url stringclasses 147
values | commit stringclasses 147
values | file_path stringlengths 7 101 | full_name stringlengths 1 94 | start stringlengths 6 10 | end stringlengths 6 11 | tactic stringlengths 1 11.2k | state_before stringlengths 3 2.09M | state_after stringlengths 6 2.09M | input stringlengths 73 2.09M |
|---|---|---|---|---|---|---|---|---|---|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | apply cc | case a
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | apply witness_independent | n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt : kr < ... | case a
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt ... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isL... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | apply cc | case a
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | rw [← c, ← lem2, Vector.get', ← wl, lem1, triple.leftPivot] | n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt : kr < ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isL... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | apply witness_independent | n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt : kr < ... | case a
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt ... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isL... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | rw [← eql] | case a
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | apply witness_independent | n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt : kr < ... | case a
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt ... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isL... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | rw [← eql] | case a
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | apply witness_independent | n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt : kr < ... | case a
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt ... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isL... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | rw [← eql] | case a
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | rw [leftLem, rightLem, topLem] | n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt : kr < ... | n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt : kr < ... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isL... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | exact triple.joinRest i iw | n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt : kr < ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isL... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | have lem1 : right.get' kr rlt =
right.get' triple.pivot triple.pivotLt := by
apply witness_independent
apply ccc | n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt : kr < ... | n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt : kr < ... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isL... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | have lem2 : valuation.get' kr rlt =
valuation.get' triple.pivot triple.pivotLt := by
apply witness_independent
apply ccc | n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt : kr < ... | n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt : kr < ... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isL... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | rw [Vector.get'] at lem1 | n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt : kr < ... | n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt : kr < ... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isL... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | have lem5 : some false = some true := by
rw [← cc, ← lem2, Vector.get', ← wr, lem1, triple.rightPivot] | n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt : kr < ... | n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt : kr < ... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isL... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | simp at lem5 | n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt : kr < ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isL... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | apply witness_independent | n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt : kr < ... | case a
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt ... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isL... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | apply ccc | case a
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | apply witness_independent | n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt : kr < ... | case a
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt ... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isL... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | apply ccc | case a
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | rw [← cc, ← lem2, Vector.get', ← wr, lem1, triple.rightPivot] | n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt : kr < ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isL... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | apply witness_independent | n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt : kr < ... | case a
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt ... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isL... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | rw [← eql] | case a
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | apply witness_independent | n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt : kr < ... | case a
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt ... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isL... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | rw [← eql] | case a
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | apply witness_independent | n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt : kr < ... | case a
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt ... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isL... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | rw [← eql] | case a
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | rw [leftLem, rightLem, topLem] | n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt : kr < ... | n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt : kr < ... | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isL... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | exact triple.joinRest i iw | n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
x✝ : ClauseSat right valuation
kr : ℕ
rlt : kr < ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
x✝¹ : ClauseSat left valuation
kl : ℕ
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isL... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | resolutionToProof | [266, 1] | [282, 78] | intro tree | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top : Clause (n + 1)
⊢ ResolutionTree clauses top →
∀ (valuation : Valuation (n + 1)),
(∀ (j : ℕ) (jw : j < num_clauses), ClauseSat (Vector.get' clauses j jw) valuation) → ClauseSat top valuation | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top : Clause (n + 1)
tree : ResolutionTree clauses top
⊢ ∀ (valuation : Valuation (n + 1)),
(∀ (j : ℕ) (jw : j < num_clauses), ClauseSat (Vector.get' clauses j jw) valuation) → ClauseSat top valuation | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top : Clause (n + 1)
⊢ ResolutionTree clauses top →
