54754dcc3601d3349097e40d5bf66317c054e0 |
cat-searcher/leandojo-benchmark-4-random | test | 438 | not_summable_of_ratio_norm_eventually_ge | Mathlib/Analysis/SpecificLimits/Normed.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases hf N₀ with ⟨N, hNN₀ : N₀ ≤ N, hN⟩ | case intro
α✝ : Type u_1
β : Type u_2
ι : Type u_3
α : Type u_4
inst✝ : SeminormedAddCommGroup α
f : ℕ → α
r : ℝ
hr : 1 < r
hf : ∀ (a : ℕ), ∃ b ≥ a, ‖f b‖ ≠ 0
N₀ : ℕ
hN₀ : ∀ b ≥ N₀, r * ‖f b‖ ≤ ‖f (b + 1)‖
⊢ ¬Summable f | case intro.intro.intro
α✝ : Type u_1
β : Type u_2
ι : Type u_3
α : Type u_4
inst✝ : SeminormedAddCommGroup α
f : ℕ → α
r : ℝ
hr : 1 < r
hf : ∀ (a : ℕ), ∃ b ≥ a, ‖f b‖ ≠ 0
N₀ : ℕ
hN₀ : ∀ b ≥ N₀, r * ‖f b‖ ≤ ‖f (b + 1)‖
N : ℕ
hNN₀ : N₀ ≤ N
hN : ‖f N‖ ≠ 0
⊢ ¬Summable f | ((:c Not) ((:c Summable) (:fv _uniq.191350) (:c Nat) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.191350) ((:c SeminormedAddCommGroup.toAddCommGroup) (:fv _uniq.191350) (:fv _uniq.191351))) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.191350) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.191350) ((:c Seminorme... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.191350))"},{"name":"f","sexp":"(:forall _ (:c Nat) (:fv _uniq.191350))"},{"name":"r","sexp":"(... | (:app (:c Not) (:arg :explicit 0 (:app (:c Summable) (:arg :implicit-type 0 (:fv FV4)) (:arg :implicit-type 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV4))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 4 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"rcases","sourceEnd":32121,"sourceStart":32115,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"contextIndex":9,"semanticRole":"local","source":"hf","sourceEnd":32124,"sourceStart":32122,"tag":"identifier"},{"children":[{"contextIndex":... | [] | [{"source":"hf N₀","source_end":32129,"source_start":32122,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨N, hNN₀ : N₀ ≤ N, hN⟩","source_end":32167,"source_start":32135,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 140 | 11 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | eaa26100ef6b6a2cb25fc2b321ba260a14bd35b0033f2f344bd27e2a4e4a524b | 283e6784fbbcca7df58e35c13d54754dcc3601d3349097e40d5bf66317c054e0 | 5f1c69287c967b18a3a85fe3c11204f69836e3f753aa619ef180e14019484d4c | aa0a795fb240acff8f2ad00dc44ce283924d77264613ca15b3d3cc481d36a580 |
cat-searcher/leandojo-benchmark-4-random | test | 439 | not_summable_of_ratio_norm_eventually_ge | Mathlib/Analysis/SpecificLimits/Normed.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← @<a>summable_nat_add_iff</a> α _ _ _ _ N] | case intro.intro.intro
α✝ : Type u_1
β : Type u_2
ι : Type u_3
α : Type u_4
inst✝ : SeminormedAddCommGroup α
f : ℕ → α
r : ℝ
hr : 1 < r
hf : ∀ (a : ℕ), ∃ b ≥ a, ‖f b‖ ≠ 0
N₀ : ℕ
hN₀ : ∀ b ≥ N₀, r * ‖f b‖ ≤ ‖f (b + 1)‖
N : ℕ
hNN₀ : N₀ ≤ N
hN : ‖f N‖ ≠ 0
⊢ ¬Summable f | case intro.intro.intro
α✝ : Type u_1
β : Type u_2
ι : Type u_3
α : Type u_4
inst✝ : SeminormedAddCommGroup α
f : ℕ → α
r : ℝ
hr : 1 < r
hf : ∀ (a : ℕ), ∃ b ≥ a, ‖f b‖ ≠ 0
N₀ : ℕ
hN₀ : ∀ b ≥ N₀, r * ‖f b‖ ≤ ‖f (b + 1)‖
N : ℕ
hNN₀ : N₀ ≤ N
hN : ‖f N‖ ≠ 0
⊢ ¬Summable fun n => f (n + N) | ((:c Not) ((:c Summable) (:fv _uniq.191350) (:c Nat) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.191350) ((:c SeminormedAddCommGroup.toAddCommGroup) (:fv _uniq.191350) (:fv _uniq.191351))) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.191350) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.191350) ((:c Seminorme... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.191350))"},{"name":"f","sexp":"(:forall _ (:c Nat) (:fv _uniq.191350))"},{"name":"r","sexp":"(... | (:app (:c Not) (:arg :explicit 0 (:app (:c Summable) (:arg :implicit-type 0 (:fv FV4)) (:arg :implicit-type 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV4))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 4 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"rw","sourceEnd":32172,"sourceStart":32170,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":32174,"sourceStart":32173,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":32177,"sourceSt... | [] | [{"source":"@summable_nat_add_iff α _ _ _ _ N","source_end":32212,"source_start":32178,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 140 | 12 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 57900fdb7059fb8cc02b2cea8dd88be9b7c88c1628961a28f8e3d9d343720750 | aa0a795fb240acff8f2ad00dc44ce283924d77264613ca15b3d3cc481d36a580 | 530f08471d072dbc9ffd7d9f3f8afd2a2cd9c2b61545b07ad75dac978c276378 | 3cd02dca97f9eb1699d5a7c34471c78438d58c8ca892cccc11f02c9b37b693d4 |
cat-searcher/leandojo-benchmark-4-random | test | 440 | not_summable_of_ratio_norm_eventually_ge | Mathlib/Analysis/SpecificLimits/Normed.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>mt</a> <a>Summable.tendsto_atTop_zero</a> fun h' ↦ <a>not_tendsto_atTop_of_tendsto_nhds</a> (tendsto_norm_zero.comp h') ?_ | case intro.intro.intro
α✝ : Type u_1
β : Type u_2
ι : Type u_3
α : Type u_4
inst✝ : SeminormedAddCommGroup α
f : ℕ → α
r : ℝ
hr : 1 < r
hf : ∀ (a : ℕ), ∃ b ≥ a, ‖f b‖ ≠ 0
N₀ : ℕ
hN₀ : ∀ b ≥ N₀, r * ‖f b‖ ≤ ‖f (b + 1)‖
N : ℕ
hNN₀ : N₀ ≤ N
hN : ‖f N‖ ≠ 0
⊢ ¬Summable fun n => f (n + N) | case intro.intro.intro
α✝ : Type u_1
β : Type u_2
ι : Type u_3
α : Type u_4
inst✝ : SeminormedAddCommGroup α
f : ℕ → α
r : ℝ
hr : 1 < r
hf : ∀ (a : ℕ), ∃ b ≥ a, ‖f b‖ ≠ 0
N₀ : ℕ
hN₀ : ∀ b ≥ N₀, r * ‖f b‖ ≤ ‖f (b + 1)‖
N : ℕ
hNN₀ : N₀ ≤ N
hN : ‖f N‖ ≠ 0
h' : Tendsto (fun n => f (n + N)) atTop (𝓝 0)
⊢ Tendsto ((fun a =>... | ((:c Not) ((:c Summable) (:fv _uniq.191350) (:c Nat) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.191350) ((:c SeminormedAddCommGroup.toAddCommGroup) (:fv _uniq.191350) (:fv _uniq.191351))) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.191350) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.191350) ((:c Seminorme... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.191350))"},{"name":"f","sexp":"(:forall _ (:c Nat) (:fv _uniq.191350))"},{"name":"r","sexp":"(... | (:app (:c Not) (:arg :explicit 0 (:app (:c Summable) (:arg :implicit-type 0 (:fv FV4)) (:arg :implicit-type 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV4))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV4))))) (:arg :explicit 4 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"refine","sourceEnd":32222,"sourceStart":32216,"tag":"atom"},{"children":[{"name":"mt","semanticRole":"global","source":"mt","sourceEnd":32225,"sourceStart":32223,"tag":"identifier"},{"children":[{"name":"Summable.tendsto_atTop_zero","semanticRole":"global","source":"Summable.tendsto_atTop_zero",... | [] | [{"source":"mt Summable.tendsto_atTop_zero\n fun h' ↦ not_tendsto_atTop_of_tendsto_nhds (tendsto_norm_zero.comp h') ?_","source_end":32333,"source_start":32223,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 140 | 15 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7e45df0501537cd6c92986f820e4dff3ba9b4a6b16079093b1da8b8f2413c44c | 3cd02dca97f9eb1699d5a7c34471c78438d58c8ca892cccc11f02c9b37b693d4 | 5e6d8f5ad0e7a525cf7bd45e63cbf871ed333d99b8da9b38aa5a15b2f4048e39 | a1f23bfb46d28124c0a96fb8f629b67dc09bbe60a853f9223ddb97556b6800ae |
cat-searcher/leandojo-benchmark-4-random | test | 441 | not_summable_of_ratio_norm_eventually_ge | Mathlib/Analysis/SpecificLimits/Normed.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert <a>tendsto_atTop_of_geom_le</a> _ hr _ | case intro.intro.intro
α✝ : Type u_1
β : Type u_2
ι : Type u_3
α : Type u_4
inst✝ : SeminormedAddCommGroup α
f : ℕ → α
r : ℝ
hr : 1 < r
hf : ∀ (a : ℕ), ∃ b ≥ a, ‖f b‖ ≠ 0
N₀ : ℕ
hN₀ : ∀ b ≥ N₀, r * ‖f b‖ ≤ ‖f (b + 1)‖
N : ℕ
hNN₀ : N₀ ≤ N
hN : ‖f N‖ ≠ 0
h' : Tendsto (fun n => f (n + N)) atTop (𝓝 0)
⊢ Tendsto ((fun a =>... | case intro.intro.intro.convert_2
α✝ : Type u_1
β : Type u_2
ι : Type u_3
α : Type u_4
inst✝ : SeminormedAddCommGroup α
f : ℕ → α
r : ℝ
hr : 1 < r
hf : ∀ (a : ℕ), ∃ b ≥ a, ‖f b‖ ≠ 0
N₀ : ℕ
hN₀ : ∀ b ≥ N₀, r * ‖f b‖ ≤ ‖f (b + 1)‖
N : ℕ
hNN₀ : N₀ ≤ N
hN : ‖f N‖ ≠ 0
h' : Tendsto (fun n => f (n + N)) atTop (𝓝 0)
⊢ 0 < ((fu... | ((:c Filter.Tendsto) (:c Nat) (:c Real) ((:c Function.comp) (:c Nat) (:fv _uniq.191350) (:c Real) (:lambda a (:fv _uniq.191350) ((:c Norm.norm) (:fv _uniq.191350) ((:c SeminormedAddGroup.toNorm) (:fv _uniq.191350) ((:c SeminormedAddCommGroup.toSeminormedAddGroup) (:fv _uniq.191350) (:fv _uniq.191351))) 0)) (:lambda n (... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.191350))"},{"name":"f","sexp":"(:forall _ (:c Nat) (:fv _uniq.191350))"},{"name":"r","sexp":"(... | (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Real)) (:arg :explicit 2 (:app (:c Function.comp) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:fv FV4)) (:arg :implicit-type 2 (:c Real)) (:arg :explicit 3 (:lambda a :explicit (:fv FV4) (:app (:c Norm.norm) (:arg :implic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"convert","sourceEnd":32343,"sourceStart":32336,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"tendsto_atTop_of_geom_le","semanticRole":"global","source":"tendsto_atTop_of_geom_le","sourceEnd":32368... | [] | [{"source":"tendsto_atTop_of_geom_le _ hr _","source_end":32375,"source_start":32344,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 140 | 16 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9c6b92a113c4d5b05106c2f489b5e0a53301589636dc20bcbb8e922cc2386e33 | a1f23bfb46d28124c0a96fb8f629b67dc09bbe60a853f9223ddb97556b6800ae | caadf4f39b7204ca63e6dd68256f122adf4ca750577e267e9c42b699ee01c865 | 0f8bd43a6e191b8580548bdfb7f89c5175a58bb1c148524b3d1472b99cfa8dd5 |
cat-searcher/leandojo-benchmark-4-random | test | 442 | not_summable_of_ratio_norm_eventually_ge | Mathlib/Analysis/SpecificLimits/Normed.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>lt_of_le_of_ne</a> (<a>norm_nonneg</a> _) ?_ | case intro.intro.intro.convert_2
α✝ : Type u_1
β : Type u_2
ι : Type u_3
α : Type u_4
inst✝ : SeminormedAddCommGroup α
f : ℕ → α
r : ℝ
hr : 1 < r
hf : ∀ (a : ℕ), ∃ b ≥ a, ‖f b‖ ≠ 0
N₀ : ℕ
hN₀ : ∀ b ≥ N₀, r * ‖f b‖ ≤ ‖f (b + 1)‖
N : ℕ
hNN₀ : N₀ ≤ N
hN : ‖f N‖ ≠ 0
h' : Tendsto (fun n => f (n + N)) atTop (𝓝 0)
⊢ 0 < ((fu... | case intro.intro.intro.convert_2
α✝ : Type u_1
β : Type u_2
ι : Type u_3
α : Type u_4
inst✝ : SeminormedAddCommGroup α
f : ℕ → α
r : ℝ
hr : 1 < r
hf : ∀ (a : ℕ), ∃ b ≥ a, ‖f b‖ ≠ 0
N₀ : ℕ
hN₀ : ∀ b ≥ N₀, r * ‖f b‖ ≤ ‖f (b + 1)‖
N : ℕ
hNN₀ : N₀ ≤ N
hN : ‖f N‖ ≠ 0
h' : Tendsto (fun n => f (n + N)) atTop (𝓝 0)
⊢ 0 ≠ ((fu... | ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c Function.comp) (:c Nat) (:fv _uniq.191350) (:c Real) (:lambda a (:fv _uniq.191350) ((:c Norm.norm) (:fv _uniq.191350) ((:c SeminormedAddGroup.toNorm) (:fv _uniq.191350) ((:c SeminormedAddC... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.191350))"},{"name":"f","sexp":"(:forall _ (:c Nat) (:fv _uniq.191350))"},{"name":"r","sexp":"(... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"refine","sourceEnd":32387,"sourceStart":32381,"tag":"atom"},{"children":[{"name":"lt_of_le_of_ne","semanticRole":"global","source":"lt_of_le_of_ne","sourceEnd":32402,"sourceStart":32388,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":32404,"sourceStart":32403,"tag":"atom"... | [] | [{"source":"lt_of_le_of_ne (norm_nonneg _) ?_","source_end":32421,"source_start":32388,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 140 | 21 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7aa3f9069eb724fbfbee555fae2e69fa7f6e64b23ae1bc9c195c6910cfbe64ba | 853c8e223ae98d19f02591e25fdee2cb96c51e24466c4ec46073019ea4aa7120 | 17b1d914e8d4a117fe807fcc9dbaa27b85b2fd1b6303b0a371331290e4f1fec2 | a93c30ec6397039b1cfbc54c90bd738fa5402e8410ab1dc7bca0d1dc44b6d445 |
cat-searcher/leandojo-benchmark-4-random | test | 443 | not_summable_of_ratio_norm_eventually_ge | Mathlib/Analysis/SpecificLimits/Normed.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro h'' | case intro.intro.intro.convert_2
α✝ : Type u_1
β : Type u_2
ι : Type u_3
α : Type u_4
inst✝ : SeminormedAddCommGroup α
f : ℕ → α
r : ℝ
hr : 1 < r
hf : ∀ (a : ℕ), ∃ b ≥ a, ‖f b‖ ≠ 0
N₀ : ℕ
hN₀ : ∀ b ≥ N₀, r * ‖f b‖ ≤ ‖f (b + 1)‖
N : ℕ
hNN₀ : N₀ ≤ N
hN : ‖f N‖ ≠ 0
h' : Tendsto (fun n => f (n + N)) atTop (𝓝 0)
⊢ 0 ≠ ((fu... | case intro.intro.intro.convert_2
α✝ : Type u_1
β : Type u_2
ι : Type u_3
α : Type u_4
inst✝ : SeminormedAddCommGroup α
f : ℕ → α
r : ℝ
hr : 1 < r
hf : ∀ (a : ℕ), ∃ b ≥ a, ‖f b‖ ≠ 0
N₀ : ℕ
hN₀ : ∀ b ≥ N₀, r * ‖f b‖ ≤ ‖f (b + 1)‖
N : ℕ
hNN₀ : N₀ ≤ N
hN : ‖f N‖ ≠ 0
h' : Tendsto (fun n => f (n + N)) atTop (𝓝 0)
h'' : 0 = ... | ((:c Ne) (:c Real) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c Function.comp) (:c Nat) (:fv _uniq.191350) (:c Real) (:lambda a (:fv _uniq.191350) ((:c Norm.norm) (:fv _uniq.191350) ((:c SeminormedAddGroup.toNorm) (:fv _uniq.191350) ((:c SeminormedAddCommGroup.toSeminorme... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.191350))"},{"name":"f","sexp":"(:forall _ (:c Nat) (:fv _uniq.191350))"},{"name":"r","sexp":"(... | (:app (:c Ne) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:lit 0))))))) (:arg :explicit 2 (:app (:c Function.comp) (:arg :implicit... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"intro","sourceEnd":32431,"sourceStart":32426,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h''","sourceEnd":32435,"sourceStart":32432,"tag":"identifier"}],"kind":"null","source":"h''","sourceEnd":32435,"sourceStart":32432,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","so... | [{"role":"fresh_name","source":"h''","source_end":32435,"source_start":32432,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 140 | 22 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 431c6e04e1681fd3123995b6f705ad817a9181fa438513c97d1d65d485a0385d | a93c30ec6397039b1cfbc54c90bd738fa5402e8410ab1dc7bca0d1dc44b6d445 | 21e2186a4dc2db5f0a6c3f32e2e22c6397af6c71a2f15a43c1d69a4af2dfbbd5 | 1d1d555f187fa270b18c9cea4b94388c6f38df1608ea79c6b790209ddcad4bfa |
cat-searcher/leandojo-benchmark-4-random | test | 444 | not_summable_of_ratio_norm_eventually_ge | Mathlib/Analysis/SpecificLimits/Normed.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | specialize hN₀ N hNN₀ | case intro.intro.intro.convert_2
α✝ : Type u_1
β : Type u_2
ι : Type u_3
α : Type u_4
inst✝ : SeminormedAddCommGroup α
f : ℕ → α
r : ℝ
hr : 1 < r
hf : ∀ (a : ℕ), ∃ b ≥ a, ‖f b‖ ≠ 0
N₀ : ℕ
hN₀ : ∀ b ≥ N₀, r * ‖f b‖ ≤ ‖f (b + 1)‖
N : ℕ
hNN₀ : N₀ ≤ N
hN : ‖f N‖ ≠ 0
h' : Tendsto (fun n => f (n + N)) atTop (𝓝 0)
h'' : 0 = ... | case intro.intro.intro.convert_2
α✝ : Type u_1
β : Type u_2
ι : Type u_3
α : Type u_4
inst✝ : SeminormedAddCommGroup α
f : ℕ → α
r : ℝ
hr : 1 < r
hf : ∀ (a : ℕ), ∃ b ≥ a, ‖f b‖ ≠ 0
N₀ N : ℕ
hNN₀ : N₀ ≤ N
hN : ‖f N‖ ≠ 0
h' : Tendsto (fun n => f (n + N)) atTop (𝓝 0)
h'' : 0 = ((fun a => ‖a‖) ∘ fun n => f (n + N)) 0
hN₀ ... | (:c False) | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.191350))"},{"name":"f","sexp":"(:forall _ (:c Nat) (:fv _uniq.191350))"},{"name":"r","sexp":"(... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"specialize","sourceEnd":32450,"sourceStart":32440,"tag":"atom"},{"children":[{"contextIndex":11,"semanticRole":"local","source":"hN₀","sourceEnd":32456,"sourceStart":32451,"tag":"identifier"},{"children":[{"contextIndex":12,"semanticRole":"local","source":"N","sourceEnd":32458,"sourceStart":3245... | [] | [{"source":"hN₀ N hNN₀","source_end":32465,"source_start":32451,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 140 | 23 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fb13e22b772951c96c701c4997fe5ceebd0c2687427eeb7ef47fd8b722ebac33 | 1d1d555f187fa270b18c9cea4b94388c6f38df1608ea79c6b790209ddcad4bfa | 73ad2e85fd7979e9db517d71c88816e962579b5de1c005df66a82efef0ac7d59 | e5018addb34da1514ba65045407394593f06f29b9b143ef7ba4257d4a8cc9689 |
cat-searcher/leandojo-benchmark-4-random | test | 445 | not_summable_of_ratio_norm_eventually_ge | Mathlib/Analysis/SpecificLimits/Normed.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Function.comp_apply</a>, <a>zero_add</a>] at h'' | case intro.intro.intro.convert_2
α✝ : Type u_1
β : Type u_2
ι : Type u_3
α : Type u_4
inst✝ : SeminormedAddCommGroup α
f : ℕ → α
r : ℝ
hr : 1 < r
hf : ∀ (a : ℕ), ∃ b ≥ a, ‖f b‖ ≠ 0
N₀ N : ℕ
hNN₀ : N₀ ≤ N
hN : ‖f N‖ ≠ 0
h' : Tendsto (fun n => f (n + N)) atTop (𝓝 0)
h'' : 0 = ((fun a => ‖a‖) ∘ fun n => f (n + N)) 0
hN₀ ... | case intro.intro.intro.convert_2
α✝ : Type u_1
β : Type u_2
ι : Type u_3
α : Type u_4
inst✝ : SeminormedAddCommGroup α
f : ℕ → α
r : ℝ
hr : 1 < r
hf : ∀ (a : ℕ), ∃ b ≥ a, ‖f b‖ ≠ 0
N₀ N : ℕ
hNN₀ : N₀ ≤ N
hN : ‖f N‖ ≠ 0
h' : Tendsto (fun n => f (n + N)) atTop (𝓝 0)
hN₀ : r * ‖f N‖ ≤ ‖f (N + 1)‖
h'' : 0 = ‖f N‖
⊢ False | (:c False) | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.191350))"},{"name":"f","sexp":"(:forall _ (:c Nat) (:fv _uniq.191350))"},{"name":"r","sexp":"(... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"simp","sourceEnd":32474,"sourceStart":32470,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":32479,"sourceStart":32475,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":324... | [] | [{"source":"comp_apply","source_end":32491,"source_start":32481,"syntax_kind":"ident"},{"source":"zero_add","source_end":32501,"source_start":32493,"syntax_kind":"ident"},{"source":"h''","source_end":32509,"source_start":32506,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 140 | 24 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fc7ffebb7630ebf0751c83206ddad2a19ecd4aa96ee7bd6d6f78df90ee914951 | e5018addb34da1514ba65045407394593f06f29b9b143ef7ba4257d4a8cc9689 | 9ce22b36e21e1c5df192baea800049fa45ed31c77066cbad23baa95de499f27d | 8718623c049a62e709db43d8a60d01ec64830e1c60ee6e4ac0da76fa8e677a6d |
cat-searcher/leandojo-benchmark-4-random | test | 446 | not_summable_of_ratio_norm_eventually_ge | Mathlib/Analysis/SpecificLimits/Normed.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hN h''.symm | case intro.intro.intro.convert_2
α✝ : Type u_1
β : Type u_2
ι : Type u_3
α : Type u_4
inst✝ : SeminormedAddCommGroup α
f : ℕ → α
r : ℝ
hr : 1 < r
hf : ∀ (a : ℕ), ∃ b ≥ a, ‖f b‖ ≠ 0
N₀ N : ℕ
hNN₀ : N₀ ≤ N
hN : ‖f N‖ ≠ 0
h' : Tendsto (fun n => f (n + N)) atTop (𝓝 0)
hN₀ : r * ‖f N‖ ≤ ‖f (N + 1)‖
h'' : 0 = ‖f N‖