∀ (valuation : Valuation (n + 1)),
(∀ (j : ℕ) (jw : j < num_clauses), ClauseSat (Vector.get' clauses j jw) valuation) → ClauseSat top... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | resolutionToProof | [266, 1] | [282, 78] | induction tree | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top : Clause (n + 1)
tree : ResolutionTree clauses top
⊢ ∀ (valuation : Valuation (n + 1)),
(∀ (j : ℕ) (jw : j < num_clauses), ClauseSat (Vector.get' clauses j jw) valuation) → ClauseSat top valuation | case assumption
num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top : Clause (n + 1)
index✝ : ℕ
indexBound✝ : index✝ < num_clauses
top✝ : Clause (n + 1)
a✝ : Vector.get' clauses index✝ indexBound✝ = top✝
⊢ ∀ (valuation : Valuation (n + 1)),
(∀ (j : ℕ) (jw : j < num_clauses), ClauseSat (Vector.get' c... | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top : Clause (n + 1)
tree : ResolutionTree clauses top
⊢ ∀ (valuation : Valuation (n + 1)),
(∀ (j : ℕ) (jw : j < num_clauses), ClauseSat (Vector.get' clauses j jw) valuation) → ClauseSat top ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | resolutionToProof | [266, 1] | [282, 78] | case assumption j jw top eqn =>
intro valuation base
rw [← eqn]
apply base | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top✝ : Clause (n + 1)
j : ℕ
jw : j < num_clauses
top : Clause (n + 1)
eqn : Vector.get' clauses j jw = top
⊢ ∀ (valuation : Valuation (n + 1)),
(∀ (j : ℕ) (jw : j < num_clauses), ClauseSat (Vector.get' clauses j jw) valuation) → ClauseSat top valuation | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top✝ : Clause (n + 1)
j : ℕ
jw : j < num_clauses
top : Clause (n + 1)
eqn : Vector.get' clauses j jw = top
⊢ ∀ (valuation : Valuation (n + 1)),
(∀ (j : ℕ) (jw : j < num_clauses), ClauseSat (V... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | resolutionToProof | [266, 1] | [282, 78] | case resolve left right top' _ _ triple lih rih =>
intro valuation base
let leftBase : ClauseSat left valuation := by
apply lih valuation base
let rightBase : ClauseSat right valuation := by
apply rih valuation base
exact triple_step left right top' triple valuation leftBase rightBase | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top left right top' : Clause (n + 1)
leftTree✝ : ResolutionTree clauses left
rightTree✝ : ResolutionTree clauses right
triple : ResolutionTriple left right top'
lih :
∀ (valuation : Valuation (n + 1)),
(∀ (j : ℕ) (jw : j < num_clauses), ClauseSat (Ve... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top left right top' : Clause (n + 1)
leftTree✝ : ResolutionTree clauses left
rightTree✝ : ResolutionTree clauses right
triple : ResolutionTriple left right top'
lih :
∀ (valuation : Valuation (... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | resolutionToProof | [266, 1] | [282, 78] | intro valuation base | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top✝ : Clause (n + 1)
j : ℕ
jw : j < num_clauses
top : Clause (n + 1)
eqn : Vector.get' clauses j jw = top
⊢ ∀ (valuation : Valuation (n + 1)),
(∀ (j : ℕ) (jw : j < num_clauses), ClauseSat (Vector.get' clauses j jw) valuation) → ClauseSat top valuation | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top✝ : Clause (n + 1)
j : ℕ
jw : j < num_clauses
top : Clause (n + 1)
eqn : Vector.get' clauses j jw = top
valuation : Valuation (n + 1)
base : ∀ (j : ℕ) (jw : j < num_clauses), ClauseSat (Vector.get' clauses j jw) valuation
⊢ ClauseSat top valuation | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top✝ : Clause (n + 1)
j : ℕ
jw : j < num_clauses
top : Clause (n + 1)
eqn : Vector.get' clauses j jw = top
⊢ ∀ (valuation : Valuation (n + 1)),
(∀ (j : ℕ) (jw : j < num_clauses), ClauseSat (V... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | resolutionToProof | [266, 1] | [282, 78] | rw [← eqn] | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top✝ : Clause (n + 1)
j : ℕ
jw : j < num_clauses
top : Clause (n + 1)
eqn : Vector.get' clauses j jw = top
valuation : Valuation (n + 1)
base : ∀ (j : ℕ) (jw : j < num_clauses), ClauseSat (Vector.get' clauses j jw) valuation
⊢ ClauseSat top valuation | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top✝ : Clause (n + 1)
j : ℕ
jw : j < num_clauses
top : Clause (n + 1)
eqn : Vector.get' clauses j jw = top
valuation : Valuation (n + 1)
base : ∀ (j : ℕ) (jw : j < num_clauses), ClauseSat (Vector.get' clauses j jw) valuation
⊢ ClauseSat (Vector.get' clause... | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top✝ : Clause (n + 1)
j : ℕ
jw : j < num_clauses
top : Clause (n + 1)
eqn : Vector.get' clauses j jw = top
valuation : Valuation (n + 1)
base : ∀ (j : ℕ) (jw : j < num_clauses), ClauseSat (Vector... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | resolutionToProof | [266, 1] | [282, 78] | apply base | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top✝ : Clause (n + 1)
j : ℕ
jw : j < num_clauses
top : Clause (n + 1)
eqn : Vector.get' clauses j jw = top
valuation : Valuation (n + 1)
base : ∀ (j : ℕ) (jw : j < num_clauses), ClauseSat (Vector.get' clauses j jw) valuation
⊢ ClauseSat (Vector.get' clause... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top✝ : Clause (n + 1)
j : ℕ
jw : j < num_clauses
top : Clause (n + 1)
eqn : Vector.get' clauses j jw = top
valuation : Valuation (n + 1)
base : ∀ (j : ℕ) (jw : j < num_clauses), ClauseSat (Vector... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | resolutionToProof | [266, 1] | [282, 78] | intro valuation base | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top left right top' : Clause (n + 1)
leftTree✝ : ResolutionTree clauses left
rightTree✝ : ResolutionTree clauses right
triple : ResolutionTriple left right top'
lih :
∀ (valuation : Valuation (n + 1)),
(∀ (j : ℕ) (jw : j < num_clauses), ClauseSat (Ve... | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top left right top' : Clause (n + 1)
leftTree✝ : ResolutionTree clauses left
rightTree✝ : ResolutionTree clauses right
triple : ResolutionTriple left right top'
lih :
∀ (valuation : Valuation (n + 1)),
(∀ (j : ℕ) (jw : j < num_clauses), ClauseSat (Ve... | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top left right top' : Clause (n + 1)
leftTree✝ : ResolutionTree clauses left
rightTree✝ : ResolutionTree clauses right
triple : ResolutionTriple left right top'
lih :
∀ (valuation : Valuation (... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | resolutionToProof | [266, 1] | [282, 78] | let leftBase : ClauseSat left valuation := by
apply lih valuation base | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top left right top' : Clause (n + 1)
leftTree✝ : ResolutionTree clauses left
rightTree✝ : ResolutionTree clauses right
triple : ResolutionTriple left right top'
lih :
∀ (valuation : Valuation (n + 1)),
(∀ (j : ℕ) (jw : j < num_clauses), ClauseSat (Ve... | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top left right top' : Clause (n + 1)
leftTree✝ : ResolutionTree clauses left
rightTree✝ : ResolutionTree clauses right
triple : ResolutionTriple left right top'
lih :
∀ (valuation : Valuation (n + 1)),
(∀ (j : ℕ) (jw : j < num_clauses), ClauseSat (Ve... | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top left right top' : Clause (n + 1)
leftTree✝ : ResolutionTree clauses left
rightTree✝ : ResolutionTree clauses right
triple : ResolutionTriple left right top'
lih :
∀ (valuation : Valuation (... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | resolutionToProof | [266, 1] | [282, 78] | let rightBase : ClauseSat right valuation := by