⊢ False | (:c False) | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.191350))"},{"name":"f","sexp":"(:forall _ (:c Nat) (:fv _uniq.191350))"},{"name":"r","sexp":"(... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"exact","sourceEnd":32519,"sourceStart":32514,"tag":"atom"},{"children":[{"contextIndex":13,"semanticRole":"local","source":"hN","sourceEnd":32522,"sourceStart":32520,"tag":"identifier"},{"children":[{"name":"Eq.symm","semanticRole":"global","source":"h''.symm","sourceEnd":32531,"sourceStart":325... | [] | [{"source":"hN h''.symm","source_end":32531,"source_start":32520,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 140 | 25 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3b5f4b595ccd8a9825cd8a9a42e2ce0e1cca8f0a028de4913f29ff395311d29f | 8718623c049a62e709db43d8a60d01ec64830e1c60ee6e4ac0da76fa8e677a6d | 63ff4c3daec94f7e2468ca76b937599e596f33ca0f4d82a3a3b701b558e398e2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 447 | not_summable_of_ratio_norm_eventually_ge | Mathlib/Analysis/SpecificLimits/Normed.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro i | case intro.intro.intro.convert_3
α✝ : Type u_1
β : Type u_2
ι : Type u_3
α : Type u_4
inst✝ : SeminormedAddCommGroup α
f : ℕ → α
r : ℝ
hr : 1 < r
hf : ∀ (a : ℕ), ∃ b ≥ a, ‖f b‖ ≠ 0
N₀ : ℕ
hN₀ : ∀ b ≥ N₀, r * ‖f b‖ ≤ ‖f (b + 1)‖
N : ℕ
hNN₀ : N₀ ≤ N
hN : ‖f N‖ ≠ 0
h' : Tendsto (fun n => f (n + N)) atTop (𝓝 0)
⊢ ∀ (n : ℕ... | case intro.intro.intro.convert_3
α✝ : Type u_1
β : Type u_2
ι : Type u_3
α : Type u_4
inst✝ : SeminormedAddCommGroup α
f : ℕ → α
r : ℝ
hr : 1 < r
hf : ∀ (a : ℕ), ∃ b ≥ a, ‖f b‖ ≠ 0
N₀ : ℕ
hN₀ : ∀ b ≥ N₀, r * ‖f b‖ ≤ ‖f (b + 1)‖
N : ℕ
hNN₀ : N₀ ≤ N
hN : ‖f N‖ ≠ 0
h' : Tendsto (fun n => f (n + N)) atTop (𝓝 0)
i : ℕ
⊢ r ... | (:forall n (:c Nat) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.191353) ((:c Function.comp) (:c Nat) (:fv _uniq.191350) (:c Real) (:lambda a (:fv _uniq.191350) ((:c Norm.norm) (:fv _uniq.191350) ((:c SeminormedAddGroup.toNor... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.191350))"},{"name":"f","sexp":"(:forall _ (:c Nat) (:fv _uniq.191350))"},{"name":"r","sexp":"(... | (:forall n :explicit (:c Nat) (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"intro","sourceEnd":32542,"sourceStart":32537,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"i","sourceEnd":32544,"sourceStart":32543,"tag":"identifier"}],"kind":"null","source":"i","sourceEnd":32544,"sourceStart":32543,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source... | [{"role":"fresh_name","source":"i","source_end":32544,"source_start":32543,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 140 | 30 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bece03373ff65439ede508e79655cfc041a5f0165dde3e21e971ede41d1b02e5 | e52a96ee2f24cbb90c2a20d845f15c50873df873be203c3046e3956869315474 | dbbb5bd97a735e823e818f7e277169eb5193225c74d8cc1ad07622a04037f7c3 | de15d29d26dbb80d8e2aabd0d033fc2b5db8437786c3dc4ede1f78a7dbf00761 |
cat-searcher/leandojo-benchmark-4-random | test | 448 | not_summable_of_ratio_norm_eventually_ge | Mathlib/Analysis/SpecificLimits/Normed.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp only [<a>Function.comp_apply</a>] | case intro.intro.intro.convert_3
α✝ : Type u_1
β : Type u_2
ι : Type u_3
α : Type u_4
inst✝ : SeminormedAddCommGroup α
f : ℕ → α
r : ℝ
hr : 1 < r
hf : ∀ (a : ℕ), ∃ b ≥ a, ‖f b‖ ≠ 0
N₀ : ℕ
hN₀ : ∀ b ≥ N₀, r * ‖f b‖ ≤ ‖f (b + 1)‖
N : ℕ
hNN₀ : N₀ ≤ N
hN : ‖f N‖ ≠ 0
h' : Tendsto (fun n => f (n + N)) atTop (𝓝 0)
i : ℕ
⊢ r ... | case intro.intro.intro.convert_3
α✝ : Type u_1
β : Type u_2
ι : Type u_3
α : Type u_4
inst✝ : SeminormedAddCommGroup α
f : ℕ → α
r : ℝ
hr : 1 < r
hf : ∀ (a : ℕ), ∃ b ≥ a, ‖f b‖ ≠ 0
N₀ : ℕ
hN₀ : ∀ b ≥ N₀, r * ‖f b‖ ≤ ‖f (b + 1)‖
N : ℕ
hNN₀ : N₀ ≤ N
hN : ‖f N‖ ≠ 0
h' : Tendsto (fun n => f (n + N)) atTop (𝓝 0)
i : ℕ
⊢ r ... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.191353) ((:c Function.comp) (:c Nat) (:fv _uniq.191350) (:c Real) (:lambda a (:fv _uniq.191350) ((:c Norm.norm) (:fv _uniq.191350) ((:c SeminormedAddGroup.toNorm) (:fv _uniq.191350... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.191350))"},{"name":"f","sexp":"(:forall _ (:c Nat) (:fv _uniq.191350))"},{"name":"r","sexp":"(... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"dsimp","sourceEnd":32554,"sourceStart":32549,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":32559,"sourceStart":32555,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":32... | [] | [{"source":"comp_apply","source_end":32571,"source_start":32561,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 140 | 31 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6e20cbe5eaa79bb7a283f885467b070eb772dacaa04137d74e8e9742ee5ce453 | de15d29d26dbb80d8e2aabd0d033fc2b5db8437786c3dc4ede1f78a7dbf00761 | d8815e04a16405af3ed1fa1fea7ae27fc03b50d299035c1bc460557886ad6af9 | 853a7aac5eeec360a3a4d7d34a50fdb08c1519d65a863f7ba3195ac8b8991b8d |
cat-searcher/leandojo-benchmark-4-random | test | 449 | not_summable_of_ratio_norm_eventually_ge | Mathlib/Analysis/SpecificLimits/Normed.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert hN₀ (i + N) (hNN₀.trans (N.le_add_left i)) using 3 | case intro.intro.intro.convert_3
α✝ : Type u_1
β : Type u_2
ι : Type u_3
α : Type u_4
inst✝ : SeminormedAddCommGroup α
f : ℕ → α
r : ℝ
hr : 1 < r
hf : ∀ (a : ℕ), ∃ b ≥ a, ‖f b‖ ≠ 0
N₀ : ℕ
hN₀ : ∀ b ≥ N₀, r * ‖f b‖ ≤ ‖f (b + 1)‖
N : ℕ
hNN₀ : N₀ ≤ N
hN : ‖f N‖ ≠ 0
h' : Tendsto (fun n => f (n + N)) atTop (𝓝 0)
i : ℕ
⊢ r ... | case h.e'_4.h.e'_3.h.e'_1
α✝ : Type u_1
β : Type u_2
ι : Type u_3
α : Type u_4
inst✝ : SeminormedAddCommGroup α
f : ℕ → α
r : ℝ
hr : 1 < r
hf : ∀ (a : ℕ), ∃ b ≥ a, ‖f b‖ ≠ 0
N₀ : ℕ
hN₀ : ∀ b ≥ N₀, r * ‖f b‖ ≤ ‖f (b + 1)‖
N : ℕ
hNN₀ : N₀ ≤ N
hN : ‖f N‖ ≠ 0
h' : Tendsto (fun n => f (n + N)) atTop (𝓝 0)
i : ℕ
⊢ i + 1 + N... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.191353) ((:c Norm.norm) (:fv _uniq.191350) ((:c SeminormedAddGroup.toNorm) (:fv _uniq.191350) ((:c SeminormedAddCommGroup.toSeminormedAddGroup) (:fv _uniq.191350) (:fv _uniq.191351... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.191350))"},{"name":"f","sexp":"(:forall _ (:c Nat) (:fv _uniq.191350))"},{"name":"r","sexp":"(... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"convert","sourceEnd":32584,"sourceStart":32577,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"contextIndex":11,"semanticRole":"local","source":"hN₀","sourceEnd":32590,"sourceStart":32585,"tag":"identifier... | [] | [{"source":"hN₀ (i + N) (hNN₀.trans (N.le_add_left i))","source_end":32631,"source_start":32585,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 140 | 32 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a2a97c73e675835564758271ffa3f6d00782ed3a37ec8f56f0fe198e5e203404 | 853a7aac5eeec360a3a4d7d34a50fdb08c1519d65a863f7ba3195ac8b8991b8d | d364493b00e0bec5e9f1ecf718f25bac1afc2b759ab73a38c37bcb2091a51df8 | 225e6b311fba26bd53d307f863948801f32e0e6e79819a20437f073210ba60e1 |
cat-searcher/leandojo-benchmark-4-random | test | 450 | not_summable_of_ratio_norm_eventually_ge | Mathlib/Analysis/SpecificLimits/Normed.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ac_rfl | case h.e'_4.h.e'_3.h.e'_1
α✝ : Type u_1
β : Type u_2
ι : Type u_3
α : Type u_4
inst✝ : SeminormedAddCommGroup α
f : ℕ → α
r : ℝ
hr : 1 < r
hf : ∀ (a : ℕ), ∃ b ≥ a, ‖f b‖ ≠ 0
N₀ : ℕ
hN₀ : ∀ b ≥ N₀, r * ‖f b‖ ≤ ‖f (b + 1)‖
N : ℕ
hNN₀ : N₀ ≤ N
hN : ‖f N‖ ≠ 0
h' : Tendsto (fun n => f (n + N)) atTop (𝓝 0)
i : ℕ
⊢ i + 1 + N... | ((:c Eq) (:c Nat) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.193999) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) (:fv _uniq.192012)) ((:c HAdd.hAdd) (:c Nat) (:c... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.191350))"},{"name":"f","sexp":"(:forall _ (:c Nat) (:fv _uniq.191350))"},{"name":"r","sexp":"(... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:c Nat))))) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"ac_rfl","sourceEnd":32650,"sourceStart":32644,"tag":"atom"}],"kind":"Lean.Parser.Tactic.acRfl","source":"ac_rfl","sourceEnd":32650,"sourceStart":32644,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190151","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.190154","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 140 | 33 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 665bdb3ca7489b793b47dac6494b65fce61b547cfa4a2a152be1ae71075871d3 | 225e6b311fba26bd53d307f863948801f32e0e6e79819a20437f073210ba60e1 | 2dd78c9d090141d123f9af8735c699cf9192b0edec0d63080dd4083a3ed0b2a9 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 451 | MultilinearMap.map_update_sum | Mathlib/LinearAlgebra/Multilinear/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | induction' t using <a>Finset.induction</a> with a t has ih h | R : Type uR
S : Type uS
ι : Type uι
n : ℕ
M : Fin n.succ → Type v
M₁ : ι → Type v₁
M₂ : Type v₂
M₃ : Type v₃
M' : Type v'
inst✝¹¹ : Semiring R
inst✝¹⁰ : (i : Fin n.succ) → AddCommMonoid (M i)
inst✝⁹ : (i : ι) → AddCommMonoid (M₁ i)
inst✝⁸ : AddCommMonoid M₂
inst✝⁷ : AddCommMonoid M₃
inst✝⁶ : AddCommMonoid M'
inst✝⁵ : (... | case empty
R : Type uR
S : Type uS
ι : Type uι
n : ℕ
M : Fin n.succ → Type v
M₁ : ι → Type v₁
M₂ : Type v₂
M₃ : Type v₃
M' : Type v'
inst✝¹¹ : Semiring R
inst✝¹⁰ : (i : Fin n.succ) → AddCommMonoid (M i)
inst✝⁹ : (i : ι) → AddCommMonoid (M₁ i)
inst✝⁸ : AddCommMonoid M₂
inst✝⁷ : AddCommMonoid M₃
inst✝⁶ : AddCommMonoid M'... | ((:c Eq) (:fv _uniq.220308) ((:c DFunLike.coe) ((:c MultilinearMap) (:fv _uniq.220291) (:fv _uniq.220295) (:fv _uniq.220306) (:fv _uniq.220308) (:fv _uniq.220315) (:fv _uniq.220331) (:fv _uniq.220334) (:fv _uniq.220405) (:fv _uniq.220429)) (:forall i (:fv _uniq.220295) ((:fv _uniq.220306) 0)) (:lambda _ (:forall i (:fv... | [{"name":"R","sexp":"(:sort (+ uR 1))"},{"name":"S","sexp":"(:sort (+ uS 1))"},{"name":"ι","sexp":"(:sort (+ uι 1))"},{"name":"n","sexp":"(:c Nat)"},{"name":"M","sexp":"(:forall _ ((:c Fin) ((:c Nat.succ) (:fv _uniq.220297))) (:sort (+ v 1)))"},{"name":"M₁","sexp":"(:forall _ (:fv _uniq.220295) (:sort (+ v₁ 1)))"},{"na... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV6)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MultilinearMap) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :explicit 2 (:fv FV5)) (:arg :explicit 3 (:fv FV6)) (:arg :instance 4 (:instance-of (:app (:c Semiring) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.220291","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.220293","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"induction'","sourceEnd":32122,"sourceStart":32112,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":28,"semanticRole":"local","source":"t","sourceEnd":32124,"sourceStart":32123,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarge... | [] | [{"source":"t","source_end":32124,"source_start":32123,"syntax_kind":"ident"},{"source":"Finset.induction","source_end":32147,"source_start":32131,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.220291","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.220293","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 124 | 7 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3dece605f8eace33e3160b7fce4207cca5fc4653d037712ced6a6fd5f6527aab | be796a31dab6a1b018c6574bd83c908b7ef706f807ae02f70234aecccb50a608 | 91538a2befab0f86bb30c7820a9bc9bdf1a4a6b2b06fad0f861a2ce42002e594 | 6c48ab22970550e30edb6ae1b58f3b569b827c5f6ee9e668acde1636049629c4 |
cat-searcher/leandojo-benchmark-4-random | test | 452 | MultilinearMap.map_update_sum | Mathlib/LinearAlgebra/Multilinear/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | case empty
R : Type uR
S : Type uS
ι : Type uι
n : ℕ
M : Fin n.succ → Type v
M₁ : ι → Type v₁
M₂ : Type v₂
M₃ : Type v₃
M' : Type v'
inst✝¹¹ : Semiring R
inst✝¹⁰ : (i : Fin n.succ) → AddCommMonoid (M i)
inst✝⁹ : (i : ι) → AddCommMonoid (M₁ i)
inst✝⁸ : AddCommMonoid M₂
inst✝⁷ : AddCommMonoid M₃
inst✝⁶ : AddCommMonoid M'... | ((:c Eq) (:fv _uniq.220308) ((:c DFunLike.coe) ((:c MultilinearMap) (:fv _uniq.220291) (:fv _uniq.220295) (:fv _uniq.220306) (:fv _uniq.220308) (:fv _uniq.220315) (:fv _uniq.220331) (:fv _uniq.220334) (:fv _uniq.220405) (:fv _uniq.220429)) (:forall i (:fv _uniq.220295) ((:fv _uniq.220306) 0)) (:lambda _ (:forall i (:fv... | [{"name":"R","sexp":"(:sort (+ uR 1))"},{"name":"S","sexp":"(:sort (+ uS 1))"},{"name":"ι","sexp":"(:sort (+ uι 1))"},{"name":"n","sexp":"(:c Nat)"},{"name":"M","sexp":"(:forall _ ((:c Fin) ((:c Nat.succ) (:fv _uniq.220297))) (:sort (+ v 1)))"},{"name":"M₁","sexp":"(:forall _ (:fv _uniq.220295) (:sort (+ v₁ 1)))"},{"na... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV6)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MultilinearMap) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :explicit 2 (:fv FV5)) (:arg :explicit 3 (:fv FV6)) (:arg :instance 4 (:instance-of (:app (:c Semiring) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.220291","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.220293","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":32177,"sourceStart":32173,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","sour... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.220291","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.220293","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 124 | 10 | exact | true | 1 | 30 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7b4af29bb36a0f4ddb6fa002520802f9bec82c4ff76b8ab121acb4b90a1a1a85 | 28b9b4c7673bc83bda2a56006588d6a4c552e676486ce1a92d738a38d4843297 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 453 | MultilinearMap.map_update_sum | Mathlib/LinearAlgebra/Multilinear/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Finset.sum_insert</a> has, ih] | case insert
R : Type uR
S : Type uS
ι : Type uι
n : ℕ
M : Fin n.succ → Type v
M₁ : ι → Type v₁
M₂ : Type v₂
M₃ : Type v₃
M' : Type v'
inst✝¹¹ : Semiring R
inst✝¹⁰ : (i : Fin n.succ) → AddCommMonoid (M i)
inst✝⁹ : (i : ι) → AddCommMonoid (M₁ i)
inst✝⁸ : AddCommMonoid M₂
inst✝⁷ : AddCommMonoid M₃
inst✝⁶ : AddCommMonoid M... | ((:c Eq) (:fv _uniq.220308) ((:c DFunLike.coe) ((:c MultilinearMap) (:fv _uniq.220291) (:fv _uniq.220295) (:fv _uniq.220306) (:fv _uniq.220308) (:fv _uniq.220315) (:fv _uniq.220331) (:fv _uniq.220334) (:fv _uniq.220405) (:fv _uniq.220429)) (:forall i (:fv _uniq.220295) ((:fv _uniq.220306) 0)) (:lambda _ (:forall i (:fv... | [{"name":"R","sexp":"(:sort (+ uR 1))"},{"name":"S","sexp":"(:sort (+ uS 1))"},{"name":"ι","sexp":"(:sort (+ uι 1))"},{"name":"n","sexp":"(:c Nat)"},{"name":"M","sexp":"(:forall _ ((:c Fin) ((:c Nat.succ) (:fv _uniq.220297))) (:sort (+ v 1)))"},{"name":"M₁","sexp":"(:forall _ (:fv _uniq.220295) (:sort (+ v₁ 1)))"},{"na... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV6)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MultilinearMap) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :explicit 2 (:fv FV5)) (:arg :explicit 3 (:fv FV6)) (:arg :instance 4 (:instance-of (:app (:c Semiring) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.220291","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.220293","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":32189,"sourceStart":32185,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"Finset.sum_insert has","source_end":32212,"source_start":32191,"syntax_kind":"Lean.Parser.Term.app"},{"source":"ih","source_end":32216,"source_start":32214,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.220291","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.220293","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 124 | 15 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6b4560cc6d021573ac52ff75d8796e6c31e93c8b6fde9bae5a3eb9a453b498df | 047678f0a95fbcbc6a9e2471b414da3bb7fb619bd933b4b707f16dd47470b97c | 1bac02040ef2a4e7cca73d5436dac5a69f060e00169081903e769c428331eae0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 454 | Ordinal.log_eq_zero | Mathlib/SetTheory/Ordinal/Exponential.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases <a>eq_or_ne</a> o 0 with (rfl | ho) | b o : Ordinal.{u_1}
hbo : o < b
⊢ log b o = 0 | ((:c Eq) (:c Ordinal) ((:c Ordinal.log) (:fv _uniq.29435) (:fv _uniq.29436)) ((:c OfNat.ofNat) (:c Ordinal) (:lit 0) ((:c Zero.toOfNat0) (:c Ordinal) (:c Ordinal.zero)))) | [{"name":"b","sexp":"(:c Ordinal)"},{"name":"o","sexp":"(:c Ordinal)"},{"name":"hbo","sexp":"((:c LT.lt) (:c Ordinal) ((:c Preorder.toLT) (:c Ordinal) ((:c PartialOrder.toPreorder) (:c Ordinal) (:c Ordinal.partialOrder))) (:fv _uniq.29436) (:fv _uniq.29435))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Ordinal)) (:arg :explicit 1 (:app (:c Ordinal.log) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Ordinal)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explic... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29435","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Ordinal)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.29436","is_instance":false,"is_let":false,"name":"o","sexp":"(:c Ordinal)"},{"binder_role":":explicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rcases","sourceEnd":14216,"sourceStart":14210,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"eq_or_ne","semanticRole":"global","source":"eq_or_ne","sourceEnd":14225,"sourceStart":14217,"t... | [] | [{"source":"eq_or_ne o 0","source_end":14229,"source_start":14217,"syntax_kind":"Lean.Parser.Term.app"},{"source":"(rfl | ho)","source_end":14245,"source_start":14235,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.paren"},{"source":"log_zero_right b","source_end":14273,"source_start":14257,"syntax_kind":"Lean.Parser.Term.... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29435","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.29436","is_instance":false,"is_let":false,"user_name":"o"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 94 | 2 | branch_opener | false | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d9c9116f367d11fc2f0be415dc6ee8366e95897cb3c5a6d81a653d8e7982bc2e | ee00a8dab05269475219a11ba03cd1309a8fe855bb86a8bdf1e27eae5b0d08e4 | a51eea12d89d1b2179bddf1e7767837908efab8c5c35c61bb9d11df12fc303e7 | e67571d23bf147640ad0d27e6590a42478117372848c4124cb36718c775045c4 | |
cat-searcher/leandojo-benchmark-4-random | test | 456 | Ordinal.log_eq_zero | Mathlib/SetTheory/Ordinal/Exponential.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Ordinal.log_zero_right</a> b | case inl
b : Ordinal.{u_1}
hbo : 0 < b
⊢ log b 0 = 0 | ((:c Eq) (:c Ordinal) ((:c Ordinal.log) (:fv _uniq.29435) ((:c OfNat.ofNat) (:c Ordinal) (:lit 0) ((:c Zero.toOfNat0) (:c Ordinal) (:c Ordinal.zero)))) ((:c OfNat.ofNat) (:c Ordinal) (:lit 0) ((:c Zero.toOfNat0) (:c Ordinal) (:c Ordinal.zero)))) | [{"name":"b","sexp":"(:c Ordinal)"},{"name":"hbo","sexp":"((:c LT.lt) (:c Ordinal) ((:c Preorder.toLT) (:c Ordinal) ((:c PartialOrder.toPreorder) (:c Ordinal) (:c Ordinal.partialOrder))) ((:c OfNat.ofNat) (:c Ordinal) (:lit 0) ((:c Zero.toOfNat0) (:c Ordinal) (:c Ordinal.zero))) (:fv _uniq.29435))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Ordinal)) (:arg :explicit 1 (:app (:c Ordinal.log) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Ordinal)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Ordinal)) (:arg :expli... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29435","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Ordinal)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.29512","is_instance":false,"is_let":false,"name":"hbo","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c ... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":14256,"sourceStart":14251,"tag":"atom"},{"children":[{"name":"Ordinal.log_zero_right","semanticRole":"global","source":"log_zero_right","sourceEnd":14271,"sourceStart":14257,"tag":"identifier"},{"children":[{"contextIndex":1,"semanticRole... | [] | [{"source":"log_zero_right b","source_end":14273,"source_start":14257,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29435","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.29512","is_instance":false,"is_let":false,"user_name":"hbo"}] | 94 | 7 | exact | true | 1 | 2 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c8d14d0f808a330c2d8b44088bda8fa2de4b24d3b1875d1bbc235f22293728ec | 5847a92cccdc515e04b3fa26ddb2f7a7a0f29641a34fa1f5f61c3ea17d9be513 | 0685a75d258e50fcccb63de8ad8a920d4983fe0d4992635d4fde8c5cab2b26ed | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 457 | Ordinal.log_eq_zero | Mathlib/SetTheory/Ordinal/Exponential.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases <a>Ordinal.le_one_iff</a>.1 hb with (rfl | rfl) | case inr.inl
b o : Ordinal.{u_1}
hbo : o < b
ho : o ≠ 0
hb : b ≤ 1
⊢ log b o = 0 | ((:c Eq) (:c Ordinal) ((:c Ordinal.log) (:fv _uniq.29435) (:fv _uniq.29436)) ((:c OfNat.ofNat) (:c Ordinal) (:lit 0) ((:c Zero.toOfNat0) (:c Ordinal) (:c Ordinal.zero)))) | [{"name":"b","sexp":"(:c Ordinal)"},{"name":"o","sexp":"(:c Ordinal)"},{"name":"hbo","sexp":"((:c LT.lt) (:c Ordinal) ((:c Preorder.toLT) (:c Ordinal) ((:c PartialOrder.toPreorder) (:c Ordinal) (:c Ordinal.partialOrder))) (:fv _uniq.29436) (:fv _uniq.29435))"},{"name":"ho","sexp":"((:c Ne) (:c Ordinal) (:fv _uniq.29436... | (:app (:c Eq) (:arg :implicit-type 0 (:c Ordinal)) (:arg :explicit 1 (:app (:c Ordinal.log) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Ordinal)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explic... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29435","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Ordinal)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.29436","is_instance":false,"is_let":false,"name":"o","sexp":"(:c Ordinal)"},{"binder_role":":explicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rcases","sourceEnd":14320,"sourceStart":14314,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"name":"Ordinal.le_one_iff","semanticRole":"global","source":"le_one_iff","sourceEnd":143... | [] | [{"source":"le_one_iff.1 hb","source_end":14336,"source_start":14321,"syntax_kind":"Lean.Parser.Term.app"},{"source":"(rfl | rfl)","source_end":14353,"source_start":14342,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.paren"},{"source":"log_zero_left o","source_end":14382,"source_start":14367,"syntax_kind":"Lean.Parser.Te... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29435","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.29436","is_instance":false,"is_let":false,"user_name":"o"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 94 | 13 | branch_opener | false | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b1996ad4caef956aaf89a0b609727e17c838e7e4461a156048ee7ad72a4c760d | c37e46385d7c5cb7d0225d4761d968f4c503c604545c5c0d1e9524126e76d0b4 | 74e0942024de72fdef0b1b99c707baadc9caebdd1727af5933d5d079129626c1 | cac75c675bb926afa04afefebe36e9e92d008a4abe8e7f08720c8cd55473a06e | |
cat-searcher/leandojo-benchmark-4-random | test | 458 | Ordinal.log_eq_zero | Mathlib/SetTheory/Ordinal/Exponential.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Ordinal.log_zero_left</a> o | case inr.inl.inl
o : Ordinal.{u_1}
ho : o ≠ 0
hbo : o < 0
hb : 0 ≤ 1
⊢ log 0 o = 0 | ((:c Eq) (:c Ordinal) ((:c Ordinal.log) ((:c OfNat.ofNat) (:c Ordinal) (:lit 0) ((:c Zero.toOfNat0) (:c Ordinal) (:c Ordinal.zero))) (:fv _uniq.29436)) ((:c OfNat.ofNat) (:c Ordinal) (:lit 0) ((:c Zero.toOfNat0) (:c Ordinal) (:c Ordinal.zero)))) | [{"name":"o","sexp":"(:c Ordinal)"},{"name":"ho","sexp":"((:c Ne) (:c Ordinal) (:fv _uniq.29436) ((:c OfNat.ofNat) (:c Ordinal) (:lit 0) ((:c Zero.toOfNat0) (:c Ordinal) (:c Ordinal.zero))))"},{"name":"hbo","sexp":"((:c LT.lt) (:c Ordinal) ((:c Preorder.toLT) (:c Ordinal) ((:c PartialOrder.toPreorder) (:c Ordinal) (:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Ordinal)) (:arg :explicit 1 (:app (:c Ordinal.log) (:arg :explicit 0 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Ordinal)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Ordinal)) (:arg :explicit 1 (:lit 0))))))) (:arg :e... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29436","is_instance":false,"is_let":false,"name":"o","sexp":"(:c Ordinal)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.29499","is_instance":false,"is_let":false,"name":"ho","sexp":"(:app (:c Ne) (:arg :implicit-type 0 (:c Ordi... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":14366,"sourceStart":14361,"tag":"atom"},{"children":[{"name":"Ordinal.log_zero_left","semanticRole":"global","source":"log_zero_left","sourceEnd":14380,"sourceStart":14367,"tag":"identifier"},{"children":[{"contextIndex":1,"semanticRole":... | [] | [{"source":"log_zero_left o","source_end":14382,"source_start":14367,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29436","is_instance":false,"is_let":false,"user_name":"o"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.29499","is_instance":false,"is_let":false,"user_name":"ho"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 94 | 18 | exact | true | 1 | 4 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e089a38eb2c5ca7e929c3f7ce51d6c37bdbbbdf43c4d85b0481adf6dd98f493a | 27099486640873ce6fc564a5b18882c9ec9c870faf0ab24c528de49ae531ffe3 | 72c4c977ab89f51c5e32da9b008815a19f324841456692822d1bc8660942cff4 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 459 | Ordinal.log_eq_zero | Mathlib/SetTheory/Ordinal/Exponential.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Ordinal.log_one_left</a> o | case inr.inl.inr
o : Ordinal.{u_1}
ho : o ≠ 0
hbo : o < 1
hb : 1 ≤ 1
⊢ log 1 o = 0 | ((:c Eq) (:c Ordinal) ((:c Ordinal.log) ((:c OfNat.ofNat) (:c Ordinal) (:lit 1) ((:c One.toOfNat1) (:c Ordinal) (:c Ordinal.one))) (:fv _uniq.29436)) ((:c OfNat.ofNat) (:c Ordinal) (:lit 0) ((:c Zero.toOfNat0) (:c Ordinal) (:c Ordinal.zero)))) | [{"name":"o","sexp":"(:c Ordinal)"},{"name":"ho","sexp":"((:c Ne) (:c Ordinal) (:fv _uniq.29436) ((:c OfNat.ofNat) (:c Ordinal) (:lit 0) ((:c Zero.toOfNat0) (:c Ordinal) (:c Ordinal.zero))))"},{"name":"hbo","sexp":"((:c LT.lt) (:c Ordinal) ((:c Preorder.toLT) (:c Ordinal) ((:c PartialOrder.toPreorder) (:c Ordinal) (:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Ordinal)) (:arg :explicit 1 (:app (:c Ordinal.log) (:arg :explicit 0 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Ordinal)) (:arg :explicit 1 (:lit 1)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Ordinal)) (:arg :explicit 1 (:lit 1))))))) (:arg :e... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29436","is_instance":false,"is_let":false,"name":"o","sexp":"(:c Ordinal)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.29499","is_instance":false,"is_let":false,"name":"ho","sexp":"(:app (:c Ne) (:arg :implicit-type 0 (:c Ordi... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":14395,"sourceStart":14390,"tag":"atom"},{"children":[{"name":"Ordinal.log_one_left","semanticRole":"global","source":"log_one_left","sourceEnd":14408,"sourceStart":14396,"tag":"identifier"},{"children":[{"contextIndex":1,"semanticRole":"l... | [] | [{"source":"log_one_left o","source_end":14410,"source_start":14396,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29436","is_instance":false,"is_let":false,"user_name":"o"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.29499","is_instance":false,"is_let":false,"user_name":"ho"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 94 | 23 | exact | true | 1 | 4 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d9332ae074857cb1eec8ca19df98869fcbc49ab9326e4f94c14d00d36a69d1f7 | 81bb4ca4470e1feff0b7eea8e84b15b96dae966999ef33a8bf6b85df447bc966 | 8ec8c6d0ae02789cec42087b9c8161a675bee726c0c413bf1cad1857e8fbc7a8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 460 | Ordinal.log_eq_zero | Mathlib/SetTheory/Ordinal/Exponential.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [← <a>Ordinal.le_zero</a>, ← <a>Order.lt_succ_iff</a>, <a>Ordinal.succ_zero</a>, ← <a>Ordinal.lt_opow_iff_log_lt</a> hb ho, <a>Ordinal.opow_one</a>] | case inr.inr
b o : Ordinal.{u_1}
hbo : o < b
ho : o ≠ 0
hb : 1 < b
⊢ log b o = 0 | ((:c Eq) (:c Ordinal) ((:c Ordinal.log) (:fv _uniq.29435) (:fv _uniq.29436)) ((:c OfNat.ofNat) (:c Ordinal) (:lit 0) ((:c Zero.toOfNat0) (:c Ordinal) (:c Ordinal.zero)))) | [{"name":"b","sexp":"(:c Ordinal)"},{"name":"o","sexp":"(:c Ordinal)"},{"name":"hbo","sexp":"((:c LT.lt) (:c Ordinal) ((:c Preorder.toLT) (:c Ordinal) ((:c PartialOrder.toPreorder) (:c Ordinal) (:c Ordinal.partialOrder))) (:fv _uniq.29436) (:fv _uniq.29435))"},{"name":"ho","sexp":"((:c Ne) (:c Ordinal) (:fv _uniq.29436... | (:app (:c Eq) (:arg :implicit-type 0 (:c Ordinal)) (:arg :explicit 1 (:app (:c Ordinal.log) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Ordinal)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explic... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29435","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Ordinal)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.29436","is_instance":false,"is_let":false,"name":"o","sexp":"(:c Ordinal)"},{"binder_role":":explicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rwa","sourceEnd":14419,"sourceStart":14416,"tag":"atom"},{"children":[{"source":"[","sourceEnd":14421,"sourceStart":14420,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":14424,"sourceStart":14421,"tag... | [] | [{"source":"Ordinal.le_zero","source_end":14440,"source_start":14425,"syntax_kind":"ident"},{"source":"lt_succ_iff","source_end":14457,"source_start":14446,"syntax_kind":"ident"},{"source":"succ_zero","source_end":14468,"source_start":14459,"syntax_kind":"ident"},{"source":"lt_opow_iff_log_lt hb ho","source_end":14498,... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29435","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.29436","is_instance":false,"is_let":false,"user_name":"o"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 94 | 28 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0b6ccc95f2b3a5e84d739b4d034e67c3562b301cec5ec0e82e59a70e1a21042d | 044543e7d42580b1f48c5a32c5ec899c71e0acfea2c8da93326151187fbf73d3 | 802a5e8436f938d8016b0ccb46770712839be055e7ce99b60c918147f2991738 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 461 | MeasureTheory.Measure.snd_prod | Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext1 s hs | α : Type u_1
α' : Type u_2
β : Type u_3
β' : Type u_4
γ : Type u_5
E : Type u_6
inst✝⁷ : MeasurableSpace α
inst✝⁶ : MeasurableSpace α'
inst✝⁵ : MeasurableSpace β
inst✝⁴ : MeasurableSpace β'
inst✝³ : MeasurableSpace γ
μ μ' : Measure α
ν ν' : Measure β
τ : Measure γ
inst✝² : NormedAddCommGroup E
inst✝¹ : SFinite ν
ρ : Me... | case h
α : Type u_1
α' : Type u_2
β : Type u_3
β' : Type u_4
γ : Type u_5
E : Type u_6
inst✝⁷ : MeasurableSpace α
inst✝⁶ : MeasurableSpace α'
inst✝⁵ : MeasurableSpace β
inst✝⁴ : MeasurableSpace β'
inst✝³ : MeasurableSpace γ
μ μ' : Measure α
ν ν' : Measure β
τ : Measure γ
inst✝² : NormedAddCommGroup E
inst✝¹ : SFinite ν... | ((:c Eq) ((:c MeasureTheory.Measure) (:fv _uniq.234273) (:fv _uniq.234291)) ((:c MeasureTheory.Measure.snd) (:fv _uniq.234267) (:fv _uniq.234273) (:fv _uniq.234285) (:fv _uniq.234291) ((:c MeasureTheory.Measure.prod) (:fv _uniq.234267) (:fv _uniq.234273) (:fv _uniq.234285) (:fv _uniq.234291) (:fv _uniq.234305) (:fv _un... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"α'","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"β'","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"E","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁷","sexp":"((:c MeasurableSpace) (:fv _uniq.234267))"},{"name":... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV2))))))) (:arg :explicit 1 (:app (:c MeasureTheory.Measure.snd) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.234267","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.234270","is_instance":false,"is_let":false,"name":"α'","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"ext1","sourceEnd":57347,"sourceStart":57343,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"s","sourceEnd":57349,"sourceStart":57348,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"s","sourceEnd":57349,"sourceStart":57348,"ta... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.234267","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.234270","is_instance":false,"is_let":false,"user_name":"α'"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 235 | 4 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 866c49d9d6b83d3990e4dd67a234cec86b72fdb8f8dbcd3af2656f4f113f05cd | 72e5fc60440d9bfe51822ed4fc72bd50042af14027cbe810d9c9a43e41cf85ff | a7e4b3abfc18eafacbe5e808ab9c7731e1f4e0d03c4828620a3b2991bc085e33 | 1555a8a35bb527adf6965b2f98a7036e4dec49580486ad77712a0af9c15cdabc |
cat-searcher/leandojo-benchmark-4-random | test | 462 | MeasureTheory.Measure.snd_prod | Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MeasureTheory.Measure.snd_apply</a> hs, ← <a>Set.univ_prod</a>, <a>MeasureTheory.Measure.prod_prod</a>, <a>MeasureTheory.IsProbabilityMeasure.measure_univ</a>, <a>one_mul</a>] | case h
α : Type u_1
α' : Type u_2
β : Type u_3
β' : Type u_4
γ : Type u_5
E : Type u_6
inst✝⁷ : MeasurableSpace α
inst✝⁶ : MeasurableSpace α'
inst✝⁵ : MeasurableSpace β
inst✝⁴ : MeasurableSpace β'
inst✝³ : MeasurableSpace γ
μ μ' : Measure α
ν ν' : Measure β
τ : Measure γ
inst✝² : NormedAddCommGroup E
inst✝¹ : SFinite ν... | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.234273) (:fv _uniq.234291)) ((:c Set) (:fv _uniq.234273)) (:lambda _ ((:c Set) (:fv _uniq.234273)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.234273) (:fv _uniq.234291)) ((:c MeasureTheory.Measure.snd) (:fv _uniq.23426... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"α'","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"β'","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"E","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁷","sexp":"((:c MeasurableSpace) (:fv _uniq.234267))"},{"name":... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV2))))))) (:arg :implicit-type 1 (:app (:c Set) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.234267","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.234270","is_instance":false,"is_let":false,"name":"α'","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"rw","sourceEnd":57357,"sourceStart":57355,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":57359,"sourceStart":57358,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Mea... | [] | [{"source":"snd_apply hs","source_end":57371,"source_start":57359,"syntax_kind":"Lean.Parser.Term.app"},{"source":"univ_prod","source_end":57386,"source_start":57377,"syntax_kind":"ident"},{"source":"prod_prod","source_end":57397,"source_start":57388,"syntax_kind":"ident"},{"source":"measure_univ","source_end":57411,"s... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.234267","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.234270","is_instance":false,"is_let":false,"user_name":"α'"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 235 | 5 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | adcb6238fa2e14705d988e211e388a137ca3eeb98141615c6108848f29aaa8c6 | 1555a8a35bb527adf6965b2f98a7036e4dec49580486ad77712a0af9c15cdabc | 2a91498f2642f6fa2c8335f774b0d8d86c1fd881601fd84d1023e75cea79c1cc | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 463 | UpperHalfPlane.dist_triangle | Mathlib/Analysis/Complex/UpperHalfPlane/Metric.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>UpperHalfPlane.dist_le_iff_le_sinh</a>, <a>UpperHalfPlane.sinh_half_dist_add_dist</a>, <a>div_mul_eq_div_div</a> _ _ (<a>Dist.dist</a> _ _), <a>le_div_iff</a>, <a>div_mul_eq_mul_div</a>] | z w : ℍ
r R : ℝ
a b c : ℍ
⊢ dist a c ≤ dist a b + dist b c | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Dist.dist) (:c UpperHalfPlane) (:c UpperHalfPlane.instDist) (:fv _uniq.23936) (:fv _uniq.23938)) ((:c HAdd.hAdd) (:c Real) (:c Real) (:c Real) ((:c instHAdd) (:c Real) (:c Real.instAdd)) ((:c Dist.dist) (:c UpperHalfPlane) (:c UpperHalfPlane.instDist) (:fv _uniq.23936) (:fv _... | [{"name":"z","sexp":"(:c UpperHalfPlane)"},{"name":"w","sexp":"(:c UpperHalfPlane)"},{"name":"r","sexp":"(:c Real)"},{"name":"R","sexp":"(:c Real)"},{"name":"a","sexp":"(:c UpperHalfPlane)"},{"name":"b","sexp":"(:c UpperHalfPlane)"},{"name":"c","sexp":"(:c UpperHalfPlane)"}] | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Dist.dist) (:arg :implicit-type 0 (:c UpperHalfPlane)) (:arg :instance 1 (:instance-of (:app (:c Dist) (:arg :explicit 0 (:c UpperHalfPlane))))) (:arg :explicit 2 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23858","is_instance":false,"is_let":false,"name":"z","sexp":"(:c UpperHalfPlane)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23860","is_instance":false,"is_let":false,"name":"w","sexp":"(:c UpperHalfPlane)"},{"binder_role":":... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":5157,"sourceStart":5155,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5159,"sourceStart":5158,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"dist_le_iff_le_sinh","source_end":5178,"source_start":5159,"syntax_kind":"ident"},{"source":"sinh_half_dist_add_dist","source_end":5203,"source_start":5180,"syntax_kind":"ident"},{"source":"div_mul_eq_div_div _ _ (dist _ _)","source_end":5238,"source_start":5205,"syntax_kind":"Lean.Parser.Term.app"},{"sourc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23858","is_instance":false,"is_let":false,"user_name":"z"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23860","is_instance":false,"is_let":false,"user_name":"w"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 30 | 2 | branch_opener | false | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e8b0fd78a323964a9a4b097e3408ea5f497f8c09dec2944136c3bc67852c12ca | 9285271933c1fbca370c4cc255c41fcc1c7d9769475bffb5b5ae014b136356b6 | cc12d766e81f5330da2436b6035e2ef18e1fc842c53118b7884da6fcc988d49c | 8e9f23f25a190d88cf952874f1ffe8eca63ea53d86b77402d7ce2c3ffcae2adf | |