apply rih valuation base | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top left right top' : Clause (n + 1)
leftTree✝ : ResolutionTree clauses left
rightTree✝ : ResolutionTree clauses right
triple : ResolutionTriple left right top'
lih :
∀ (valuation : Valuation (n + 1)),
(∀ (j : ℕ) (jw : j < num_clauses), ClauseSat (Ve... | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top left right top' : Clause (n + 1)
leftTree✝ : ResolutionTree clauses left
rightTree✝ : ResolutionTree clauses right
triple : ResolutionTriple left right top'
lih :
∀ (valuation : Valuation (n + 1)),
(∀ (j : ℕ) (jw : j < num_clauses), ClauseSat (Ve... | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top left right top' : Clause (n + 1)
leftTree✝ : ResolutionTree clauses left
rightTree✝ : ResolutionTree clauses right
triple : ResolutionTriple left right top'
lih :
∀ (valuation : Valuation (... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | resolutionToProof | [266, 1] | [282, 78] | exact triple_step left right top' triple valuation leftBase rightBase | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top left right top' : Clause (n + 1)
leftTree✝ : ResolutionTree clauses left
rightTree✝ : ResolutionTree clauses right
triple : ResolutionTriple left right top'
lih :
∀ (valuation : Valuation (n + 1)),
(∀ (j : ℕ) (jw : j < num_clauses), ClauseSat (Ve... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top left right top' : Clause (n + 1)
leftTree✝ : ResolutionTree clauses left
rightTree✝ : ResolutionTree clauses right
triple : ResolutionTriple left right top'
lih :
∀ (valuation : Valuation (... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | resolutionToProof | [266, 1] | [282, 78] | apply lih valuation base | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top left right top' : Clause (n + 1)
leftTree✝ : ResolutionTree clauses left
rightTree✝ : ResolutionTree clauses right
triple : ResolutionTriple left right top'
lih :
∀ (valuation : Valuation (n + 1)),
(∀ (j : ℕ) (jw : j < num_clauses), ClauseSat (Ve... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top left right top' : Clause (n + 1)
leftTree✝ : ResolutionTree clauses left
rightTree✝ : ResolutionTree clauses right
triple : ResolutionTriple left right top'
lih :
∀ (valuation : Valuation (... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | resolutionToProof | [266, 1] | [282, 78] | apply rih valuation base | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top left right top' : Clause (n + 1)
leftTree✝ : ResolutionTree clauses left
rightTree✝ : ResolutionTree clauses right
triple : ResolutionTriple left right top'
lih :
∀ (valuation : Valuation (n + 1)),
(∀ (j : ℕ) (jw : j < num_clauses), ClauseSat (Ve... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
top left right top' : Clause (n + 1)
leftTree✝ : ResolutionTree clauses left
rightTree✝ : ResolutionTree clauses right
triple : ResolutionTriple left right top'
lih :
∀ (valuation : Valuation (... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | trees_preserve_notsomebranch | [349, 1] | [386, 30] | have lem1 : Not (top.get' k kw = some bf) := by
rw [← chk]
exact (base ind bd) | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
bf : Bool
k : ℕ
kw : k < n + 1
base : ∀ (j : ℕ) (lt : j < num_clauses), ¬Vector.get' (Vector.get' clauses j lt) k kw = some bf
top : Clause (n + 1)
tree : ResolutionTree clauses top
ind : ℕ
bd : ind < num_clauses
chk : Vector.get' clauses ind bd = top
hyp ... | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
bf : Bool
k : ℕ
kw : k < n + 1
base : ∀ (j : ℕ) (lt : j < num_clauses), ¬Vector.get' (Vector.get' clauses j lt) k kw = some bf
top : Clause (n + 1)
tree : ResolutionTree clauses top
ind : ℕ
bd : ind < num_clauses
chk : Vector.get' clauses ind bd = top
hyp ... | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
bf : Bool
k : ℕ
kw : k < n + 1
base : ∀ (j : ℕ) (lt : j < num_clauses), ¬Vector.get' (Vector.get' clauses j lt) k kw = some bf
top : Clause (n + 1)
tree : ResolutionTree clauses top
ind : ℕ
bd : ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | trees_preserve_notsomebranch | [349, 1] | [386, 30] | contradiction | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
bf : Bool
k : ℕ
kw : k < n + 1
base : ∀ (j : ℕ) (lt : j < num_clauses), ¬Vector.get' (Vector.get' clauses j lt) k kw = some bf
top : Clause (n + 1)
tree : ResolutionTree clauses top
ind : ℕ
bd : ind < num_clauses
chk : Vector.get' clauses ind bd = top
hyp ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
bf : Bool
k : ℕ
kw : k < n + 1
base : ∀ (j : ℕ) (lt : j < num_clauses), ¬Vector.get' (Vector.get' clauses j lt) k kw = some bf
top : Clause (n + 1)
tree : ResolutionTree clauses top
ind : ℕ
bd : ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | trees_preserve_notsomebranch | [349, 1] | [386, 30] | rw [← chk] | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
bf : Bool
k : ℕ
kw : k < n + 1
base : ∀ (j : ℕ) (lt : j < num_clauses), ¬Vector.get' (Vector.get' clauses j lt) k kw = some bf
top : Clause (n + 1)
tree : ResolutionTree clauses top
ind : ℕ
bd : ind < num_clauses
chk : Vector.get' clauses ind bd = top
hyp ... | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
bf : Bool
k : ℕ
kw : k < n + 1
base : ∀ (j : ℕ) (lt : j < num_clauses), ¬Vector.get' (Vector.get' clauses j lt) k kw = some bf
top : Clause (n + 1)
tree : ResolutionTree clauses top
ind : ℕ
bd : ind < num_clauses
chk : Vector.get' clauses ind bd = top
hyp ... | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
bf : Bool
k : ℕ
kw : k < n + 1
base : ∀ (j : ℕ) (lt : j < num_clauses), ¬Vector.get' (Vector.get' clauses j lt) k kw = some bf
top : Clause (n + 1)
tree : ResolutionTree clauses top
ind : ℕ
bd : ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | trees_preserve_notsomebranch | [349, 1] | [386, 30] | exact (base ind bd) | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
bf : Bool
k : ℕ
kw : k < n + 1
base : ∀ (j : ℕ) (lt : j < num_clauses), ¬Vector.get' (Vector.get' clauses j lt) k kw = some bf
top : Clause (n + 1)
tree : ResolutionTree clauses top
ind : ℕ
bd : ind < num_clauses
chk : Vector.get' clauses ind bd = top
hyp ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
bf : Bool
k : ℕ
kw : k < n + 1
base : ∀ (j : ℕ) (lt : j < num_clauses), ¬Vector.get' (Vector.get' clauses j lt) k kw = some bf
top : Clause (n + 1)
tree : ResolutionTree clauses top
ind : ℕ
bd : ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | trees_preserve_notsomebranch | [349, 1] | [386, 30] | let j := skipInverse triple.pivot k c | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
bf : Bool
k : ℕ
kw : k < n + 1
base : ∀ (j : ℕ) (lt : j < num_clauses), ¬Vector.get' (Vector.get' clauses j lt) k kw = some bf
top : Clause (n + 1)
tree : ResolutionTree clauses top
left right : Clause (n + 1)
leftTree : ResolutionTree clauses left
rightTr... | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
bf : Bool
k : ℕ
kw : k < n + 1
base : ∀ (j : ℕ) (lt : j < num_clauses), ¬Vector.get' (Vector.get' clauses j lt) k kw = some bf
top : Clause (n + 1)
tree : ResolutionTree clauses top
left right : Clause (n + 1)
leftTree : ResolutionTree clauses left
rightTr... | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
bf : Bool
k : ℕ
kw : k < n + 1
base : ∀ (j : ℕ) (lt : j < num_clauses), ¬Vector.get' (Vector.get' clauses j lt) k kw = some bf
top : Clause (n + 1)
tree : ResolutionTree clauses top
left right : ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | trees_preserve_notsomebranch | [349, 1] | [386, 30] | let eqn := skipInverse_eq triple.pivot k c | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
bf : Bool
k : ℕ
kw : k < n + 1
base : ∀ (j : ℕ) (lt : j < num_clauses), ¬Vector.get' (Vector.get' clauses j lt) k kw = some bf
top : Clause (n + 1)
tree : ResolutionTree clauses top
left right : Clause (n + 1)
leftTree : ResolutionTree clauses left
rightTr... | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
bf : Bool
k : ℕ
kw : k < n + 1
base : ∀ (j : ℕ) (lt : j < num_clauses), ¬Vector.get' (Vector.get' clauses j lt) k kw = some bf
top : Clause (n + 1)
tree : ResolutionTree clauses top
left right : Clause (n + 1)
leftTree : ResolutionTree clauses left
rightTr... | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
bf : Bool
k : ℕ
kw : k < n + 1
base : ∀ (j : ℕ) (lt : j < num_clauses), ¬Vector.get' (Vector.get' clauses j lt) k kw = some bf
top : Clause (n + 1)
tree : ResolutionTree clauses top
left right : ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | trees_preserve_notsomebranch | [349, 1] | [386, 30] | let jw := skip_preimage_lt triple.pivotLt kw eqn | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
bf : Bool
k : ℕ
kw : k < n + 1
base : ∀ (j : ℕ) (lt : j < num_clauses), ¬Vector.get' (Vector.get' clauses j lt) k kw = some bf
top : Clause (n + 1)
tree : ResolutionTree clauses top
left right : Clause (n + 1)
leftTree : ResolutionTree clauses left
rightTr... | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
bf : Bool
k : ℕ
kw : k < n + 1
base : ∀ (j : ℕ) (lt : j < num_clauses), ¬Vector.get' (Vector.get' clauses j lt) k kw = some bf
top : Clause (n + 1)
tree : ResolutionTree clauses top
left right : Clause (n + 1)
leftTree : ResolutionTree clauses left
rightTr... | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
bf : Bool
k : ℕ
kw : k < n + 1
base : ∀ (j : ℕ) (lt : j < num_clauses), ¬Vector.get' (Vector.get' clauses j lt) k kw = some bf
top : Clause (n + 1)
tree : ResolutionTree clauses top
left right : ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | trees_preserve_notsomebranch | [349, 1] | [386, 30] | let joinIm := triple.joinRest j jw | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
bf : Bool
k : ℕ
kw : k < n + 1
base : ∀ (j : ℕ) (lt : j < num_clauses), ¬Vector.get' (Vector.get' clauses j lt) k kw = some bf
top : Clause (n + 1)
tree : ResolutionTree clauses top
left right : Clause (n + 1)
leftTree : ResolutionTree clauses left
rightTr... | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
bf : Bool
k : ℕ
kw : k < n + 1
base : ∀ (j : ℕ) (lt : j < num_clauses), ¬Vector.get' (Vector.get' clauses j lt) k kw = some bf
top : Clause (n + 1)
tree : ResolutionTree clauses top
left right : Clause (n + 1)
leftTree : ResolutionTree clauses left
rightTr... | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
bf : Bool
k : ℕ
kw : k < n + 1
base : ∀ (j : ℕ) (lt : j < num_clauses), ¬Vector.get' (Vector.get' clauses j lt) k kw = some bf
top : Clause (n + 1)
tree : ResolutionTree clauses top
left right : ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | trees_preserve_notsomebranch | [349, 1] | [386, 30] | match (skip triple.pivot j), eqn, (skip_le_succ jw), joinIm with
| .(k), rfl, .(kw), join =>
apply top_of_join_not_positive bf
(left.get' k kw) (right.get' k kw) (top.get' k kw) join
leftLem rightLem
exact hyp | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
bf : Bool
k : ℕ
kw : k < n + 1
base : ∀ (j : ℕ) (lt : j < num_clauses), ¬Vector.get' (Vector.get' clauses j lt) k kw = some bf
top : Clause (n + 1)
tree : ResolutionTree clauses top
left right : Clause (n + 1)
leftTree : ResolutionTree clauses left
rightTr... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
bf : Bool
k : ℕ
kw : k < n + 1
base : ∀ (j : ℕ) (lt : j < num_clauses), ¬Vector.get' (Vector.get' clauses j lt) k kw = some bf
top : Clause (n + 1)
tree : ResolutionTree clauses top
left right : ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | trees_preserve_notsomebranch | [349, 1] | [386, 30] | apply top_of_join_not_positive bf
(left.get' k kw) (right.get' k kw) (top.get' k kw) join
leftLem rightLem | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
bf : Bool
k : ℕ
kw : k < n + 1
base : ∀ (j : ℕ) (lt : j < num_clauses), ¬Vector.get' (Vector.get' clauses j lt) k kw = some bf
top : Clause (n + 1)
tree : ResolutionTree clauses top
left right : Clause (n + 1)
leftTree : ResolutionTree clauses left
rightTr... | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
bf : Bool
k : ℕ
kw : k < n + 1
base : ∀ (j : ℕ) (lt : j < num_clauses), ¬Vector.get' (Vector.get' clauses j lt) k kw = some bf
top : Clause (n + 1)
tree : ResolutionTree clauses top
left right : Clause (n + 1)
leftTree : ResolutionTree clauses left
rightTr... | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
bf : Bool
k : ℕ
kw : k < n + 1
base : ∀ (j : ℕ) (lt : j < num_clauses), ¬Vector.get' (Vector.get' clauses j lt) k kw = some bf
top : Clause (n + 1)
tree : ResolutionTree clauses top
left right : ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | trees_preserve_notsomebranch | [349, 1] | [386, 30] | exact hyp | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
bf : Bool
k : ℕ
kw : k < n + 1
base : ∀ (j : ℕ) (lt : j < num_clauses), ¬Vector.get' (Vector.get' clauses j lt) k kw = some bf
top : Clause (n + 1)
tree : ResolutionTree clauses top
left right : Clause (n + 1)
leftTree : ResolutionTree clauses left
rightTr... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
bf : Bool
k : ℕ
kw : k < n + 1
base : ∀ (j : ℕ) (lt : j < num_clauses), ¬Vector.get' (Vector.get' clauses j lt) k kw = some bf
top : Clause (n + 1)
tree : ResolutionTree clauses top
left right : ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | Vector.ext' | [19, 1] | [27, 15] | intro h | α : Type
n : ℕ
v1 v2 : Vector α n
⊢ get' v1 = get' v2 → v1 = v2 | α : Type
n : ℕ
v1 v2 : Vector α n
h : get' v1 = get' v2
⊢ v1 = v2 | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n : ℕ
v1 v2 : Vector α n
⊢ get' v1 = get' v2 → v1 = v2
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | Vector.ext' | [19, 1] | [27, 15] | apply Vector.ext | α : Type
n : ℕ
v1 v2 : Vector α n
h : get' v1 = get' v2
⊢ v1 = v2 | case x
α : Type
n : ℕ
v1 v2 : Vector α n
h : get' v1 = get' v2
⊢ ∀ (m : Fin n), get v1 m = get v2 m | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n : ℕ
v1 v2 : Vector α n
h : get' v1 = get' v2
⊢ v1 = v2
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | Vector.ext' | [19, 1] | [27, 15] | intro ⟨i, iw⟩ | case x
α : Type
n : ℕ
v1 v2 : Vector α n
h : get' v1 = get' v2
⊢ ∀ (m : Fin n), get v1 m = get v2 m | case x
α : Type
n : ℕ
v1 v2 : Vector α n
h : get' v1 = get' v2
i : ℕ
iw : i < n
⊢ get v1 { val := i, isLt := iw } = get v2 { val := i, isLt := iw } | Please generate a tactic in lean4 to solve the state.
STATE:
case x
α : Type
n : ℕ
v1 v2 : Vector α n
h : get' v1 = get' v2
⊢ ∀ (m : Fin n), get v1 m = get v2 m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | Vector.ext' | [19, 1] | [27, 15] | show get' v1 i iw = get' v2 i iw | case x
α : Type
n : ℕ
v1 v2 : Vector α n
h : get' v1 = get' v2
i : ℕ
iw : i < n
⊢ get v1 { val := i, isLt := iw } = get v2 { val := i, isLt := iw } | case x
α : Type
n : ℕ
v1 v2 : Vector α n
h : get' v1 = get' v2
i : ℕ
iw : i < n
⊢ get' v1 i iw = get' v2 i iw | Please generate a tactic in lean4 to solve the state.