cat-searcher/leandojo-benchmark-4-random | test | 464 | UpperHalfPlane.dist_triangle | Mathlib/Analysis/Complex/UpperHalfPlane/Metric.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr | z w : ℍ
r R : ℝ
a b c : ℍ
⊢ dist ↑a ↑c * dist (↑b) ((starRingEnd ℂ) ↑b) / (2 * √(a.im * c.im)) ≤
(dist ↑a ↑b * dist (↑c) ((starRingEnd ℂ) ↑b) + dist ↑b ↑c * dist (↑a) ((starRingEnd ℂ) ↑b)) / (2 * √(a.im * c.im)) | case hab
z w : ℍ
r R : ℝ
a b c : ℍ
⊢ dist ↑a ↑c * dist (↑b) ((starRingEnd ℂ) ↑b) ≤
dist ↑a ↑b * dist (↑c) ((starRingEnd ℂ) ↑b) + dist ↑b ↑c * dist (↑a) ((starRingEnd ℂ) ↑b) | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c StrictOrderedSemiring.toPartialOrder) (:c Real) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:c Real) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:c Real) ((:c LinearOrderedSemifield.toLinearOrderedComm... | [{"name":"z","sexp":"(:c UpperHalfPlane)"},{"name":"w","sexp":"(:c UpperHalfPlane)"},{"name":"r","sexp":"(:c Real)"},{"name":"R","sexp":"(:c Real)"},{"name":"a","sexp":"(:c UpperHalfPlane)"},{"name":"b","sexp":"(:c UpperHalfPlane)"},{"name":"c","sexp":"(:c UpperHalfPlane)"}] | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23858","is_instance":false,"is_let":false,"name":"z","sexp":"(:c UpperHalfPlane)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23860","is_instance":false,"is_let":false,"name":"w","sexp":"(:c UpperHalfPlane)"},{"binder_role":":... | {"children":[{"source":"gcongr","sourceEnd":5287,"sourceStart":5281,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.GCongr.tacticGcongr__With__","source":"gcongr","sourceEnd":5287,"sourceStart":5281,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23858","is_instance":false,"is_let":false,"user_name":"z"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23860","is_instance":false,"is_let":false,"user_name":"w"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 30 | 15 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b5db92995cba2c48c0e075178b934b1c4c19145a563f5f33ca7dc8e05e4d4bf9 | 0ffdaff35330d080cf5d367068b6ed734cc7ac8880eaffea666b455d4b82dff3 | 7681489794c20ff221cf115a6d6f5e4351c46b6ec8b1f901575d361640dc6cdf | 090f988d5199325221ef7ac5050a104668ce5cce68c7a4d759a153fc2034e32b |
cat-searcher/leandojo-benchmark-4-random | test | 465 | UpperHalfPlane.dist_triangle | Mathlib/Analysis/Complex/UpperHalfPlane/Metric.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>EuclideanGeometry.mul_dist_le_mul_dist_add_mul_dist</a> (a : ℂ) b c (conj (b : ℂ)) | case hab
z w : ℍ
r R : ℝ
a b c : ℍ
⊢ dist ↑a ↑c * dist (↑b) ((starRingEnd ℂ) ↑b) ≤
dist ↑a ↑b * dist (↑c) ((starRingEnd ℂ) ↑b) + dist ↑b ↑c * dist (↑a) ((starRingEnd ℂ) ↑b) | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c StrictOrderedSemiring.toPartialOrder) (:c Real) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:c Real) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:c Real) ((:c LinearOrderedSemifield.toLinearOrderedComm... | [{"name":"z","sexp":"(:c UpperHalfPlane)"},{"name":"w","sexp":"(:c UpperHalfPlane)"},{"name":"r","sexp":"(:c Real)"},{"name":"R","sexp":"(:c Real)"},{"name":"a","sexp":"(:c UpperHalfPlane)"},{"name":"b","sexp":"(:c UpperHalfPlane)"},{"name":"c","sexp":"(:c UpperHalfPlane)"}] | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23858","is_instance":false,"is_let":false,"name":"z","sexp":"(:c UpperHalfPlane)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23860","is_instance":false,"is_let":false,"name":"w","sexp":"(:c UpperHalfPlane)"},{"binder_role":":... | {"children":[{"source":"exact","sourceEnd":5297,"sourceStart":5292,"tag":"atom"},{"children":[{"name":"EuclideanGeometry.mul_dist_le_mul_dist_add_mul_dist","semanticRole":"global","source":"EuclideanGeometry.mul_dist_le_mul_dist_add_mul_dist","sourceEnd":5349,"sourceStart":5298,"tag":"identifier"},{"children":[{"childr... | [] | [{"source":"EuclideanGeometry.mul_dist_le_mul_dist_add_mul_dist (a : ℂ) b c (conj (b : ℂ))","source_end":5380,"source_start":5298,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23858","is_instance":false,"is_let":false,"user_name":"z"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23860","is_instance":false,"is_let":false,"user_name":"w"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 30 | 16 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 29e0ea96771c5d5584536c317a8f887c153505803eb54a027acd292fd14093b3 | 090f988d5199325221ef7ac5050a104668ce5cce68c7a4d759a153fc2034e32b | af03d7d52ed1a546f90fe47a43e3c72b6ffb1d8bbf5db03c938ef5283e5103dc | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 466 | UpperHalfPlane.dist_triangle | Mathlib/Analysis/Complex/UpperHalfPlane/Metric.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>dist_comm</a>, <a>dist_pos</a>, <a>Ne</a>, <a>Complex.conj_eq_iff_im</a>] | z w : ℍ
r R : ℝ
a b c : ℍ
⊢ 0 < dist (↑b) ((starRingEnd ℂ) ↑b) | z w : ℍ
r R : ℝ
a b c : ℍ
⊢ ¬(↑b).im = 0 | ((:c LT.lt) (:c Real) ((:c Preorder.toLT) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c StrictOrderedSemiring.toPartialOrder) (:c Real) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:c Real) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:c Real) ((:c LinearOrderedSemifield.toLinearOrderedComm... | [{"name":"z","sexp":"(:c UpperHalfPlane)"},{"name":"w","sexp":"(:c UpperHalfPlane)"},{"name":"r","sexp":"(:c Real)"},{"name":"R","sexp":"(:c Real)"},{"name":"a","sexp":"(:c UpperHalfPlane)"},{"name":"b","sexp":"(:c UpperHalfPlane)"},{"name":"c","sexp":"(:c UpperHalfPlane)"}] | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23858","is_instance":false,"is_let":false,"name":"z","sexp":"(:c UpperHalfPlane)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23860","is_instance":false,"is_let":false,"name":"w","sexp":"(:c UpperHalfPlane)"},{"binder_role":":... | {"children":[{"source":"rw","sourceEnd":5388,"sourceStart":5386,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5390,"sourceStart":5389,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"dist_comm","semantic... | [] | [{"source":"dist_comm","source_end":5399,"source_start":5390,"syntax_kind":"ident"},{"source":"dist_pos","source_end":5409,"source_start":5401,"syntax_kind":"ident"},{"source":"Ne","source_end":5413,"source_start":5411,"syntax_kind":"ident"},{"source":"Complex.conj_eq_iff_im","source_end":5437,"source_start":5415,"synt... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23858","is_instance":false,"is_let":false,"user_name":"z"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23860","is_instance":false,"is_let":false,"user_name":"w"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 30 | 21 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 503488e7f8c5a05ceaa13e1a53876a75ecb17ebf721159029ae28efb05646a20 | f3d8cf9e6f1ab818f51bd95a2220a897abb61df45f81cd88203efa79662e385b | 763178857abb3d87ac625c060aa8a8a65a262caa3c35dde26257a415e8080cf9 | 33ebeeb3b639428e8c097c836fdb06c39e9889141d70700ce115454968cbc34f |
cat-searcher/leandojo-benchmark-4-random | test | 467 | UpperHalfPlane.dist_triangle | Mathlib/Analysis/Complex/UpperHalfPlane/Metric.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact b.im_ne_zero | z w : ℍ
r R : ℝ
a b c : ℍ
⊢ ¬(↑b).im = 0 | ((:c Not) ((:c Eq) (:c Real) ((:c Complex.im) ((:c UpperHalfPlane.coe) (:fv _uniq.23937))) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))))) | [{"name":"z","sexp":"(:c UpperHalfPlane)"},{"name":"w","sexp":"(:c UpperHalfPlane)"},{"name":"r","sexp":"(:c Real)"},{"name":"R","sexp":"(:c Real)"},{"name":"a","sexp":"(:c UpperHalfPlane)"},{"name":"b","sexp":"(:c UpperHalfPlane)"},{"name":"c","sexp":"(:c UpperHalfPlane)"}] | (:app (:c Not) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Complex.im) (:arg :explicit 0 (:app (:c UpperHalfPlane.coe) (:arg :explicit 0 (:fv FV6)))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23858","is_instance":false,"is_let":false,"name":"z","sexp":"(:c UpperHalfPlane)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23860","is_instance":false,"is_let":false,"name":"w","sexp":"(:c UpperHalfPlane)"},{"binder_role":":... | {"children":[{"source":"exact","sourceEnd":5448,"sourceStart":5443,"tag":"atom"},{"name":"UpperHalfPlane.im_ne_zero","semanticRole":"global","source":"b.im_ne_zero","sourceEnd":5461,"sourceStart":5449,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact b.im_ne_zero","sourceEnd":5461,"sourceStart":544... | [] | [{"source":"b.im_ne_zero","source_end":5461,"source_start":5449,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23858","is_instance":false,"is_let":false,"user_name":"z"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23860","is_instance":false,"is_let":false,"user_name":"w"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 30 | 27 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 631e09f29a7f819edec9bda3dd0d29e9e1e2c10baf532eb9806d10ab87925c4e | 33ebeeb3b639428e8c097c836fdb06c39e9889141d70700ce115454968cbc34f | 0e91778d7ebe59bf3966f0bc2f45a028d409f201929219a0229df32320746f6a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 468 | Matrix.Pivot.listTransvecCol_mul_last_row_drop | Mathlib/LinearAlgebra/Matrix/Transvection.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>Nat.decreasingInduction'</a> ?_ hk ?_ | n : Type u_1
p : Type u_2
R : Type u₂
𝕜 : Type u_3
inst✝³ : Field 𝕜
inst✝² : DecidableEq n
inst✝¹ : DecidableEq p
inst✝ : CommRing R
r : ℕ
M : Matrix (Fin r ⊕ Unit) (Fin r ⊕ Unit) 𝕜
i : Fin r ⊕ Unit
k : ℕ
hk : k ≤ r
⊢ ((List.drop k (listTransvecCol M)).prod * M) (inr ()) i = M (inr ()) i | case refine_1
n : Type u_1
p : Type u_2
R : Type u₂
𝕜 : Type u_3
inst✝³ : Field 𝕜
inst✝² : DecidableEq n
inst✝¹ : DecidableEq p
inst✝ : CommRing R
r : ℕ
M : Matrix (Fin r ⊕ Unit) (Fin r ⊕ Unit) 𝕜
i : Fin r ⊕ Unit
k : ℕ
hk : k ≤ r
⊢ ∀ k_1 < r,
k ≤ k_1 →
((List.drop (k_1 + 1) (listTransvecCol M)).prod * M) (... | ((:c Eq) (:fv _uniq.95154) ((:c HMul.hMul) ((:c Matrix) ((:c Sum) ((:c Fin) (:fv _uniq.95180)) (:c Unit)) ((:c Sum) ((:c Fin) (:fv _uniq.95180)) (:c Unit)) (:fv _uniq.95154)) ((:c Matrix) ((:c Sum) ((:c Fin) (:fv _uniq.95180)) (:c Unit)) ((:c Sum) ((:c Fin) (:fv _uniq.95180)) (:c Unit)) (:fv _uniq.95154)) ((:c Matrix) ... | [{"name":"n","sexp":"(:sort (+ u_1 1))"},{"name":"p","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u₂ 1))"},{"name":"𝕜","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.95154))"},{"name":"inst✝²","sexp":"((:c DecidableEq) (:fv _uniq.95146))"},{"name":"inst✝¹","sexp":"((:c Decidab... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (:c Matrix) (:arg :explicit 0 (:app (:c Sum) (:arg :explicit 0 (:app (:c Fin) (:arg :explicit 0 (:fv FV8)))) (:arg :explicit 1 (:c Unit)))) (:arg :explicit 1 (:app (:c Sum) (:arg :explicit 0 (:app (:c Fin... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.95146","is_instance":false,"is_let":false,"name":"n","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.95149","is_instance":false,"is_let":false,"name":"p","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"refine","sourceEnd":16778,"sourceStart":16772,"tag":"atom"},{"children":[{"name":"Nat.decreasingInduction'","semanticRole":"global","source":"Nat.decreasingInduction'","sourceEnd":16803,"sourceStart":16779,"tag":"identifier"},{"children":[{"children":[{"source":"?","sourceEnd":16805,"sourceStart... | [] | [{"source":"Nat.decreasingInduction' ?_ hk ?_","source_end":16812,"source_start":16779,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.95146","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.95149","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 87 | 4 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 392eaf87be1af29fc4bda028f4e55a749da39cecb984323a2aa38f0d7e37dda2 | 9f7ad4556e813833b6a3077f174dabf8d204b9b2e0401b0896191f2bd89f95ab | 946cdb952552a447ba99146a592280326fd29ed4b882957615e5f3f4a9f87778 | b88ed5e0f49a0ceb46191bfdeeb6162662205bebe32eb4b4cf51e55c544bc5ca |
cat-searcher/leandojo-benchmark-4-random | test | 469 | Matrix.Pivot.listTransvecCol_mul_last_row_drop | Mathlib/LinearAlgebra/Matrix/Transvection.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro n hn _ IH | case refine_1
n : Type u_1
p : Type u_2
R : Type u₂
𝕜 : Type u_3
inst✝³ : Field 𝕜
inst✝² : DecidableEq n
inst✝¹ : DecidableEq p
inst✝ : CommRing R
r : ℕ
M : Matrix (Fin r ⊕ Unit) (Fin r ⊕ Unit) 𝕜
i : Fin r ⊕ Unit
k : ℕ
hk : k ≤ r
⊢ ∀ k_1 < r,
k ≤ k_1 →
((List.drop (k_1 + 1) (listTransvecCol M)).prod * M) (... | case refine_1
n✝ : Type u_1
p : Type u_2
R : Type u₂
𝕜 : Type u_3
inst✝³ : Field 𝕜
inst✝² : DecidableEq n✝
inst✝¹ : DecidableEq p
inst✝ : CommRing R
r : ℕ
M : Matrix (Fin r ⊕ Unit) (Fin r ⊕ Unit) 𝕜
i : Fin r ⊕ Unit
k : ℕ
hk : k ≤ r
n : ℕ
hn : n < r
a✝ : k ≤ n
IH : ((List.drop (n + 1) (listTransvecCol M)).prod * M) (... | (:forall k (:c Nat) (:forall _ ((:c LT.lt) (:c Nat) (:c instLTNat) 0 (:fv _uniq.95180)) (:forall _ ((:c LE.le) (:c Nat) (:c instLENat) (:fv _uniq.95960) 1) (:forall _ ((:c Eq) (:fv _uniq.95154) ((:c HMul.hMul) ((:c Matrix) ((:c Sum) ((:c Fin) (:fv _uniq.95180)) (:c Unit)) ((:c Sum) ((:c Fin) (:fv _uniq.95180)) (:c Unit... | [{"name":"n","sexp":"(:sort (+ u_1 1))"},{"name":"p","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u₂ 1))"},{"name":"𝕜","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.95154))"},{"name":"inst✝²","sexp":"((:c DecidableEq) (:fv _uniq.95146))"},{"name":"inst✝¹","sexp":"((:c Decidab... | (:forall k :explicit (:c Nat) (:forall _ :explicit (:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 0) (:arg :explicit 3 (:fv FV8))) (:forall _ :explicit (:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.95146","is_instance":false,"is_let":false,"name":"n","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.95149","is_instance":false,"is_let":false,"name":"p","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"intro","sourceEnd":16823,"sourceStart":16818,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"n","sourceEnd":16825,"sourceStart":16824,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hn","sourceEnd":16828,"sourceStart":16826,"tag":"identifier"},{"children":[{"sour... | [{"role":"fresh_name","source":"n","source_end":16825,"source_start":16824,"syntax_kind":"ident"},{"role":"fresh_name","source":"hn","source_end":16828,"source_start":16826,"syntax_kind":"ident"},{"role":"fresh_name","source":"IH","source_end":16833,"source_start":16831,"syntax_kind":"ident"}] | [] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.95146","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.95149","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 87 | 9 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5bc3c600ff67fdfa4e3642d4277b92f46e8d1e248d19fd46c9e2ae1b7495115b | 2e20cb5331cdf1f7dc44704adbf9f68546539492d4bd7168ee3621a77ff59ad4 | fa42a27983392f226ef77a47b9f2727fbc1c52fe35642690e3e30f80513c8d23 | 34a07a620a2a7ee4961d71d70c82913cc558f86b83c8bfbaa3a3c90c9ce0f476 |
cat-searcher/leandojo-benchmark-4-random | test | 470 | Matrix.Pivot.listTransvecCol_mul_last_row_drop | Mathlib/LinearAlgebra/Matrix/Transvection.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hn' : n < (<a>Matrix.Pivot.listTransvecCol</a> M).<a>List.length</a> := by simpa [<a>Matrix.Pivot.listTransvecCol</a>] using hn | case refine_1
n✝ : Type u_1
p : Type u_2
R : Type u₂
𝕜 : Type u_3
inst✝³ : Field 𝕜
inst✝² : DecidableEq n✝
inst✝¹ : DecidableEq p
inst✝ : CommRing R
r : ℕ
M : Matrix (Fin r ⊕ Unit) (Fin r ⊕ Unit) 𝕜
i : Fin r ⊕ Unit
k : ℕ
hk : k ≤ r
n : ℕ
hn : n < r
a✝ : k ≤ n
IH : ((List.drop (n + 1) (listTransvecCol M)).prod * M) (... | case refine_1
n✝ : Type u_1
p : Type u_2
R : Type u₂
𝕜 : Type u_3
inst✝³ : Field 𝕜
inst✝² : DecidableEq n✝
inst✝¹ : DecidableEq p
inst✝ : CommRing R
r : ℕ
M : Matrix (Fin r ⊕ Unit) (Fin r ⊕ Unit) 𝕜
i : Fin r ⊕ Unit
k : ℕ
hk : k ≤ r
n : ℕ
hn : n < r
a✝ : k ≤ n
IH : ((List.drop (n + 1) (listTransvecCol M)).prod * M) (... | ((:c Eq) (:fv _uniq.95154) ((:c HMul.hMul) ((:c Matrix) ((:c Sum) ((:c Fin) (:fv _uniq.95180)) (:c Unit)) ((:c Sum) ((:c Fin) (:fv _uniq.95180)) (:c Unit)) (:fv _uniq.95154)) ((:c Matrix) ((:c Sum) ((:c Fin) (:fv _uniq.95180)) (:c Unit)) ((:c Sum) ((:c Fin) (:fv _uniq.95180)) (:c Unit)) (:fv _uniq.95154)) ((:c Matrix) ... | [{"name":"n✝","sexp":"(:sort (+ u_1 1))"},{"name":"p","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u₂ 1))"},{"name":"𝕜","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.95154))"},{"name":"inst✝²","sexp":"((:c DecidableEq) (:fv _uniq.95146))"},{"name":"inst✝¹","sexp":"((:c Decida... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (:c Matrix) (:arg :explicit 0 (:app (:c Sum) (:arg :explicit 0 (:app (:c Fin) (:arg :explicit 0 (:fv FV8)))) (:arg :explicit 1 (:c Unit)))) (:arg :explicit 1 (:app (:c Sum) (:arg :explicit 0 (:app (:c Fin... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.95146","is_instance":false,"is_let":false,"name":"n✝","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.95149","is_instance":false,"is_let":false,"name":"p","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"have","sourceEnd":16842,"sourceStart":16838,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hn'","sourceEnd":16846,"sourceStart":16843,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hn'","sourceEnd":16846,"sourceStart":16843,"tag":"n... | [] | [{"source":"n < (listTransvecCol M).length","source_end":16879,"source_start":16849,"syntax_kind":"«term_<_»"},{"source":"listTransvecCol","source_end":16908,"source_start":16893,"syntax_kind":"ident"},{"source":"hn","source_end":16918,"source_start":16916,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.95146","is_instance":false,"is_let":false,"user_name":"n✝"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.95149","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 87 | 10 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 99c5f17b1dfda0c78f208a80644371eafb33f1fc749f5eb0dfca1163c6d063a3 | 34a07a620a2a7ee4961d71d70c82913cc558f86b83c8bfbaa3a3c90c9ce0f476 | c55201b9b257863371725e0a76695c606d9112e537425f8ade8c6b6074edb9fa | 55d9053f9ec583a34732a881dc3216919ddb01211c5606186095c91a9a3dca4f |