STATE:
case x
α : Type
n : ℕ
v1 v2 : Vector α n
h : get' v1 = get' v2
i : ℕ
iw : i < n
⊢ get v1 { val := i, isLt := iw } = get v2 { val := i, isLt := iw }
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | Vector.ext' | [19, 1] | [27, 15] | let lem := congrFun h i | case x
α : Type
n : ℕ
v1 v2 : Vector α n
h : get' v1 = get' v2
i : ℕ
iw : i < n
⊢ get' v1 i iw = get' v2 i iw | case x
α : Type
n : ℕ
v1 v2 : Vector α n
h : get' v1 = get' v2
i : ℕ
iw : i < n
lem : get' v1 i = get' v2 i := congrFun h i
⊢ get' v1 i iw = get' v2 i iw | Please generate a tactic in lean4 to solve the state.
STATE:
case x
α : Type
n : ℕ
v1 v2 : Vector α n
h : get' v1 = get' v2
i : ℕ
iw : i < n
⊢ get' v1 i iw = get' v2 i iw
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | Vector.ext' | [19, 1] | [27, 15] | let lem' := (congrFun lem iw) | case x
α : Type
n : ℕ
v1 v2 : Vector α n
h : get' v1 = get' v2
i : ℕ
iw : i < n
lem : get' v1 i = get' v2 i := congrFun h i
⊢ get' v1 i iw = get' v2 i iw | case x
α : Type
n : ℕ
v1 v2 : Vector α n
h : get' v1 = get' v2
i : ℕ
iw : i < n
lem : get' v1 i = get' v2 i := congrFun h i
lem' : get' v1 i iw = get' v2 i iw := congrFun lem iw
⊢ get' v1 i iw = get' v2 i iw | Please generate a tactic in lean4 to solve the state.
STATE:
case x
α : Type
n : ℕ
v1 v2 : Vector α n
h : get' v1 = get' v2
i : ℕ
iw : i < n
lem : get' v1 i = get' v2 i := congrFun h i
⊢ get' v1 i iw = get' v2 i iw
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | Vector.ext' | [19, 1] | [27, 15] | exact lem' | case x
α : Type
n : ℕ
v1 v2 : Vector α n
h : get' v1 = get' v2
i : ℕ
iw : i < n
lem : get' v1 i = get' v2 i := congrFun h i
lem' : get' v1 i iw = get' v2 i iw := congrFun lem iw
⊢ get' v1 i iw = get' v2 i iw | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case x
α : Type
n : ℕ
v1 v2 : Vector α n
h : get' v1 = get' v2
i : ℕ
iw : i < n
lem : get' v1 i = get' v2 i := congrFun h i
lem' : get' v1 i iw = get' v2 i iw := congrFun lem iw
⊢ get' v1 i iw = get' v2 i iw
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | Vector.of_Fn'_get' | [29, 1] | [36, 35] | intro seq | α : Type
n : ℕ
⊢ ∀ (seq : FinSeq n α), get' (ofFn' seq) = seq | α : Type
n : ℕ
seq : FinSeq n α
⊢ get' (ofFn' seq) = seq | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n : ℕ
⊢ ∀ (seq : FinSeq n α), get' (ofFn' seq) = seq
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | Vector.of_Fn'_get' | [29, 1] | [36, 35] | apply funext | α : Type
n : ℕ
seq : FinSeq n α
⊢ get' (ofFn' seq) = seq | case h
α : Type
n : ℕ
seq : FinSeq n α
⊢ ∀ (x : ℕ), get' (ofFn' seq) x = seq x | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n : ℕ
seq : FinSeq n α
⊢ get' (ofFn' seq) = seq
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | Vector.of_Fn'_get' | [29, 1] | [36, 35] | intro k | case h
α : Type
n : ℕ
seq : FinSeq n α
⊢ ∀ (x : ℕ), get' (ofFn' seq) x = seq x | case h
α : Type
n : ℕ
seq : FinSeq n α
k : ℕ
⊢ get' (ofFn' seq) k = seq k | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type
n : ℕ
seq : FinSeq n α
⊢ ∀ (x : ℕ), get' (ofFn' seq) x = seq x
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | Vector.of_Fn'_get' | [29, 1] | [36, 35] | apply funext | case h
α : Type
n : ℕ
seq : FinSeq n α
k : ℕ
⊢ get' (ofFn' seq) k = seq k | case h.h
α : Type
n : ℕ
seq : FinSeq n α
k : ℕ
⊢ ∀ (x : k < n), get' (ofFn' seq) k x = seq k x | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type
n : ℕ
seq : FinSeq n α
k : ℕ
⊢ get' (ofFn' seq) k = seq k
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | Vector.of_Fn'_get' | [29, 1] | [36, 35] | intro kw | case h.h
α : Type
n : ℕ
seq : FinSeq n α
k : ℕ
⊢ ∀ (x : k < n), get' (ofFn' seq) k x = seq k x | case h.h
α : Type
n : ℕ
seq : FinSeq n α
k : ℕ
kw : k < n
⊢ get' (ofFn' seq) k kw = seq k kw | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h
α : Type
n : ℕ
seq : FinSeq n α
k : ℕ
⊢ ∀ (x : k < n), get' (ofFn' seq) k x = seq k x
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | Vector.of_Fn'_get' | [29, 1] | [36, 35] | simp [Vector.get', Vector.ofFn'] | case h.h
α : Type
n : ℕ
seq : FinSeq n α
k : ℕ
kw : k < n
⊢ get' (ofFn' seq) k kw = seq k kw | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h
α : Type
n : ℕ
seq : FinSeq n α
k : ℕ
kw : k < n
⊢ get' (ofFn' seq) k kw = seq k kw
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | Vector.of_Fn'_get | [38, 1] | [44, 13] | intro seq ⟨k, kw⟩ | α : Type
n : ℕ
⊢ ∀ (seq : FinSeq n α) (k : Fin n), get (ofFn' seq) k = seq ↑k (_ : ↑k < n) | α : Type
n : ℕ
seq : FinSeq n α
k : ℕ
kw : k < n
⊢ get (ofFn' seq) { val := k, isLt := kw } = seq ↑{ val := k, isLt := kw } (_ : ↑{ val := k, isLt := kw } < n) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n : ℕ
⊢ ∀ (seq : FinSeq n α) (k : Fin n), get (ofFn' seq) k = seq ↑k (_ : ↑k < n)
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | Vector.of_Fn'_get | [38, 1] | [44, 13] | let lem := congrFun (Vector.of_Fn'_get' seq) k | α : Type
n : ℕ
seq : FinSeq n α
k : ℕ
kw : k < n
⊢ get (ofFn' seq) { val := k, isLt := kw } = seq ↑{ val := k, isLt := kw } (_ : ↑{ val := k, isLt := kw } < n) | α : Type
n : ℕ
seq : FinSeq n α
k : ℕ
kw : k < n
lem : get' (ofFn' seq) k = seq k := congrFun (of_Fn'_get' seq) k
⊢ get (ofFn' seq) { val := k, isLt := kw } = seq ↑{ val := k, isLt := kw } (_ : ↑{ val := k, isLt := kw } < n) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n : ℕ
seq : FinSeq n α
k : ℕ
kw : k < n
⊢ get (ofFn' seq) { val := k, isLt := kw } = seq ↑{ val := k, isLt := kw } (_ : ↑{ val := k, isLt := kw } < n)
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | Vector.of_Fn'_get | [38, 1] | [44, 13] | let lem' := (congrFun lem kw) | α : Type
n : ℕ
seq : FinSeq n α
k : ℕ
kw : k < n
lem : get' (ofFn' seq) k = seq k := congrFun (of_Fn'_get' seq) k
⊢ get (ofFn' seq) { val := k, isLt := kw } = seq ↑{ val := k, isLt := kw } (_ : ↑{ val := k, isLt := kw } < n) | α : Type
n : ℕ
seq : FinSeq n α
k : ℕ
kw : k < n
lem : get' (ofFn' seq) k = seq k := congrFun (of_Fn'_get' seq) k
lem' : get' (ofFn' seq) k kw = seq k kw := congrFun lem kw
⊢ get (ofFn' seq) { val := k, isLt := kw } = seq ↑{ val := k, isLt := kw } (_ : ↑{ val := k, isLt := kw } < n) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n : ℕ
seq : FinSeq n α
k : ℕ
kw : k < n
lem : get' (ofFn' seq) k = seq k := congrFun (of_Fn'_get' seq) k
⊢ get (ofFn' seq) { val := k, isLt := kw } = seq ↑{ val := k, isLt := kw } (_ : ↑{ val := k, isLt := kw } < n)
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | Vector.of_Fn'_get | [38, 1] | [44, 13] | exact lem' | α : Type
n : ℕ
seq : FinSeq n α
k : ℕ
kw : k < n
lem : get' (ofFn' seq) k = seq k := congrFun (of_Fn'_get' seq) k
lem' : get' (ofFn' seq) k kw = seq k kw := congrFun lem kw
⊢ get (ofFn' seq) { val := k, isLt := kw } = seq ↑{ val := k, isLt := kw } (_ : ↑{ val := k, isLt := kw } < n) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n : ℕ
seq : FinSeq n α
k : ℕ
kw : k < n
lem : get' (ofFn' seq) k = seq k := congrFun (of_Fn'_get' seq) k
lem' : get' (ofFn' seq) k kw = seq k kw := congrFun lem kw
⊢ get (ofFn' seq) { val := k, isLt := kw } = seq ↑{ val := k, isLt := kw } (_ : ↑{ val... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | cons_commutes | [46, 1] | [58, 18] | apply funext | α : Type
n : ℕ
head : α
tail : Vector α n
⊢ get' (head ::ᵥ tail) = head+|get' tail | case h
α : Type
n : ℕ
head : α
tail : Vector α n
⊢ ∀ (x : ℕ), get' (head ::ᵥ tail) x = (head+|get' tail) x | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n : ℕ
head : α
tail : Vector α n
⊢ get' (head ::ᵥ tail) = head+|get' tail
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | cons_commutes | [46, 1] | [58, 18] | intro k | case h
α : Type
n : ℕ
head : α
tail : Vector α n
⊢ ∀ (x : ℕ), get' (head ::ᵥ tail) x = (head+|get' tail) x | case h
α : Type
n : ℕ
head : α
tail : Vector α n
k : ℕ
⊢ get' (head ::ᵥ tail) k = (head+|get' tail) k | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type
n : ℕ
head : α
tail : Vector α n
⊢ ∀ (x : ℕ), get' (head ::ᵥ tail) x = (head+|get' tail) x
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | cons_commutes | [46, 1] | [58, 18] | induction k with
| zero =>
apply funext
intro kw
rfl
| succ k' =>
apply funext
intro kw
rfl | case h
α : Type
n : ℕ
head : α
tail : Vector α n
k : ℕ
⊢ get' (head ::ᵥ tail) k = (head+|get' tail) k | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α : Type
n : ℕ
head : α
tail : Vector α n
k : ℕ
⊢ get' (head ::ᵥ tail) k = (head+|get' tail) k
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | cons_commutes | [46, 1] | [58, 18] | apply funext | case h.zero
α : Type
n : ℕ
head : α
tail : Vector α n
⊢ get' (head ::ᵥ tail) zero = (head+|get' tail) zero | case h.zero.h
α : Type
n : ℕ
head : α
tail : Vector α n
⊢ ∀ (x : zero < succ n), get' (head ::ᵥ tail) zero x = (head+|get' tail) zero x | Please generate a tactic in lean4 to solve the state.
STATE:
case h.zero
α : Type
n : ℕ
head : α
tail : Vector α n
⊢ get' (head ::ᵥ tail) zero = (head+|get' tail) zero
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | cons_commutes | [46, 1] | [58, 18] | intro kw | case h.zero.h
α : Type
n : ℕ
head : α
tail : Vector α n
⊢ ∀ (x : zero < succ n), get' (head ::ᵥ tail) zero x = (head+|get' tail) zero x | case h.zero.h
α : Type
n : ℕ
head : α
tail : Vector α n
kw : zero < succ n
⊢ get' (head ::ᵥ tail) zero kw = (head+|get' tail) zero kw | Please generate a tactic in lean4 to solve the state.
STATE:
case h.zero.h
α : Type
n : ℕ
head : α
tail : Vector α n
⊢ ∀ (x : zero < succ n), get' (head ::ᵥ tail) zero x = (head+|get' tail) zero x
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | cons_commutes | [46, 1] | [58, 18] | rfl | case h.zero.h
α : Type
n : ℕ
head : α
tail : Vector α n
kw : zero < succ n
⊢ get' (head ::ᵥ tail) zero kw = (head+|get' tail) zero kw | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.zero.h
α : Type
n : ℕ
head : α
tail : Vector α n
kw : zero < succ n
⊢ get' (head ::ᵥ tail) zero kw = (head+|get' tail) zero kw
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | cons_commutes | [46, 1] | [58, 18] | apply funext | case h.succ
α : Type
n : ℕ
head : α
tail : Vector α n
k' : ℕ
n_ih✝ : get' (head ::ᵥ tail) k' = (head+|get' tail) k'
⊢ get' (head ::ᵥ tail) (succ k') = (head+|get' tail) (succ k') | case h.succ.h
α : Type
n : ℕ
head : α
tail : Vector α n
k' : ℕ
n_ih✝ : get' (head ::ᵥ tail) k' = (head+|get' tail) k'
⊢ ∀ (x : succ k' < succ n), get' (head ::ᵥ tail) (succ k') x = (head+|get' tail) (succ k') x | Please generate a tactic in lean4 to solve the state.