cat-searcher/leandojo-benchmark-4-random | test | 471 | Matrix.Pivot.listTransvecCol_mul_last_row_drop | Mathlib/LinearAlgebra/Matrix/Transvection.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>List.drop_eq_getElem_cons</a> hn'] | case refine_1
n✝ : Type u_1
p : Type u_2
R : Type u₂
𝕜 : Type u_3
inst✝³ : Field 𝕜
inst✝² : DecidableEq n✝
inst✝¹ : DecidableEq p
inst✝ : CommRing R
r : ℕ
M : Matrix (Fin r ⊕ Unit) (Fin r ⊕ Unit) 𝕜
i : Fin r ⊕ Unit
k : ℕ
hk : k ≤ r
n : ℕ
hn : n < r
a✝ : k ≤ n
IH : ((List.drop (n + 1) (listTransvecCol M)).prod * M) (... | case refine_1
n✝ : Type u_1
p : Type u_2
R : Type u₂
𝕜 : Type u_3
inst✝³ : Field 𝕜
inst✝² : DecidableEq n✝
inst✝¹ : DecidableEq p
inst✝ : CommRing R
r : ℕ
M : Matrix (Fin r ⊕ Unit) (Fin r ⊕ Unit) 𝕜
i : Fin r ⊕ Unit
k : ℕ
hk : k ≤ r
n : ℕ
hn : n < r
a✝ : k ≤ n
IH : ((List.drop (n + 1) (listTransvecCol M)).prod * M) (... | ((:c Eq) (:fv _uniq.95154) ((:c HMul.hMul) ((:c Matrix) ((:c Sum) ((:c Fin) (:fv _uniq.95180)) (:c Unit)) ((:c Sum) ((:c Fin) (:fv _uniq.95180)) (:c Unit)) (:fv _uniq.95154)) ((:c Matrix) ((:c Sum) ((:c Fin) (:fv _uniq.95180)) (:c Unit)) ((:c Sum) ((:c Fin) (:fv _uniq.95180)) (:c Unit)) (:fv _uniq.95154)) ((:c Matrix) ... | [{"name":"n✝","sexp":"(:sort (+ u_1 1))"},{"name":"p","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u₂ 1))"},{"name":"𝕜","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.95154))"},{"name":"inst✝²","sexp":"((:c DecidableEq) (:fv _uniq.95146))"},{"name":"inst✝¹","sexp":"((:c Decida... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (:c Matrix) (:arg :explicit 0 (:app (:c Sum) (:arg :explicit 0 (:app (:c Fin) (:arg :explicit 0 (:fv FV8)))) (:arg :explicit 1 (:c Unit)))) (:arg :explicit 1 (:app (:c Sum) (:arg :explicit 0 (:app (:c Fin... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.95146","is_instance":false,"is_let":false,"name":"n✝","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.95149","is_instance":false,"is_let":false,"name":"p","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"rw","sourceEnd":16925,"sourceStart":16923,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16927,"sourceStart":16926,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Lis... | [] | [{"source":"List.drop_eq_getElem_cons hn'","source_end":16956,"source_start":16927,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.95146","is_instance":false,"is_let":false,"user_name":"n✝"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.95149","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 87 | 13 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | eb4be0a53d8c3225f510d5b4a1521ca7fa4898ad2f03c27f74416e0a58f3b046 | 55d9053f9ec583a34732a881dc3216919ddb01211c5606186095c91a9a3dca4f | 409c22c46c86ce4044974646f76b47ff9f4ca9187763e7d02d61ab1557f8c653 | 53e793c19fb64a6b3a9e2d913ff0b3c612c377ad42407aafc53c79fbcac333e8 |
cat-searcher/leandojo-benchmark-4-random | test | 472 | Matrix.Pivot.listTransvecCol_mul_last_row_drop | Mathlib/LinearAlgebra/Matrix/Transvection.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa [<a>Matrix.Pivot.listTransvecCol</a>, <a>Matrix.mul_assoc</a>] | case refine_1
n✝ : Type u_1
p : Type u_2
R : Type u₂
𝕜 : Type u_3
inst✝³ : Field 𝕜
inst✝² : DecidableEq n✝
inst✝¹ : DecidableEq p
inst✝ : CommRing R
r : ℕ
M : Matrix (Fin r ⊕ Unit) (Fin r ⊕ Unit) 𝕜
i : Fin r ⊕ Unit
k : ℕ
hk : k ≤ r
n : ℕ
hn : n < r
a✝ : k ≤ n
IH : ((List.drop (n + 1) (listTransvecCol M)).prod * M) (... | ((:c Eq) (:fv _uniq.95154) ((:c HMul.hMul) ((:c Matrix) ((:c Sum) ((:c Fin) (:fv _uniq.95180)) (:c Unit)) ((:c Sum) ((:c Fin) (:fv _uniq.95180)) (:c Unit)) (:fv _uniq.95154)) ((:c Matrix) ((:c Sum) ((:c Fin) (:fv _uniq.95180)) (:c Unit)) ((:c Sum) ((:c Fin) (:fv _uniq.95180)) (:c Unit)) (:fv _uniq.95154)) ((:c Matrix) ... | [{"name":"n✝","sexp":"(:sort (+ u_1 1))"},{"name":"p","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u₂ 1))"},{"name":"𝕜","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.95154))"},{"name":"inst✝²","sexp":"((:c DecidableEq) (:fv _uniq.95146))"},{"name":"inst✝¹","sexp":"((:c Decida... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (:c Matrix) (:arg :explicit 0 (:app (:c Sum) (:arg :explicit 0 (:app (:c Fin) (:arg :explicit 0 (:fv FV8)))) (:arg :explicit 1 (:c Unit)))) (:arg :explicit 1 (:app (:c Sum) (:arg :explicit 0 (:app (:c Fin... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.95146","is_instance":false,"is_let":false,"name":"n✝","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.95149","is_instance":false,"is_let":false,"name":"p","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"simpa","sourceEnd":16967,"sourceStart":16962,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"ch... | [] | [{"source":"listTransvecCol","source_end":16984,"source_start":16969,"syntax_kind":"ident"},{"source":"Matrix.mul_assoc","source_end":17002,"source_start":16986,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.95146","is_instance":false,"is_let":false,"user_name":"n✝"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.95149","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 87 | 16 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9603c48ec0f10ace226013bd7371d39c641ecc44ab4a864f72857fe87cc038c2 | 53e793c19fb64a6b3a9e2d913ff0b3c612c377ad42407aafc53c79fbcac333e8 | adaafedc719a32ff0424a812ec1497d7bfa23a580e51fdc7517d806a7d41ca3f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 473 | Matrix.Pivot.listTransvecCol_mul_last_row_drop | Mathlib/LinearAlgebra/Matrix/Transvection.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa [<a>Matrix.Pivot.listTransvecCol</a>] using hn | n✝ : Type u_1
p : Type u_2
R : Type u₂
𝕜 : Type u_3
inst✝³ : Field 𝕜
inst✝² : DecidableEq n✝
inst✝¹ : DecidableEq p
inst✝ : CommRing R
r : ℕ
M : Matrix (Fin r ⊕ Unit) (Fin r ⊕ Unit) 𝕜
i : Fin r ⊕ Unit
k : ℕ
hk : k ≤ r
n : ℕ
hn : n < r
a✝ : k ≤ n
IH : ((List.drop (n + 1) (listTransvecCol M)).prod * M) (inr ()) i = M ... | ((:c LT.lt) (:c Nat) (:c instLTNat) (:fv _uniq.95997) ((:c List.length) ((:c Matrix) ((:c Sum) ((:c Fin) (:fv _uniq.95180)) (:c Unit)) ((:c Sum) ((:c Fin) (:fv _uniq.95180)) (:c Unit)) (:fv _uniq.95154)) ((:c Matrix.Pivot.listTransvecCol) (:fv _uniq.95154) (:fv _uniq.95157) (:fv _uniq.95180) (:fv _uniq.95189)))) | [{"name":"n✝","sexp":"(:sort (+ u_1 1))"},{"name":"p","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u₂ 1))"},{"name":"𝕜","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.95154))"},{"name":"inst✝²","sexp":"((:c DecidableEq) (:fv _uniq.95146))"},{"name":"inst✝¹","sexp":"((:c Decida... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:fv FV14)) (:arg :explicit 3 (:app (:c List.length) (:arg :implicit-type 0 (:app (:c Matrix) (:arg :explicit 0 (:app (:c Sum) (:arg :explicit 0 (:app (:c Fin) (:arg :explicit... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.95146","is_instance":false,"is_let":false,"name":"n✝","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.95149","is_instance":false,"is_let":false,"name":"p","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"simpa","sourceEnd":16891,"sourceStart":16886,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"ch... | [] | [{"source":"listTransvecCol","source_end":16908,"source_start":16893,"syntax_kind":"ident"},{"source":"hn","source_end":16918,"source_start":16916,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.95146","is_instance":false,"is_let":false,"user_name":"n✝"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.95149","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 87 | 12 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fa1c736340a5c87f48df0283bca2fcee368cad05ad9d0dba6e5350bc9a54aa74 | db8dde9ebe00b368717a16606c0710a14d5e38e774cca482914fb257d0b52791 | d916b953eafca59dbafc39994529d803db8f27696e86d9b5b6a44c64b5d6d252 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 474 | Matrix.Pivot.listTransvecCol_mul_last_row_drop | Mathlib/LinearAlgebra/Matrix/Transvection.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Matrix.Pivot.listTransvecCol</a>, <a>List.length_ofFn</a>, <a>le_refl</a>, <a>List.drop_eq_nil_of_le</a>, <a>List.prod_nil</a>, <a>Matrix.one_mul</a>] | case refine_2
n : Type u_1
p : Type u_2
R : Type u₂
𝕜 : Type u_3
inst✝³ : Field 𝕜
inst✝² : DecidableEq n
inst✝¹ : DecidableEq p
inst✝ : CommRing R
r : ℕ
M : Matrix (Fin r ⊕ Unit) (Fin r ⊕ Unit) 𝕜
i : Fin r ⊕ Unit
k : ℕ
hk : k ≤ r
⊢ ((List.drop r (listTransvecCol M)).prod * M) (inr ()) i = M (inr ()) i | ((:c Eq) (:fv _uniq.95154) ((:c HMul.hMul) ((:c Matrix) ((:c Sum) ((:c Fin) (:fv _uniq.95180)) (:c Unit)) ((:c Sum) ((:c Fin) (:fv _uniq.95180)) (:c Unit)) (:fv _uniq.95154)) ((:c Matrix) ((:c Sum) ((:c Fin) (:fv _uniq.95180)) (:c Unit)) ((:c Sum) ((:c Fin) (:fv _uniq.95180)) (:c Unit)) (:fv _uniq.95154)) ((:c Matrix) ... | [{"name":"n","sexp":"(:sort (+ u_1 1))"},{"name":"p","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u₂ 1))"},{"name":"𝕜","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.95154))"},{"name":"inst✝²","sexp":"((:c DecidableEq) (:fv _uniq.95146))"},{"name":"inst✝¹","sexp":"((:c Decidab... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (:c Matrix) (:arg :explicit 0 (:app (:c Sum) (:arg :explicit 0 (:app (:c Fin) (:arg :explicit 0 (:fv FV8)))) (:arg :explicit 1 (:c Unit)))) (:arg :explicit 1 (:app (:c Sum) (:arg :explicit 0 (:app (:c Fin... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.95146","is_instance":false,"is_let":false,"name":"n","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.95149","is_instance":false,"is_let":false,"name":"p","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":17013,"sourceStart":17009,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":17018,"sourceStart":17014,"tag":"atom"}],"kind"... | [] | [{"source":"listTransvecCol","source_end":17035,"source_start":17020,"syntax_kind":"ident"},{"source":"List.length_ofFn","source_end":17053,"source_start":17037,"syntax_kind":"ident"},{"source":"le_refl","source_end":17062,"source_start":17055,"syntax_kind":"ident"},{"source":"List.drop_eq_nil_of_le","source_end":17086... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.95146","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.95149","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 87 | 19 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3eb0738c8522fb7870b38e9066c7f3e73e4207836a2aefb619f24833a57fbbe2 | 50de26c16fb97bd9a59ff99fc3264f15821974d82e6cb67427ce6228d52d016e | 0f0378fe013fe0e8ee7116c245c2d88ae90fca128eb976fc4f7b0dc6a12e6c5f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 475 | TrivSqZeroExt.map_comp_map | Mathlib/Algebra/TrivSqZeroExt.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>TrivSqZeroExt.algHom_ext</a> | S : Type u_1
R R' : Type u
M : Type v
inst✝²⁶ : CommSemiring S
inst✝²⁵ : Semiring R
inst✝²⁴ : CommSemiring R'
inst✝²³ : AddCommMonoid M
inst✝²² : Algebra S R
inst✝²¹ : Algebra S R'
inst✝²⁰ : Module S M
inst✝¹⁹ : Module R M
inst✝¹⁸ : Module Rᵐᵒᵖ M
inst✝¹⁷ : SMulCommClass R Rᵐᵒᵖ M
inst✝¹⁶ : IsScalarTower S R M
inst✝¹⁵ : ... | case h
S : Type u_1
R R' : Type u
M : Type v
inst✝²⁶ : CommSemiring S
inst✝²⁵ : Semiring R
inst✝²⁴ : CommSemiring R'
inst✝²³ : AddCommMonoid M
inst✝²² : Algebra S R
inst✝²¹ : Algebra S R'
inst✝²⁰ : Module S M
inst✝¹⁹ : Module R M
inst✝¹⁸ : Module Rᵐᵒᵖ M
inst✝¹⁷ : SMulCommClass R Rᵐᵒᵖ M
inst✝¹⁶ : IsScalarTower S R M
ins... | ((:c Eq) ((:c AlgHom) (:fv _uniq.1003163) ((:c TrivSqZeroExt) (:fv _uniq.1003163) (:fv _uniq.1003165)) ((:c TrivSqZeroExt) (:fv _uniq.1003163) (:fv _uniq.1011724)) (:fv _uniq.1003174) ((:c TrivSqZeroExt.semiring) (:fv _uniq.1003163) (:fv _uniq.1003165) ((:c CommSemiring.toSemiring) (:fv _uniq.1003163) (:fv _uniq.100317... | [{"name":"S","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"R'","sexp":"(:sort (+ u 1))"},{"name":"M","sexp":"(:sort (+ v 1))"},{"name":"inst✝²⁶","sexp":"((:c CommSemiring) (:fv _uniq.1003159))"},{"name":"inst✝²⁵","sexp":"((:c Semiring) (:fv _uniq.1003161))"},{"name":"inst✝²⁴","sexp":"((:c C... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c AlgHom) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:app (:c TrivSqZeroExt) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV3)))) (:arg :explicit 2 (:app (:c TrivSqZeroExt) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV25)))) (:arg :instance 3 (:instance-... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1003159","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1003161","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit",... | {"children":[{"source":"apply","sourceEnd":42618,"sourceStart":42613,"tag":"atom"},{"name":"TrivSqZeroExt.algHom_ext","semanticRole":"global","source":"algHom_ext","sourceEnd":42629,"sourceStart":42619,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply algHom_ext","sourceEnd":42629,"sourceStart":426... | [] | [{"source":"algHom_ext","source_end":42629,"source_start":42619,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1003159","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1003161","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":... | 297 | 4 | exact | true | 1 | 36 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5f03218cf25086d876ea4cc236f7694425b580265ef7aeb6c252b41995bceb08 | f9fe2ac582aacfa34a61a7e80503f951730274b098223b30a630a9b7f1fd784c | 90b2b5d439210e72a4395b9f7c6494f634de869367ee68421e0d8f5e062d324f | 8c700946d50fa5fe40265ae66ed5b1dd6f2a1d8a56c1afa42deeab72ce32949a |
cat-searcher/leandojo-benchmark-4-random | test | 476 | TrivSqZeroExt.map_comp_map | Mathlib/Algebra/TrivSqZeroExt.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>TrivSqZeroExt.map_inr</a>, <a>LinearMap.coe_comp</a>, <a>Function.comp_apply</a>, <a>AlgHom.coe_comp</a>, <a>forall_const</a>] | case h
S : Type u_1
R R' : Type u
M : Type v
inst✝²⁶ : CommSemiring S
inst✝²⁵ : Semiring R
inst✝²⁴ : CommSemiring R'
inst✝²³ : AddCommMonoid M
inst✝²² : Algebra S R
inst✝²¹ : Algebra S R'
inst✝²⁰ : Module S M
inst✝¹⁹ : Module R M
inst✝¹⁸ : Module Rᵐᵒᵖ M
inst✝¹⁷ : SMulCommClass R Rᵐᵒᵖ M
inst✝¹⁶ : IsScalarTower S R M
ins... | (:forall m (:fv _uniq.1003165) ((:c Eq) ((:c TrivSqZeroExt) (:fv _uniq.1003163) (:fv _uniq.1011724)) ((:c DFunLike.coe) ((:c AlgHom) (:fv _uniq.1003163) ((:c TrivSqZeroExt) (:fv _uniq.1003163) (:fv _uniq.1003165)) ((:c TrivSqZeroExt) (:fv _uniq.1003163) (:fv _uniq.1011724)) (:fv _uniq.1003174) ((:c TrivSqZeroExt.semiri... | [{"name":"S","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"R'","sexp":"(:sort (+ u 1))"},{"name":"M","sexp":"(:sort (+ v 1))"},{"name":"inst✝²⁶","sexp":"((:c CommSemiring) (:fv _uniq.1003159))"},{"name":"inst✝²⁵","sexp":"((:c Semiring) (:fv _uniq.1003161))"},{"name":"inst✝²⁴","sexp":"((:c C... | (:forall m :explicit (:fv FV3) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c TrivSqZeroExt) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV25)))) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c AlgHom) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:app (:c TrivSqZeroExt) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1003159","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1003161","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit",... | {"children":[{"source":"simp","sourceEnd":42636,"sourceStart":42632,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":42641,"sourceStart":42637,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":426... | [] | [{"source":"map_inr","source_end":42650,"source_start":42643,"syntax_kind":"ident"},{"source":"LinearMap.coe_comp","source_end":42670,"source_start":42652,"syntax_kind":"ident"},{"source":"Function.comp_apply","source_end":42691,"source_start":42672,"syntax_kind":"ident"},{"source":"AlgHom.coe_comp","source_end":42708,... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1003159","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1003161","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":... | 297 | 5 | exact | true | 1 | 36 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1d34ca24180d0de655315a88a917a0bca7e1b5a3aad3bb1577deff691317c277 | 8c700946d50fa5fe40265ae66ed5b1dd6f2a1d8a56c1afa42deeab72ce32949a | 244f5a58ba953074f126414f83ed5cf0fbf164127fc901bf5ac683be799cc4d7 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 477 | Dense.biUnion_uniformity_ball | Mathlib/Topology/UniformSpace/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>Set.iUnion₂_eq_univ_iff</a>.2 fun y => ?_ | α : Type ua
β : Type ub
γ : Type uc
δ : Type ud
ι : Sort u_1
inst✝ : UniformSpace α
s : Set α
U : Set (α × α)
hs : Dense s
hU : U ∈ 𝓤 α
⊢ ⋃ x ∈ s, ball x U = univ | α : Type ua
β : Type ub
γ : Type uc
δ : Type ud
ι : Sort u_1
inst✝ : UniformSpace α
s : Set α
U : Set (α × α)
hs : Dense s
hU : U ∈ 𝓤 α
y : α
⊢ ∃ i, ∃ (_ : i ∈ s), y ∈ ball i U | ((:c Eq) ((:c Set) (:fv _uniq.100102)) ((:c Set.iUnion) (:fv _uniq.100102) (:fv _uniq.100102) (:lambda x (:fv _uniq.100102) ((:c Set.iUnion) (:fv _uniq.100102) ((:c Membership.mem) (:fv _uniq.100102) ((:c Set) (:fv _uniq.100102)) ((:c Set.instMembership) (:fv _uniq.100102)) 0 (:fv _uniq.100307)) (:lambda _ ((:c Members... | [{"name":"α","sexp":"(:sort (+ ua 1))"},{"name":"β","sexp":"(:sort (+ ub 1))"},{"name":"γ","sexp":"(:sort (+ uc 1))"},{"name":"δ","sexp":"(:sort (+ ud 1))"},{"name":"ι","sexp":"(:sort u_1)"},{"name":"inst✝","sexp":"((:c UniformSpace) (:fv _uniq.100102))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.100102))"},{"name":"U",... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Set.iUnion) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :explicit 2 (:lambda x :explicit (:fv FV0) (:app (:c Set.iUnion) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100102","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.100104","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":49454,"sourceStart":49448,"tag":"atom"},{"children":[{"children":[{"name":"Set.iUnion₂_eq_univ_iff","semanticRole":"global","source":"iUnion₂_eq_univ_iff","sourceEnd":49476,"sourceStart":49455,"tag":"identifier"},{"source":".","sourceEnd":49477,"sourceStart":49476,"tag":"atom... | [] | [{"source":"iUnion₂_eq_univ_iff.2 fun y => ?_","source_end":49490,"source_start":49455,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100102","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.100104","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 267 | 4 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 071ee68b3d740a777bc13c76cdd4d115d3438904721a83a05b32acc178118dc8 | a97c48c240eb2196bc85109b9cf122e81bf5cac7d0514a4433fb5832bd3e3c80 | ae218b729aa8fb7af577272895101916b7f365e00dcf209c936f96723b151ad7 | ec0ee47f32eaafcf0885225d0f643841c47da086e982851c8b29ce4f30ac6409 |
cat-searcher/leandojo-benchmark-4-random | test | 478 | Dense.biUnion_uniformity_ball | Mathlib/Topology/UniformSpace/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases hs.inter_nhds_nonempty (<a>mem_nhds_right</a> y hU) with ⟨x, hxs, hxy : (x, y) ∈ U⟩ | α : Type ua
β : Type ub
γ : Type uc
δ : Type ud
ι : Sort u_1
inst✝ : UniformSpace α
s : Set α
U : Set (α × α)
hs : Dense s
hU : U ∈ 𝓤 α
y : α
⊢ ∃ i, ∃ (_ : i ∈ s), y ∈ ball i U | case intro.intro
α : Type ua
β : Type ub
γ : Type uc
δ : Type ud
ι : Sort u_1
inst✝ : UniformSpace α
s : Set α
U : Set (α × α)
hs : Dense s
hU : U ∈ 𝓤 α
y x : α
hxs : x ∈ s
hxy : (x, y) ∈ U
⊢ ∃ i, ∃ (_ : i ∈ s), y ∈ ball i U | ((:c Exists) (:fv _uniq.100102) (:lambda i (:fv _uniq.100102) ((:c Exists) ((:c Membership.mem) (:fv _uniq.100102) ((:c Set) (:fv _uniq.100102)) ((:c Set.instMembership) (:fv _uniq.100102)) 0 (:fv _uniq.100307)) (:lambda j ((:c Membership.mem) (:fv _uniq.100102) ((:c Set) (:fv _uniq.100102)) ((:c Set.instMembership) (:... | [{"name":"α","sexp":"(:sort (+ ua 1))"},{"name":"β","sexp":"(:sort (+ ub 1))"},{"name":"γ","sexp":"(:sort (+ uc 1))"},{"name":"δ","sexp":"(:sort (+ ud 1))"},{"name":"ι","sexp":"(:sort u_1)"},{"name":"inst✝","sexp":"((:c UniformSpace) (:fv _uniq.100102))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.100102))"},{"name":"U",... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda i :explicit (:fv FV0) (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Members... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100102","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.100104","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rcases","sourceEnd":49499,"sourceStart":49493,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"hs.inter_nhds_nonempty","sourceEnd":49522,"sourceStart":49500,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEn... | [] | [{"source":"hs.inter_nhds_nonempty (mem_nhds_right y hU)","source_end":49544,"source_start":49500,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨x, hxs, hxy : (x, y) ∈ U⟩","source_end":49582,"source_start":49550,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100102","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.100104","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 267 | 5 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a81bfc6d94d630b6df0916ce062cf781fca4c98b69772aa49193f90f0031f0fd | ec0ee47f32eaafcf0885225d0f643841c47da086e982851c8b29ce4f30ac6409 | bd96fc455849e42ae37f06e5bac4316a8e4960b0f1b3fff7dafe9cdb374cff57 | 0cf35651eaba12fee108bc208748075ab77cc7e3a16196448c242a5d181e7294 |
cat-searcher/leandojo-benchmark-4-random | test | 479 | Dense.biUnion_uniformity_ball | Mathlib/Topology/UniformSpace/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨x, hxs, hxy⟩ | case intro.intro
α : Type ua
β : Type ub
γ : Type uc
δ : Type ud
ι : Sort u_1
inst✝ : UniformSpace α
s : Set α
U : Set (α × α)
hs : Dense s
hU : U ∈ 𝓤 α
y x : α
hxs : x ∈ s
hxy : (x, y) ∈ U
⊢ ∃ i, ∃ (_ : i ∈ s), y ∈ ball i U | ((:c Exists) (:fv _uniq.100102) (:lambda i (:fv _uniq.100102) ((:c Exists) ((:c Membership.mem) (:fv _uniq.100102) ((:c Set) (:fv _uniq.100102)) ((:c Set.instMembership) (:fv _uniq.100102)) 0 (:fv _uniq.100307)) (:lambda j ((:c Membership.mem) (:fv _uniq.100102) ((:c Set) (:fv _uniq.100102)) ((:c Set.instMembership) (:... | [{"name":"α","sexp":"(:sort (+ ua 1))"},{"name":"β","sexp":"(:sort (+ ub 1))"},{"name":"γ","sexp":"(:sort (+ uc 1))"},{"name":"δ","sexp":"(:sort (+ ud 1))"},{"name":"ι","sexp":"(:sort u_1)"},{"name":"inst✝","sexp":"((:c UniformSpace) (:fv _uniq.100102))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.100102))"},{"name":"U",... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda i :explicit (:fv FV0) (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Members... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100102","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.100104","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":49590,"sourceStart":49585,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":49594,"sourceStart":49591,"tag":"atom"},{"children":[{"contextIndex":12,"semanticRole":"local","source":"x","sourceEnd":49595,"sourceStart":49594,"tag":"identifier"},{"source":",","sourceEnd":49596,... | [] | [{"source":"⟨x, hxs, hxy⟩","source_end":49608,"source_start":49591,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100102","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.100104","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 267 | 6 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 53cc2a54f8ad4fb03cb2294ebcb3feb4cd0075be4a012deb11f410b7eae641dd | 0cf35651eaba12fee108bc208748075ab77cc7e3a16196448c242a5d181e7294 | e2cd66dddfcb872221e8adc9b7c9d84962af3f707500701f3bfae3fefbef6a80 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 480 | units_smul_eq_self_iff | Mathlib/LinearAlgebra/Ray.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | induction' v using <a>Module.Ray.ind</a> with v hv | R : Type u_1
inst✝³ : LinearOrderedCommRing R
M : Type u_2
inst✝² : AddCommGroup M
inst✝¹ : Module R M
inst✝ : NoZeroSMulDivisors R M
u : Rˣ
v : Module.Ray R M
⊢ u • v = v ↔ 0 < ↑u | case h
R : Type u_1
inst✝³ : LinearOrderedCommRing R
M : Type u_2
inst✝² : AddCommGroup M
inst✝¹ : Module R M
inst✝ : NoZeroSMulDivisors R M
u : Rˣ
v : M
hv : v ≠ 0
⊢ u • rayOfNeZero R v hv = rayOfNeZero R v hv ↔ 0 < ↑u | ((:c Iff) ((:c Eq) ((:c Module.Ray) (:fv _uniq.287587) ((:c LinearOrderedCommSemiring.toStrictOrderedCommSemiring) (:fv _uniq.287587) ((:c LinearOrderedCommRing.toLinearOrderedCommSemiring) (:fv _uniq.287587) (:fv _uniq.287590))) (:fv _uniq.287593) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.287593) (:fv _uniq.287596... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c LinearOrderedCommRing) (:fv _uniq.287587))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.287593))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.287587) (:fv _uniq.287593) ((:c StrictOrderedSemi... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Module.Ray) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c StrictOrderedCommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.287587","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.287590","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c LinearOrderedCommRing... | {"children":[{"source":"induction'","sourceEnd":23553,"sourceStart":23543,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":8,"semanticRole":"local","source":"v","sourceEnd":23555,"sourceStart":23554,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget... | [] | [{"source":"v","source_end":23555,"source_start":23554,"syntax_kind":"ident"},{"source":"Module.Ray.ind","source_end":23576,"source_start":23562,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.287587","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.287590","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":implicit","context_index":2,"inte... | 185 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9dc1f3d77c4002723db37dd32975b58b7a6258e0a2d6584f9ca6e5a092ce5a64 | 2047925bccb6ff535e8b162dc05bd1fc0ac1b5c8bef0d1cf3858397b2a8ec6b4 | 8d64903ad0b7f05a75a983dc9795d1c362f1ff188c351a72b0506924637d6fc3 | a6011631fd2551622f574fd8e5b8c3f85431c3f68edcfe694f02280be54c6cac |
cat-searcher/leandojo-benchmark-4-random | test | 481 | units_smul_eq_self_iff | Mathlib/LinearAlgebra/Ray.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>smul_rayOfNeZero</a>, <a>ray_eq_iff</a>, <a>Units.smul_def</a>, <a>sameRay_smul_left_iff_of_ne</a> hv u.ne_zero] | case h
R : Type u_1
inst✝³ : LinearOrderedCommRing R
M : Type u_2
inst✝² : AddCommGroup M
inst✝¹ : Module R M
inst✝ : NoZeroSMulDivisors R M
u : Rˣ
v : M
hv : v ≠ 0
⊢ u • rayOfNeZero R v hv = rayOfNeZero R v hv ↔ 0 < ↑u | ((:c Iff) ((:c Eq) ((:c Module.Ray) (:fv _uniq.287587) ((:c LinearOrderedCommSemiring.toStrictOrderedCommSemiring) (:fv _uniq.287587) ((:c LinearOrderedCommRing.toLinearOrderedCommSemiring) (:fv _uniq.287587) (:fv _uniq.287590))) (:fv _uniq.287593) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.287593) (:fv _uniq.287596... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c LinearOrderedCommRing) (:fv _uniq.287587))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.287593))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.287587) (:fv _uniq.287593) ((:c StrictOrderedSemi... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Module.Ray) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c StrictOrderedCommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.287587","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.287590","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c LinearOrderedCommRing... | {"children":[{"source":"simp","sourceEnd":23593,"sourceStart":23589,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":23598,"sourceStart":23594,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":235... | [] | [{"source":"smul_rayOfNeZero","source_end":23616,"source_start":23600,"syntax_kind":"ident"},{"source":"ray_eq_iff","source_end":23628,"source_start":23618,"syntax_kind":"ident"},{"source":"Units.smul_def","source_end":23644,"source_start":23630,"syntax_kind":"ident"},{"source":"sameRay_smul_left_iff_of_ne hv u.ne_zero... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.287587","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.287590","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":implicit","context_index":2,"inte... | 185 | 5 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4b8b4c853b4a9dcf9b1ea8c710fd09cbec75b0ec31276ac73beae8837ccf4326 | a6011631fd2551622f574fd8e5b8c3f85431c3f68edcfe694f02280be54c6cac | cb21655c4dd0616a8532d49c60af655cb8b4cd9891a0e166c2f545d5192138df | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 482 | List.nodup_permutations'Aux_iff | Mathlib/Data/List/Perm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨fun h => ?_, <a>List.nodup_permutations'Aux_of_not_mem</a> _ _⟩ | α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
⊢ (permutations'Aux x s).Nodup ↔ x ∉ s | α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h : (permutations'Aux x s).Nodup
⊢ x ∉ s | ((:c Iff) ((:c List.Nodup) ((:c List) (:fv _uniq.54225)) ((:c List.permutations'Aux) (:fv _uniq.54225) (:fv _uniq.54268) (:fv _uniq.54267))) ((:c Not) ((:c Membership.mem) (:fv _uniq.54225) ((:c List) (:fv _uniq.54225)) ((:c List.instMembership) (:fv _uniq.54225)) (:fv _uniq.54268) (:fv _uniq.54267)))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"a","sexp":"(:fv _uniq.54225)"},{"name":"s","sexp":"((:c List) (:fv _uniq... | (:app (:c Iff) (:arg :explicit 0 (:app (:c List.Nodup) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c List.permutations'Aux) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV8)) (:arg :explicit 2 (:fv FV7)))))) (:arg :explicit 1 (:app (:c Not) (:arg :explicit... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"refine","sourceEnd":31902,"sourceStart":31896,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":31906,"sourceStart":31903,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":31909,"sourceStart":31906,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","sourc... | [] | [{"source":"⟨fun h => ?_, nodup_permutations'Aux_of_not_mem _ _⟩","source_end":31959,"source_start":31903,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 248 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b7e9fe66170c4de9b61ee51202e654ab7eb78e06ab267dd05b7b89fbfe9ef753 | f360f6060e176d44acab5833a8063f0935afdde47b0c31d177ee597a21149bbb | 708f71c96e3a3a1ed045d81fec46bc1abb27588a9f6133ea4b6a30b79573ed9b | dc6c57867558d1f0db2fa9444063b868763335fb27aa27ea54314c31dfd6b920 |
cat-searcher/leandojo-benchmark-4-random | test | 483 | List.nodup_permutations'Aux_iff | Mathlib/Data/List/Perm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro H | α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h : (permutations'Aux x s).Nodup
⊢ x ∉ s | α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h : (permutations'Aux x s).Nodup
H : x ∈ s
⊢ False | ((:c Not) ((:c Membership.mem) (:fv _uniq.54225) ((:c List) (:fv _uniq.54225)) ((:c List.instMembership) (:fv _uniq.54225)) (:fv _uniq.54268) (:fv _uniq.54267))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"a","sexp":"(:fv _uniq.54225)"},{"name":"s","sexp":"((:c List) (:fv _uniq... | (:app (:c Not) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c List) (:arg :explicit 0 (:fv FV0))))))) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"intro","sourceEnd":31967,"sourceStart":31962,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"H","sourceEnd":31969,"sourceStart":31968,"tag":"identifier"}],"kind":"null","source":"H","sourceEnd":31969,"sourceStart":31968,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source... | [{"role":"fresh_name","source":"H","source_end":31969,"source_start":31968,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 248 | 5 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9d2025001a9e99a5b6d4d2ac6f5997114fda5839ac9eb57a5f9f9f051bc099d1 | dc6c57867558d1f0db2fa9444063b868763335fb27aa27ea54314c31dfd6b920 | f272eeeb4cc80522a90d2c354625a65b5f7f88eabe478c9b214db02c98442ee1 | d8423ef8324d380ff1d90112f36bc2bca32c0e8d002fa371eee52ffd19980e32 |
cat-searcher/leandojo-benchmark-4-random | test | 484 | List.nodup_permutations'Aux_iff | Mathlib/Data/List/Perm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨k, hk, hk'⟩ := <a>List.nthLe_of_mem</a> H | α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h : (permutations'Aux x s).Nodup
H : x ∈ s
⊢ False | case intro.intro
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h : (permutations'Aux x s).Nodup
H : x ∈ s
k : ℕ
hk : k < s.length
hk' : s.nthLe k hk = x
⊢ False | (:c False) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"a","sexp":"(:fv _uniq.54225)"},{"name":"s","sexp":"((:c List) (:fv _uniq... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"obtain","sourceEnd":31978,"sourceStart":31972,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":31982,"sourceStart":31979,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"k","sourceEn... | [] | [{"source":"nthLe_of_mem H","source_end":32013,"source_start":31999,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨k, hk, hk'⟩","source_end":31995,"source_start":31979,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 248 | 6 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b89d220546dbd80347a0bac2aec4d87dda590e0b12b1034f5dabf7811d83e2d6 | d8423ef8324d380ff1d90112f36bc2bca32c0e8d002fa371eee52ffd19980e32 | ef299480008c21beabad7cb04f400fdb55201e233d9e9f00694d79dafda93810 | 045e2c6d01362577d896b7dae7381bdd0be15234a33c1d648ca2779243ad9493 |
cat-searcher/leandojo-benchmark-4-random | test | 485 | List.nodup_permutations'Aux_iff | Mathlib/Data/List/Perm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>List.nodup_iff_nthLe_inj</a>] at h | case intro.intro
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h : (permutations'Aux x s).Nodup
H : x ∈ s
k : ℕ
hk : k < s.length
hk' : s.nthLe k hk = x
⊢ False | case intro.intro
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H : x ∈ s
k : ℕ
hk : k < s.length
hk' : s.nthLe k hk =... | (:c False) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"a","sexp":"(:fv _uniq.54225)"},{"name":"s","sexp":"((:c List) (:fv _uniq... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":32018,"sourceStart":32016,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":32020,"sourceStart":32019,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"List.nodup_iff_n... | [] | [{"source":"nodup_iff_nthLe_inj","source_end":32039,"source_start":32020,"syntax_kind":"ident"},{"source":"h","source_end":32045,"source_start":32044,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 248 | 7 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c328aef0fd8a605e40dbd77a1a1ba6329a1588bafa086ed04b80c37b05e00e23 | 045e2c6d01362577d896b7dae7381bdd0be15234a33c1d648ca2779243ad9493 | 049fe078229daa3381b1cde25e9d58da44db8926c77843612be36201d91513dc | 840aca333e4f8f99bfa0eca6616a2cbcdc0aacfb7abdedd7ba036402b5406fcd |
cat-searcher/leandojo-benchmark-4-random | test | 486 | List.nodup_permutations'Aux_iff | Mathlib/Data/List/Perm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine k.succ_ne_self.symm $ h k (k + 1) ?_ ?_ ?_ | case intro.intro
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H : x ∈ s
k : ℕ
hk : k < s.length
hk' : s.nthLe k hk =... | case intro.intro.refine_1
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H : x ∈ s
k : ℕ
hk : k < s.length
hk' : s.nth... | (:c False) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"a","sexp":"(:fv _uniq.54225)"},{"name":"s","sexp":"((:c List) (:fv _uniq... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"refine","sourceEnd":32054,"sourceStart":32048,"tag":"atom"},{"children":[{"source":"k.succ_ne_self.symm","sourceEnd":32074,"sourceStart":32055,"tag":"identifier"},{"source":"$","sourceEnd":32076,"sourceStart":32075,"tag":"atom"},{"children":[{"contextIndex":9,"semanticRole":"local","source":"h",... | [] | [{"source":"k.succ_ne_self.symm $ h k (k + 1) ?_ ?_ ?_","source_end":32097,"source_start":32055,"syntax_kind":"«term_$__»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 248 | 10 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 274cbf2bcedc26c76d54c3a87b5da6b72de22adf4b92b2bdcc4135a936b5cb1e | 840aca333e4f8f99bfa0eca6616a2cbcdc0aacfb7abdedd7ba036402b5406fcd | 59a13eb13bb1954e0634c5fd32434bdffdca6b5783c267d621398391b71c7e4c | 63fb6ea819f9e24a65843f6508fdca630f21e298453ba63744687f5796a667cb |
cat-searcher/leandojo-benchmark-4-random | test | 487 | List.nodup_permutations'Aux_iff | Mathlib/Data/List/Perm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>List.nthLe_permutations'Aux</a>, <a>List.nthLe_permutations'Aux</a>] | case intro.intro.refine_3
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H : x ∈ s
k : ℕ
hk : k < s.length
hk' : s.nth... | case intro.intro.refine_3
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H : x ∈ s
k : ℕ
hk : k < s.length