STATE:
case h.succ
α : Type
n : ℕ
head : α
tail : Vector α n
k' : ℕ
n_ih✝ : get' (head ::ᵥ tail) k' = (head+|get' tail) k'
⊢ get' (head ::ᵥ tail) (succ k') = (head+|get' tail) (succ k')
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | cons_commutes | [46, 1] | [58, 18] | intro kw | case h.succ.h
α : Type
n : ℕ
head : α
tail : Vector α n
k' : ℕ
n_ih✝ : get' (head ::ᵥ tail) k' = (head+|get' tail) k'
⊢ ∀ (x : succ k' < succ n), get' (head ::ᵥ tail) (succ k') x = (head+|get' tail) (succ k') x | case h.succ.h
α : Type
n : ℕ
head : α
tail : Vector α n
k' : ℕ
n_ih✝ : get' (head ::ᵥ tail) k' = (head+|get' tail) k'
kw : succ k' < succ n
⊢ get' (head ::ᵥ tail) (succ k') kw = (head+|get' tail) (succ k') kw | Please generate a tactic in lean4 to solve the state.
STATE:
case h.succ.h
α : Type
n : ℕ
head : α
tail : Vector α n
k' : ℕ
n_ih✝ : get' (head ::ᵥ tail) k' = (head+|get' tail) k'
⊢ ∀ (x : succ k' < succ n), get' (head ::ᵥ tail) (succ k') x = (head+|get' tail) (succ k') x
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | cons_commutes | [46, 1] | [58, 18] | rfl | case h.succ.h
α : Type
n : ℕ
head : α
tail : Vector α n
k' : ℕ
n_ih✝ : get' (head ::ᵥ tail) k' = (head+|get' tail) k'
kw : succ k' < succ n
⊢ get' (head ::ᵥ tail) (succ k') kw = (head+|get' tail) (succ k') kw | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.succ.h
α : Type
n : ℕ
head : α
tail : Vector α n
k' : ℕ
n_ih✝ : get' (head ::ᵥ tail) k' = (head+|get' tail) k'
kw : succ k' < succ n
⊢ get' (head ::ᵥ tail) (succ k') kw = (head+|get' tail) (succ k') kw
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | Vector.get'_of_Fn' | [60, 1] | [65, 26] | let lem := Vector.of_Fn'_get' f | α : Type
n : ℕ
f : (k : ℕ) → k < n → α
k : ℕ
kw : k < n
⊢ get' (ofFn' f) k kw = f k kw | α : Type
n : ℕ
f : (k : ℕ) → k < n → α
k : ℕ
kw : k < n
lem : get' (ofFn' f) = f := of_Fn'_get' f
⊢ get' (ofFn' f) k kw = f k kw | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n : ℕ
f : (k : ℕ) → k < n → α
k : ℕ
kw : k < n
⊢ get' (ofFn' f) k kw = f k kw
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | Vector.get'_of_Fn' | [60, 1] | [65, 26] | let lem' := congrFun lem k | α : Type
n : ℕ
f : (k : ℕ) → k < n → α
k : ℕ
kw : k < n
lem : get' (ofFn' f) = f := of_Fn'_get' f
⊢ get' (ofFn' f) k kw = f k kw | α : Type
n : ℕ
f : (k : ℕ) → k < n → α
k : ℕ
kw : k < n
lem : get' (ofFn' f) = f := of_Fn'_get' f
lem' : get' (ofFn' f) k = f k := congrFun lem k
⊢ get' (ofFn' f) k kw = f k kw | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n : ℕ
f : (k : ℕ) → k < n → α
k : ℕ
kw : k < n
lem : get' (ofFn' f) = f := of_Fn'_get' f
⊢ get' (ofFn' f) k kw = f k kw
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | Vector.get'_of_Fn' | [60, 1] | [65, 26] | apply congrFun lem' | α : Type
n : ℕ
f : (k : ℕ) → k < n → α
k : ℕ
kw : k < n
lem : get' (ofFn' f) = f := of_Fn'_get' f
lem' : get' (ofFn' f) k = f k := congrFun lem k
⊢ get' (ofFn' f) k kw = f k kw | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n : ℕ
f : (k : ℕ) → k < n → α
k : ℕ
kw : k < n
lem : get' (ofFn' f) = f := of_Fn'_get' f
lem' : get' (ofFn' f) k = f k := congrFun lem k
⊢ get' (ofFn' f) k kw = f k kw
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | get'_cons_succ | [67, 1] | [71, 12] | rfl | α : Type
n : ℕ
x : α
ys : Vector α n
i : ℕ
iw : i < n
⊢ get' (x ::ᵥ ys) (i + 1) (_ : succ (i + 1) ≤ succ n) = get' ys i iw | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n : ℕ
x : α
ys : Vector α n
i : ℕ
iw : i < n
⊢ get' (x ::ᵥ ys) (i + 1) (_ : succ (i + 1) ≤ succ n) = get' ys i iw
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | get'_map | [74, 1] | [78, 14] | rw [get'] | α β : Type
n : ℕ
vec : Vector α n
f : α → β
j : ℕ
jw : Nat.lt j n
⊢ get' (map f vec) j jw = f (get' vec j jw) | α β : Type
n : ℕ
vec : Vector α n
f : α → β
j : ℕ
jw : Nat.lt j n
⊢ Vector.get (map f vec) { val := j, isLt := jw } = f (get' vec j jw) | Please generate a tactic in lean4 to solve the state.
STATE:
α β : Type
n : ℕ
vec : Vector α n
f : α → β
j : ℕ
jw : Nat.lt j n
⊢ get' (map f vec) j jw = f (get' vec j jw)
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | get'_map | [74, 1] | [78, 14] | simp [Vector.get_map] | α β : Type
n : ℕ
vec : Vector α n
f : α → β
j : ℕ
jw : Nat.lt j n
⊢ Vector.get (map f vec) { val := j, isLt := jw } = f (get' vec j jw) | α β : Type
n : ℕ
vec : Vector α n
f : α → β
j : ℕ
jw : Nat.lt j n
⊢ f (Vector.get vec { val := j, isLt := jw }) = f (get' vec j jw) | Please generate a tactic in lean4 to solve the state.