hk' : s.nth... | ((:c Eq) ((:c List) (:fv _uniq.54225)) ((:c List.nthLe) ((:c List) (:fv _uniq.54225)) ((:c List.permutations'Aux) (:fv _uniq.54225) (:fv _uniq.54268) (:fv _uniq.54267)) (:fv _uniq.54388) ((:c Eq.mpr) ((:c LT.lt) (:c Nat) (:c instLTNat) (:fv _uniq.54388) ((:c List.length) ((:c List) (:fv _uniq.54225)) ((:c List.permutat... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"a","sexp":"(:fv _uniq.54225)"},{"name":"s","sexp":"((:c List) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c List.nthLe) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c List.permutations'Aux) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV8)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":32163,"sourceStart":32161,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":32165,"sourceStart":32164,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"List.nthLe_permu... | [] | [{"source":"nthLe_permutations'Aux","source_end":32187,"source_start":32165,"syntax_kind":"ident"},{"source":"nthLe_permutations'Aux","source_end":32211,"source_start":32189,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 248 | 21 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 513f0d1b354aebe2394652af3ad729d402d8ea28ededd93f6c1ff733e647994d | 98536f8ddc0cd3817ddfb81c21961620502305a5860a93bac20770eedd0b694b | 62e4b36622cf9d4f88c67e320f61dd15d3b31ed9195d805a3f8d0dc0ee8a27ca | 385deed7234a842a6b296e81ddb6b7da8db241390f0ad54be11541f8d9596549 |
cat-searcher/leandojo-benchmark-4-random | test | 488 | List.nodup_permutations'Aux_iff | Mathlib/Data/List/Perm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hl : <a>List.length</a> (<a>List.insertNth</a> k x s) = <a>List.length</a> (<a>List.insertNth</a> (k + 1) x s) := by rw [<a>List.length_insertNth</a> _ _ hk.le, <a>List.length_insertNth</a> _ _ (<a>Nat.succ_le_of_lt</a> hk)] | case intro.intro.refine_3
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H : x ∈ s
k : ℕ
hk : k < s.length
hk' : s.nth... | case intro.intro.refine_3
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H : x ∈ s
k : ℕ
hk : k < s.length
hk' : s.nth... | ((:c Eq) ((:c List) (:fv _uniq.54225)) ((:c List.insertNth) (:fv _uniq.54225) (:fv _uniq.54388) (:fv _uniq.54268) (:fv _uniq.54267)) ((:c List.insertNth) (:fv _uniq.54225) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.54388) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instO... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"a","sexp":"(:fv _uniq.54225)"},{"name":"s","sexp":"((:c List) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c List.insertNth) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV11)) (:arg :explicit 2 (:fv FV8)) (:arg :explicit 3 (:fv FV7)))) (:arg :explicit 2 (:app (:c List.insertNth) (:arg :implicit-type 0 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"have","sourceEnd":32219,"sourceStart":32215,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hl","sourceEnd":32222,"sourceStart":32220,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hl","sourceEnd":32222,"sourceStart":32220,"tag":"nod... | [] | [{"source":"length (insertNth k x s) = length (insertNth (k + 1) x s)","source_end":32282,"source_start":32225,"syntax_kind":"«term_=_»"},{"source":"length_insertNth _ _ hk.le","source_end":32323,"source_start":32297,"syntax_kind":"Lean.Parser.Term.app"},{"source":"length_insertNth _ _ (Nat.succ_le_of_lt hk)","source_e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 248 | 25 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 85fe12610450305088a1181df7c6d8b520375f4e74a5c9042e5d391a52616c9e | 385deed7234a842a6b296e81ddb6b7da8db241390f0ad54be11541f8d9596549 | 6ce3f2f9d6e951534b88a22751e7fa018b7966493b9c69ff126faa6468cbc7f5 | 1509adedee45ec6871e410763dbb2d92849e75a781987244343ad0a738fad502 |
cat-searcher/leandojo-benchmark-4-random | test | 489 | List.nodup_permutations'Aux_iff | Mathlib/Data/List/Perm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>List.ext_nthLe</a> hl fun n hn hn' => ?_ | case intro.intro.refine_3
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H : x ∈ s
k : ℕ
hk : k < s.length
hk' : s.nth... | case intro.intro.refine_3
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H : x ∈ s
k : ℕ
hk : k < s.length
hk' : s.nth... | ((:c Eq) ((:c List) (:fv _uniq.54225)) ((:c List.insertNth) (:fv _uniq.54225) (:fv _uniq.54388) (:fv _uniq.54268) (:fv _uniq.54267)) ((:c List.insertNth) (:fv _uniq.54225) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.54388) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instO... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"a","sexp":"(:fv _uniq.54225)"},{"name":"s","sexp":"((:c List) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c List.insertNth) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV11)) (:arg :explicit 2 (:fv FV8)) (:arg :explicit 3 (:fv FV7)))) (:arg :explicit 2 (:app (:c List.insertNth) (:arg :implicit-type 0 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"refine","sourceEnd":32378,"sourceStart":32372,"tag":"atom"},{"children":[{"name":"List.ext_nthLe","semanticRole":"global","source":"ext_nthLe","sourceEnd":32388,"sourceStart":32379,"tag":"identifier"},{"children":[{"contextIndex":14,"semanticRole":"local","source":"hl","sourceEnd":32391,"sourceS... | [] | [{"source":"ext_nthLe hl fun n hn hn' => ?_","source_end":32410,"source_start":32379,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 248 | 31 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f29ce988e5550fd9fc97216f3a809c2eef478ec2bd0e36002adc19cba7cf0232 | 1509adedee45ec6871e410763dbb2d92849e75a781987244343ad0a738fad502 | d500cefdcb05a64be9365d92c5258aa18a64a5d3b10cbf1dae0511452187fa89 | bba7a9b51ad1e569e81c936d130f8e0966a8febc1065477d0f59f211ab9fa919 |
cat-searcher/leandojo-benchmark-4-random | test | 490 | List.nodup_permutations'Aux_iff | Mathlib/Data/List/Perm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases <a>lt_trichotomy</a> n k with (H | rfl | H) | case intro.intro.refine_3
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H : x ∈ s
k : ℕ
hk : k < s.length
hk' : s.nth... | case intro.intro.refine_3.inl
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H✝ : x ∈ s
k : ℕ
hk : k < s.length
hk' : ... | ((:c Eq) (:fv _uniq.54225) ((:c List.nthLe) (:fv _uniq.54225) ((:c List.insertNth) (:fv _uniq.54225) (:fv _uniq.54388) (:fv _uniq.54268) (:fv _uniq.54267)) (:fv _uniq.55245) (:fv _uniq.55248)) ((:c List.nthLe) (:fv _uniq.54225) ((:c List.insertNth) (:fv _uniq.54225) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instH... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"a","sexp":"(:fv _uniq.54225)"},{"name":"s","sexp":"((:c List) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c List.nthLe) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c List.insertNth) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV11)) (:arg :explicit 2 (:fv FV8)) (:arg :explicit 3 (:fv FV7)))) (:arg :explicit 2 (:fv FV15)) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rcases","sourceEnd":32419,"sourceStart":32413,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"lt_trichotomy","semanticRole":"global","source":"lt_trichotomy","sourceEnd":32433,"sourceStart":32420,"tag":"identifier"},{"children"... | [] | [{"source":"lt_trichotomy n k","source_end":32437,"source_start":32420,"syntax_kind":"Lean.Parser.Term.app"},{"source":"(H | rfl | H)","source_end":32456,"source_start":32443,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.paren"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 248 | 32 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b48a5e554851026e2e11ce37f9fcad0067d96bd6a5576d192351ca5adaaedaf3 | bba7a9b51ad1e569e81c936d130f8e0966a8febc1065477d0f59f211ab9fa919 | 6900a8b7d0eaf06cdca4208ef16c31b84be7ea82e9e93ed1c10d20649447840a | 4c66d6790847466f514c54f19f14f5e0c208594df3f67e5894d44dd35e507c83 |
cat-searcher/leandojo-benchmark-4-random | test | 491 | List.nodup_permutations'Aux_iff | Mathlib/Data/List/Perm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa [<a>Nat.lt_succ_iff</a>] using hk.le | case intro.intro.refine_1
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H : x ∈ s
k : ℕ
hk : k < s.length
hk' : s.nth... | ((:c LT.lt) (:c Nat) (:c instLTNat) (:fv _uniq.54388) ((:c List.length) ((:c List) (:fv _uniq.54225)) ((:c List.permutations'Aux) (:fv _uniq.54225) (:fv _uniq.54268) (:fv _uniq.54267)))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"a","sexp":"(:fv _uniq.54225)"},{"name":"s","sexp":"((:c List) (:fv _uniq... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:fv FV11)) (:arg :explicit 3 (:app (:c List.length) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c List.permutations'Aux) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":32108,"sourceStart":32103,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [{"source":"Nat.lt_succ_iff","source_end":32125,"source_start":32110,"syntax_kind":"ident"},{"source":"hk.le","source_end":32138,"source_start":32133,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 248 | 13 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 505f4eb1ccbf604e7bdd25bddd5dacce7ed9b384e42f9136178719ad84fcaad5 | 4aeec122883475713a1614b4935a4b7896a3127faa8420daaf678128132b8c6a | f63b857ad40b47c211eadc9f344c9fda0300bf5a1f75ccdbc43a7a1a96c1b9e4 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 492 | List.nodup_permutations'Aux_iff | Mathlib/Data/List/Perm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa using hk | case intro.intro.refine_2
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H : x ∈ s
k : ℕ
hk : k < s.length
hk' : s.nth... | ((:c LT.lt) (:c Nat) (:c instLTNat) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.54388) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) ((:c List.length) ((:c List) (:fv _uniq.54225)) ((:c List.permutations'Aux) (:fv _uniq.54225) (:fv _uniq.54268) (:f... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"a","sexp":"(:fv _uniq.54225)"},{"name":"s","sexp":"((:c List) (:fv _uniq... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":32149,"sourceStart":32144,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [{"source":"hk","source_end":32158,"source_start":32156,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 248 | 18 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2adcb2bbc512eea35c57b31ba3b05e0aa0cf2383c9940e4237104fb7ff6f35c7 | 40a7d91f58a36b5071799f37b7448f415b0b09b136b22ad9f8b55415abd79b8e | 6fd6fbf138442f81b7f5e0815ea4113218ffba600180024a2ee82fa062a53e53 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 493 | List.nodup_permutations'Aux_iff | Mathlib/Data/List/Perm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>List.length_insertNth</a> _ _ hk.le, <a>List.length_insertNth</a> _ _ (<a>Nat.succ_le_of_lt</a> hk)] | α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H : x ∈ s
k : ℕ
hk : k < s.length
hk' : s.nthLe k hk = x
⊢ (insertNth k... | ((:c Eq) (:c Nat) ((:c List.length) (:fv _uniq.54225) ((:c List.insertNth) (:fv _uniq.54225) (:fv _uniq.54388) (:fv _uniq.54268) (:fv _uniq.54267))) ((:c List.length) (:fv _uniq.54225) ((:c List.insertNth) (:fv _uniq.54225) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.5... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"a","sexp":"(:fv _uniq.54225)"},{"name":"s","sexp":"((:c List) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c List.length) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c List.insertNth) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV11)) (:arg :explicit 2 (:fv FV8)) (:arg :explicit 3 (:fv FV7)))))) (:arg :explicit 2 (:app (:c ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":32295,"sourceStart":32293,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":32297,"sourceStart":32296,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Lis... | [] | [{"source":"length_insertNth _ _ hk.le","source_end":32323,"source_start":32297,"syntax_kind":"Lean.Parser.Term.app"},{"source":"length_insertNth _ _ (Nat.succ_le_of_lt hk)","source_end":32368,"source_start":32325,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 248 | 27 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ca93d94c1a557490c90299533d43bd56bb125259730fc7ed584a8cd6cfab267d | ee5f4318932f1deb4367efa6e00776ee72d90c478f1e1079a0708e99e16cd88a | 77aa81c7af4eb553958bb1562380a77c7841e8e6b0056f190323df55bc01cda9 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 494 | List.nodup_permutations'Aux_iff | Mathlib/Data/List/Perm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>List.nthLe_insertNth_of_lt</a> _ _ _ _ H (H.trans hk), <a>List.nthLe_insertNth_of_lt</a> _ _ _ _ (H.trans (<a>Nat.lt_succ_self</a> _))] | case intro.intro.refine_3.inl
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H✝ : x ∈ s
k : ℕ
hk : k < s.length
hk' : ... | ((:c Eq) (:fv _uniq.54225) ((:c List.nthLe) (:fv _uniq.54225) ((:c List.insertNth) (:fv _uniq.54225) (:fv _uniq.54388) (:fv _uniq.54268) (:fv _uniq.54267)) (:fv _uniq.55245) (:fv _uniq.55248)) ((:c List.nthLe) (:fv _uniq.54225) ((:c List.insertNth) (:fv _uniq.54225) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instH... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"a","sexp":"(:fv _uniq.54225)"},{"name":"s","sexp":"((:c List) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c List.nthLe) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c List.insertNth) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV11)) (:arg :explicit 2 (:fv FV8)) (:arg :explicit 3 (:fv FV7)))) (:arg :explicit 2 (:fv FV15)) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":32464,"sourceStart":32462,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":32466,"sourceStart":32465,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"nthLe_insertNth_of_lt _ _ _ _ H (H.trans hk)","source_end":32510,"source_start":32466,"syntax_kind":"Lean.Parser.Term.app"},{"source":"nthLe_insertNth_of_lt _ _ _ _ (H.trans (Nat.lt_succ_self _))","source_end":32578,"source_start":32518,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 248 | 35 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6a77294922390ead95fc725597e0d841c9a341320555fa910d6b0f0bf8bd3bfa | cbc1153254649c3693e754fb44ede4011c0fd1125e5e579d25810b6a44ff1211 | 353540f4856fa287c0bc75e51ade45556f9ee9515356c16bf7221ae843375744 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 495 | List.nodup_permutations'Aux_iff | Mathlib/Data/List/Perm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>List.nthLe_insertNth_self</a> _ _ _ hk.le, <a>List.nthLe_insertNth_of_lt</a> _ _ _ _ (<a>Nat.lt_succ_self</a> _) hk, hk'] | case intro.intro.refine_3.inr.inl
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H : x ∈ s
n : ℕ
hk : n < s.length
hk'... | ((:c Eq) (:fv _uniq.54225) ((:c List.nthLe) (:fv _uniq.54225) ((:c List.insertNth) (:fv _uniq.54225) (:fv _uniq.55245) (:fv _uniq.54268) (:fv _uniq.54267)) (:fv _uniq.55245) (:fv _uniq.55339)) ((:c List.nthLe) (:fv _uniq.54225) ((:c List.insertNth) (:fv _uniq.54225) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instH... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"a","sexp":"(:fv _uniq.54225)"},{"name":"s","sexp":"((:c List) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c List.nthLe) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c List.insertNth) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV11)) (:arg :explicit 2 (:fv FV8)) (:arg :explicit 3 (:fv FV7)))) (:arg :explicit 2 (:fv FV11)) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":32587,"sourceStart":32585,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":32589,"sourceStart":32588,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"nthLe_insertNth_self _ _ _ hk.le","source_end":32621,"source_start":32589,"syntax_kind":"Lean.Parser.Term.app"},{"source":"nthLe_insertNth_of_lt _ _ _ _ (Nat.lt_succ_self _) hk","source_end":32676,"source_start":32623,"syntax_kind":"Lean.Parser.Term.app"},{"source":"hk'","source_end":32687,"source_start":32... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 248 | 43 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | eba4c1030752567667b15a8043d4b03961e62a43a70b8e0a953d5991a08c0e6c | 9b8eb420ab45ca8cc0b5f7036bf8e83212d72d0c276dc8de4184ff38ce281707 | e7196d0e58508808164903a0a2e4495f627f7db47bb2cf496df6d367ef3d0281 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 496 | List.nodup_permutations'Aux_iff | Mathlib/Data/List/Perm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases (<a>Nat.succ_le_of_lt</a> H).<a>LE.le.eq_or_lt</a> with (rfl | H') | case intro.intro.refine_3.inr.inr
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H✝ : x ∈ s
k : ℕ
hk : k < s.length
hk... | case intro.intro.refine_3.inr.inr.inl
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H✝ : x ∈ s
k : ℕ
hk : k < s.lengt... | ((:c Eq) (:fv _uniq.54225) ((:c List.nthLe) (:fv _uniq.54225) ((:c List.insertNth) (:fv _uniq.54225) (:fv _uniq.54388) (:fv _uniq.54268) (:fv _uniq.54267)) (:fv _uniq.55245) (:fv _uniq.55248)) ((:c List.nthLe) (:fv _uniq.54225) ((:c List.insertNth) (:fv _uniq.54225) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instH... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"a","sexp":"(:fv _uniq.54225)"},{"name":"s","sexp":"((:c List) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c List.nthLe) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c List.insertNth) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV11)) (:arg :explicit 2 (:fv FV8)) (:arg :explicit 3 (:fv FV7)))) (:arg :explicit 2 (:fv FV15)) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rcases","sourceEnd":32700,"sourceStart":32694,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":"(","sourceEnd":32702,"sourceStart":32701,"tag":"atom"},{"children":[{"name":"Nat.succ_le_of_lt","semanticRole":"global... | [] | [{"source":"(Nat.succ_le_of_lt H).eq_or_lt","source_end":32731,"source_start":32701,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"(rfl | H')","source_end":32747,"source_start":32737,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.paren"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 248 | 54 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2a45be289745de17eb9172c2cf4891c9328009a93dd9a740db4ad40f399b1b47 | 4c1d39801445498066d4fa325988ee5f08ca37c6e406be13d5072fbbee5a00b7 | f2acd3649950f037d7d7b0301f91912af2ce7ce2318a9a9cad5996ee70ce39fd | ffaeae186c92dbdd365a27afa45dd58ddbfc918a9017e1af783524a7e47cd731 |
cat-searcher/leandojo-benchmark-4-random | test | 497 | List.nodup_permutations'Aux_iff | Mathlib/Data/List/Perm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>List.nthLe_insertNth_self</a> _ _ _ (<a>Nat.succ_le_of_lt</a> hk)] | case intro.intro.refine_3.inr.inr.inl
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H✝ : x ∈ s
k : ℕ
hk : k < s.lengt... | case intro.intro.refine_3.inr.inr.inl
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H✝ : x ∈ s
k : ℕ
hk : k < s.lengt... | ((:c Eq) (:fv _uniq.54225) ((:c List.nthLe) (:fv _uniq.54225) ((:c List.insertNth) (:fv _uniq.54225) (:fv _uniq.54388) (:fv _uniq.54268) (:fv _uniq.54267)) ((:c Nat.succ) (:fv _uniq.54388)) (:fv _uniq.55583)) ((:c List.nthLe) (:fv _uniq.54225) ((:c List.insertNth) (:fv _uniq.54225) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"a","sexp":"(:fv _uniq.54225)"},{"name":"s","sexp":"((:c List) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c List.nthLe) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c List.insertNth) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV11)) (:arg :explicit 2 (:fv FV8)) (:arg :explicit 3 (:fv FV7)))) (:arg :explicit 2 (:app (:c Na... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":32757,"sourceStart":32755,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":32759,"sourceStart":32758,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Lis... | [] | [{"source":"nthLe_insertNth_self _ _ _ (Nat.succ_le_of_lt hk)","source_end":32808,"source_start":32759,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 248 | 59 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3753c11b6603c8cb7e4f1fdd64fda94fdfca3de8f12bb219fd6d749b20b66442 | c8b05a6e9f630fbca6ac628f38072836dedb9947346102511cf498c2a238800c | eb9d54e3827d13ea1b9b5f3cf7138cfae1936a151f1e39aa1ba581cab49d0fc1 | 41862a76b170b84bf1204298aab13b58ba9fe42ae4e45a6dbb63d94e26a9d8cf |
cat-searcher/leandojo-benchmark-4-random | test | 498 | List.nodup_permutations'Aux_iff | Mathlib/Data/List/Perm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert hk' using 1 | case intro.intro.refine_3.inr.inr.inl
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H✝ : x ∈ s
k : ℕ
hk : k < s.lengt... | case h.e'_2
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H✝ : x ∈ s
k : ℕ
hk : k < s.length
hk' : s.nthLe k hk = x
h... | ((:c Eq) (:fv _uniq.54225) ((:c List.nthLe) (:fv _uniq.54225) ((:c List.insertNth) (:fv _uniq.54225) (:fv _uniq.54388) (:fv _uniq.54268) (:fv _uniq.54267)) ((:c Nat.succ) (:fv _uniq.54388)) (:fv _uniq.55583)) (:fv _uniq.54268)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"a","sexp":"(:fv _uniq.54225)"},{"name":"s","sexp":"((:c List) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c List.nthLe) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c List.insertNth) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV11)) (:arg :explicit 2 (:fv FV8)) (:arg :explicit 3 (:fv FV7)))) (:arg :explicit 2 (:app (:c Na... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"convert","sourceEnd":32823,"sourceStart":32816,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":13,"semanticRole":"local","source":"hk'","sourceEnd":32827,"sourceStart":32824,"tag":"identifier"},{"children... | [] | [{"source":"hk'","source_end":32827,"source_start":32824,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 248 | 62 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e95595f1d16c4fc09c8caf4dbb82935bce3e75c511c9d654ab37b27e209f373f | 41862a76b170b84bf1204298aab13b58ba9fe42ae4e45a6dbb63d94e26a9d8cf | 3eb40a7c5ac6059d5e0aa9d45ee2f030cb8bd07febb27a46f55d051674b97fe5 | 3a643041fe138d98bfd9ebe5bba5501c65b068911dcab4e07b09ef6e9e6d6630 |
cat-searcher/leandojo-benchmark-4-random | test | 499 | List.nodup_permutations'Aux_iff | Mathlib/Data/List/Perm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>List.nthLe_insertNth_add_succ</a> _ _ _ 0 _ | case h.e'_2
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H✝ : x ∈ s
k : ℕ
hk : k < s.length
hk' : s.nthLe k hk = x
h... | ((:c Eq) (:fv _uniq.54225) ((:c List.nthLe) (:fv _uniq.54225) ((:c List.insertNth) (:fv _uniq.54225) (:fv _uniq.54388) (:fv _uniq.54268) (:fv _uniq.54267)) ((:c Nat.succ) (:fv _uniq.54388)) (:fv _uniq.55583)) ((:c List.nthLe) (:fv _uniq.54225) (:fv _uniq.54267) (:fv _uniq.54388) (:fv _uniq.54389))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"a","sexp":"(:fv _uniq.54225)"},{"name":"s","sexp":"((:c List) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c List.nthLe) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c List.insertNth) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV11)) (:arg :explicit 2 (:fv FV8)) (:arg :explicit 3 (:fv FV7)))) (:arg :explicit 2 (:app (:c Na... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":32847,"sourceStart":32842,"tag":"atom"},{"children":[{"name":"List.nthLe_insertNth_add_succ","semanticRole":"global","source":"nthLe_insertNth_add_succ","sourceEnd":32872,"sourceStart":32848,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":32874,"sourceS... | [] | [{"source":"nthLe_insertNth_add_succ _ _ _ 0 _","source_end":32882,"source_start":32848,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 248 | 63 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7625523472502e55b487bda7a6b5c5f1fa34ff03500c75fd69e0ff90cfb0613b | 3a643041fe138d98bfd9ebe5bba5501c65b068911dcab4e07b09ef6e9e6d6630 | 1c840a8665966cb28dd8dea47f168ece157bb43c8fd61fae021a57cde82eaf9f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 500 | List.nodup_permutations'Aux_iff | Mathlib/Data/List/Perm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨m, rfl⟩ := <a>Nat.exists_eq_add_of_lt</a> H' | case intro.intro.refine_3.inr.inr.inr
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H✝ : x ∈ s
k : ℕ
hk : k < s.lengt... | case intro.intro.refine_3.inr.inr.inr.intro
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H✝ : x ∈ s
k : ℕ
hk : k < s... | ((:c Eq) (:fv _uniq.54225) ((:c List.nthLe) (:fv _uniq.54225) ((:c List.insertNth) (:fv _uniq.54225) (:fv _uniq.54388) (:fv _uniq.54268) (:fv _uniq.54267)) (:fv _uniq.55245) (:fv _uniq.55248)) ((:c List.nthLe) (:fv _uniq.54225) ((:c List.insertNth) (:fv _uniq.54225) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instH... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"a","sexp":"(:fv _uniq.54225)"},{"name":"s","sexp":"((:c List) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c List.nthLe) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c List.insertNth) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV11)) (:arg :explicit 2 (:fv FV8)) (:arg :explicit 3 (:fv FV7)))) (:arg :explicit 2 (:fv FV15)) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"obtain","sourceEnd":32896,"sourceStart":32890,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":32900,"sourceStart":32897,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"m","sourceEn... | [] | [{"source":"Nat.exists_eq_add_of_lt H'","source_end":32939,"source_start":32913,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨m, rfl⟩","source_end":32909,"source_start":32897,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 248 | 68 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fd83438f64839cb09388123cc01a6b1dff9163258d34d9addeaaedbc5fbd4d65 | 18a6330a63b7308cbd8da27896db17920a85053e19e8401e5c7e0b9d6dabb1e5 | 3f034cbdae5045b5e8aa0601f63179379fce88debd7d5a014b55817130932df1 | b987516f7702190429d6143fa3b93d5c96d782e334e2555489112c4b88c55840 |
cat-searcher/leandojo-benchmark-4-random | test | 501 | List.nodup_permutations'Aux_iff | Mathlib/Data/List/Perm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | erw [<a>List.length_insertNth</a> _ _ hk.le, <a>Nat.succ_lt_succ_iff</a>, <a>Nat.succ_add</a>] at hn | case intro.intro.refine_3.inr.inr.inr.intro
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H✝ : x ∈ s
k : ℕ
hk : k < s... | case intro.intro.refine_3.inr.inr.inr.intro
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H✝ : x ∈ s
k : ℕ
hk : k < s... | ((:c Eq) (:fv _uniq.54225) ((:c List.nthLe) (:fv _uniq.54225) ((:c List.insertNth) (:fv _uniq.54225) (:fv _uniq.54388) (:fv _uniq.54268) (:fv _uniq.54267)) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNa... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"a","sexp":"(:fv _uniq.54225)"},{"name":"s","sexp":"((:c List) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c List.nthLe) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c List.insertNth) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV11)) (:arg :explicit 2 (:fv FV8)) (:arg :explicit 3 (:fv FV7)))) (:arg :explicit 2 (:app (:c HA... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"erw","sourceEnd":32949,"sourceStart":32946,"tag":"atom"},{"children":[{"source":"[","sourceEnd":32951,"sourceStart":32950,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"List.length_insertNth","semanticRole":"global","source":"... | [] | [{"source":"hn","source_end":33020,"source_start":33018,"syntax_kind":"ident"},{"source":"length_insertNth _ _ hk.le","source_end":32977,"source_start":32951,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Nat.succ_lt_succ_iff","source_end":32999,"source_start":32979,"syntax_kind":"ident"},{"source":"Nat.succ_add","so... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 248 | 69 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 31bb1a279bd0fc979fe8437196d2c062930488431d22d548c8d670e31de463ce | b987516f7702190429d6143fa3b93d5c96d782e334e2555489112c4b88c55840 | bb378df01714350a2788b38b3887d851e520d89d1b526d0a453b9808b676ad2f | b4280cce9bd95b08420bf6b9064fbb161d48c41cefae7b2f18250e163ccc51dc |
cat-searcher/leandojo-benchmark-4-random | test | 502 | List.nodup_permutations'Aux_iff | Mathlib/Data/List/Perm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>List.nthLe_insertNth_add_succ</a>] | case intro.intro.refine_3.inr.inr.inr.intro
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H✝ : x ∈ s
k : ℕ
hk : k < s... | case intro.intro.refine_3.inr.inr.inr.intro
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H✝ : x ∈ s
k : ℕ
hk : k < s... | ((:c Eq) (:fv _uniq.54225) ((:c List.nthLe) (:fv _uniq.54225) ((:c List.insertNth) (:fv _uniq.54225) (:fv _uniq.54388) (:fv _uniq.54268) (:fv _uniq.54267)) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNa... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"a","sexp":"(:fv _uniq.54225)"},{"name":"s","sexp":"((:c List) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c List.nthLe) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c List.insertNth) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV11)) (:arg :explicit 2 (:fv FV8)) (:arg :explicit 3 (:fv FV7)))) (:arg :explicit 2 (:app (:c HA... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":33029,"sourceStart":33027,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":33031,"sourceStart":33030,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"List.nthLe_inser... | [] | [{"source":"nthLe_insertNth_add_succ","source_end":33055,"source_start":33031,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 248 | 74 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1072a4566843f6d302999b22d5844f7eb39e354e438e18e31451203eb0dba248 | b4280cce9bd95b08420bf6b9064fbb161d48c41cefae7b2f18250e163ccc51dc | e96c390fe934829c277a8542673b0e97c8042ad725927c7ca1f85335cc0d4aea | 77a18096f0a889d6370f243f05b0856a8204801679f43d9f03eeb103cd17b953 |
cat-searcher/leandojo-benchmark-4-random | test | 503 | List.nodup_permutations'Aux_iff | Mathlib/Data/List/Perm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert <a>List.nthLe_insertNth_add_succ</a> s x k m.succ (by simpa using hn) using 2 | case intro.intro.refine_3.inr.inr.inr.intro
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H✝ : x ∈ s
k : ℕ
hk : k < s... | case h.e'_2.h.e'_3
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H✝ : x ∈ s
k : ℕ
hk : k < s.length
hk' : s.nthLe k h... | ((:c Eq) (:fv _uniq.54225) ((:c List.nthLe) (:fv _uniq.54225) ((:c List.insertNth) (:fv _uniq.54225) (:fv _uniq.54388) (:fv _uniq.54268) (:fv _uniq.54267)) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNa... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"a","sexp":"(:fv _uniq.54225)"},{"name":"s","sexp":"((:c List) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c List.nthLe) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c List.insertNth) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV11)) (:arg :explicit 2 (:fv FV8)) (:arg :explicit 3 (:fv FV7)))) (:arg :explicit 2 (:app (:c HA... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"convert","sourceEnd":33073,"sourceStart":33066,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"List.nthLe_insertNth_add_succ","semanticRole":"global","source":"nthLe_insertNth_add_succ","sourceEnd":... | [] | [{"source":"nthLe_insertNth_add_succ s x k m.succ (by simpa using hn)","source_end":33131,"source_start":33074,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 248 | 81 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2d67aa1efef93f773d6b0de22cc859c00088614d3ebef4bc954e06d0b86a99dc | 414421e01dabf4a3a2acf0fadf49e84a733ff7c0ddf00f1adbd4a25b76540e9f | 992a6b5be4bb714b9b35196414646836606a0b7795a3cb870d3482f004328bb5 | 961b9315c2eda3d33c64c1ea1b29e24f78e1f2adfe36b19a49f79a190d486570 |
cat-searcher/leandojo-benchmark-4-random | test | 504 | List.nodup_permutations'Aux_iff | Mathlib/Data/List/Perm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa using hn | α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H✝ : x ∈ s
k : ℕ
hk : k < s.length
hk' : s.nthLe k hk = x
hl : (insertN... | ((:c LT.lt) (:c Nat) (:c instLTNat) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.54388) ((:c Nat.succ) (:fv _uniq.56042))) ((:c List.length) (:fv _uniq.54225) (:fv _uniq.54267))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"a","sexp":"(:fv _uniq.54225)"},{"name":"s","sexp":"((:c List) (:fv _uniq... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":33121,"sourceStart":33116,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [{"source":"hn","source_end":33130,"source_start":33128,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 248 | 84 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8c7e8597ba6f16349cf60ea2d29d6eb32de86693240cb730427f60a3fbdd7954 | ab914dba4e38cdad2531f269c50732df5ca697b0167ceb216cda13688f30dd45 | 631deff478a1c2b467dee5054a563052e9871a003e5362dcad837f821d7b6d76 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 505 | List.nodup_permutations'Aux_iff | Mathlib/Data/List/Perm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Nat.add_assoc</a>, <a>Nat.add_left_comm</a>] | case h.e'_2.h.e'_3
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H✝ : x ∈ s
k : ℕ
hk : k < s.length
hk' : s.nthLe k h... | ((:c Eq) (:c Nat) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c Nat.succ) (:fv _uniq.54388)) (:fv _uniq.56042)) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) ((:c HAdd.hAdd... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"a","sexp":"(:fv _uniq.54225)"},{"name":"s","sexp":"((:c List) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:c Nat))))) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":33155,"sourceStart":33151,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"Nat.add_assoc","source_end":33170,"source_start":33157,"syntax_kind":"ident"},{"source":"Nat.add_left_comm","source_end":33189,"source_start":33172,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 248 | 89 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2eff39acfbb3b8ffebaec58d43b83b1c4bf5f667116e170463a8a78ceb43e537 | 26b8aec90b148f0c9905a92e50c7e5bef5c2b9ce4cea4ad82f5debd24dc97e56 | 48b93d3c0ed4ac38fb5fd25f334719cb7a04ea1e590c78e541ce7ceddc6c9535 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 506 | List.nodup_permutations'Aux_iff | Mathlib/Data/List/Perm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Nat.add_left_comm</a>, <a>Nat.add_comm</a>] | case h.e'_3.h.e'_3
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H✝ : x ∈ s
k : ℕ
hk : k < s.length
hk' : s.nthLe k h... | ((:c Eq) (:c Nat) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.54388) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) (:fv _uniq.56042)) ((:c HAdd.hAdd) (:c Nat) (:c N... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"a","sexp":"(:fv _uniq.54225)"},{"name":"s","sexp":"((:c List) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:c Nat))))) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":33206,"sourceStart":33202,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"Nat.add_left_comm","source_end":33225,"source_start":33208,"syntax_kind":"ident"},{"source":"Nat.add_comm","source_end":33239,"source_start":33227,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 248 | 94 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e839c72e5baae57356e4619fec18e08b1ead0d336feda698af3c2cf39a04a709 | 26945fb9a4d922d25850c6dd49fdde5d8ea529fdcab7fa57051ca7f4638540ef | c2b82caee099b44576c86a5a3a17a637efa9523da25658b02852a870a4930bc0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 507 | List.nodup_permutations'Aux_iff | Mathlib/Data/List/Perm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa [<a>Nat.succ_add</a>] using hn | case intro.intro.refine_3.inr.inr.inr.intro.hk'
α : Type u_1
β : Type u_2
l l₁ l₂ : List α
a : α
s : List α
x : α
h :
∀ (i j : ℕ) (h₁ : i < (permutations'Aux x s).length) (h₂ : j < (permutations'Aux x s).length),
(permutations'Aux x s).nthLe i h₁ = (permutations'Aux x s).nthLe j h₂ → i = j
H✝ : x ∈ s
k : ℕ
hk : k... | ((:c LT.lt) (:c Nat) (:c instLTNat) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.54388) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) (:fv _uniq.56042)) ((:c List.le... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.54225))"},{"name":"a","sexp":"(:fv _uniq.54225)"},{"name":"s","sexp":"((:c List) (:fv _uniq... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":33255,"sourceStart":33250,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [{"source":"Nat.succ_add","source_end":33269,"source_start":33257,"syntax_kind":"ident"},{"source":"hn","source_end":33279,"source_start":33277,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.54225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.54228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 248 | 99 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0c311c36d1c98642e3a58838845ef8f5caf5b4070c7145e0de6766f95ebd125b | 87348f171d0031e700e689abafa609dd0a7970b7b930414e8bc0fb2415573212 | d29e44afb51b28e2df79c3bf1ba55fb01353a5b281d2356ab3da0dd2000a8663 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 |
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