STATE:
α β : Type
n : ℕ
vec : Vector α n
f : α → β
j : ℕ
jw : Nat.lt j n
⊢ Vector.get (map f vec) { val := j, isLt := jw } = f (get' vec j jw)
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Vector.lean | get'_map | [74, 1] | [78, 14] | rfl | α β : Type
n : ℕ
vec : Vector α n
f : α → β
j : ℕ
jw : Nat.lt j n
⊢ f (Vector.get vec { val := j, isLt := jw }) = f (get' vec j jw) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α β : Type
n : ℕ
vec : Vector α n
f : α → β
j : ℕ
jw : Nat.lt j n
⊢ f (Vector.get vec { val := j, isLt := jw }) = f (get' vec j jw)
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Core.lean | not_sat_and_unsat | [83, 1] | [84, 81] | intro ⟨v, p⟩ h2 | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
⊢ IsSat clauses → IsUnSat clauses → False | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
v : Valuation (n + 1)
p :
∀ (p : ℕ) (pw : p < num_clauses),
∃ k kw,
Vector.get (Vector.get clauses { val := p, isLt := pw }) { val := k, isLt := kw } =
some (Vector.get v { val := k, isLt := kw })
h2 : IsUnSat clauses
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
⊢ IsSat clauses → IsUnSat clauses → False
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Core.lean | not_sat_and_unsat | [83, 1] | [84, 81] | exact h2 v p | num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
v : Valuation (n + 1)
p :
∀ (p : ℕ) (pw : p < num_clauses),
∃ k kw,
Vector.get (Vector.get clauses { val := p, isLt := pw }) { val := k, isLt := kw } =
some (Vector.get v { val := k, isLt := kw })
h2 : IsUnSat clauses
⊢ False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
clauses : Vector (Clause (n + 1)) num_clauses
v : Valuation (n + 1)
p :
∀ (p : ℕ) (pw : p < num_clauses),
∃ k kw,
Vector.get (Vector.get clauses { val := p, isLt := pw }) { val := k, isLt := kw } =
some (Vector.get v { va... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | match n with
| zero =>
intro s seq1 seq2 k
have ss : l = m := by
rw [← s]
apply Nat.zero_add
have sf : FinSeq l α = FinSeq m α := by
rw [ss]
apply And.intro
focus
intro kw
exact nomatch kw
match l, m, ss, sf, seq2 with
| d, .(d), rfl, rfl, seq =>
... | α : Type
n m l : ℕ
⊢ ∀ (s : n + m = l) (seq1 : FinSeq n α) (seq2 : FinSeq m α) (k : ℕ),
(∀ (kw : k < n) (w : k < l), concatSeqAux s seq1 seq2 k w = seq1 k kw) ∧
∀ (kw : k < m) (w : n + k < l), concatSeqAux s seq1 seq2 (n + k) w = seq2 k kw | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l : ℕ
⊢ ∀ (s : n + m = l) (seq1 : FinSeq n α) (seq2 : FinSeq m α) (k : ℕ),
(∀ (kw : k < n) (w : k < l), concatSeqAux s seq1 seq2 k w = seq1 k kw) ∧
∀ (kw : k < m) (w : n + k < l), concatSeqAux s seq1 seq2 (n + k) w = seq2 k kw
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | intro s seq1 seq2 k | α : Type
n m l : ℕ
⊢ ∀ (s : zero + m = l) (seq1 : FinSeq zero α) (seq2 : FinSeq m α) (k : ℕ),
(∀ (kw : k < zero) (w : k < l), concatSeqAux s seq1 seq2 k w = seq1 k kw) ∧
∀ (kw : k < m) (w : zero + k < l), concatSeqAux s seq1 seq2 (zero + k) w = seq2 k kw | α : Type
n m l : ℕ
s : zero + m = l
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
⊢ (∀ (kw : k < zero) (w : k < l), concatSeqAux s seq1 seq2 k w = seq1 k kw) ∧
∀ (kw : k < m) (w : zero + k < l), concatSeqAux s seq1 seq2 (zero + k) w = seq2 k kw | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l : ℕ
⊢ ∀ (s : zero + m = l) (seq1 : FinSeq zero α) (seq2 : FinSeq m α) (k : ℕ),
(∀ (kw : k < zero) (w : k < l), concatSeqAux s seq1 seq2 k w = seq1 k kw) ∧
∀ (kw : k < m) (w : zero + k < l), concatSeqAux s seq1 seq2 (zero + k) w = seq2... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | have ss : l = m := by
rw [← s]
apply Nat.zero_add | α : Type
n m l : ℕ
s : zero + m = l
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
⊢ (∀ (kw : k < zero) (w : k < l), concatSeqAux s seq1 seq2 k w = seq1 k kw) ∧
∀ (kw : k < m) (w : zero + k < l), concatSeqAux s seq1 seq2 (zero + k) w = seq2 k kw | α : Type
n m l : ℕ
s : zero + m = l
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
ss : l = m
⊢ (∀ (kw : k < zero) (w : k < l), concatSeqAux s seq1 seq2 k w = seq1 k kw) ∧
∀ (kw : k < m) (w : zero + k < l), concatSeqAux s seq1 seq2 (zero + k) w = seq2 k kw | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l : ℕ
s : zero + m = l
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
⊢ (∀ (kw : k < zero) (w : k < l), concatSeqAux s seq1 seq2 k w = seq1 k kw) ∧
∀ (kw : k < m) (w : zero + k < l), concatSeqAux s seq1 seq2 (zero + k) w = seq2 k kw
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | have sf : FinSeq l α = FinSeq m α := by
rw [ss] | α : Type
n m l : ℕ
s : zero + m = l
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
ss : l = m
⊢ (∀ (kw : k < zero) (w : k < l), concatSeqAux s seq1 seq2 k w = seq1 k kw) ∧
∀ (kw : k < m) (w : zero + k < l), concatSeqAux s seq1 seq2 (zero + k) w = seq2 k kw | α : Type
n m l : ℕ
s : zero + m = l
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
ss : l = m
sf : FinSeq l α = FinSeq m α
⊢ (∀ (kw : k < zero) (w : k < l), concatSeqAux s seq1 seq2 k w = seq1 k kw) ∧
∀ (kw : k < m) (w : zero + k < l), concatSeqAux s seq1 seq2 (zero + k) w = seq2 k kw | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l : ℕ
s : zero + m = l
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
ss : l = m
⊢ (∀ (kw : k < zero) (w : k < l), concatSeqAux s seq1 seq2 k w = seq1 k kw) ∧
∀ (kw : k < m) (w : zero + k < l), concatSeqAux s seq1 seq2 (zero + k) w = seq2 k kw
... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | apply And.intro | α : Type
n m l : ℕ
s : zero + m = l
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
ss : l = m
sf : FinSeq l α = FinSeq m α
⊢ (∀ (kw : k < zero) (w : k < l), concatSeqAux s seq1 seq2 k w = seq1 k kw) ∧
∀ (kw : k < m) (w : zero + k < l), concatSeqAux s seq1 seq2 (zero + k) w = seq2 k kw | case left
α : Type
n m l : ℕ
s : zero + m = l
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
ss : l = m
sf : FinSeq l α = FinSeq m α
⊢ ∀ (kw : k < zero) (w : k < l), concatSeqAux s seq1 seq2 k w = seq1 k kw
case right
α : Type
n m l : ℕ
s : zero + m = l
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
ss : l = m
sf : FinSeq... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l : ℕ
s : zero + m = l
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
ss : l = m
sf : FinSeq l α = FinSeq m α
⊢ (∀ (kw : k < zero) (w : k < l), concatSeqAux s seq1 seq2 k w = seq1 k kw) ∧
∀ (kw : k < m) (w : zero + k < l), concatSeqAux s seq1 s... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | focus
intro kw
exact nomatch kw | case left
α : Type
n m l : ℕ
s : zero + m = l
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
ss : l = m
sf : FinSeq l α = FinSeq m α
⊢ ∀ (kw : k < zero) (w : k < l), concatSeqAux s seq1 seq2 k w = seq1 k kw
case right
α : Type
n m l : ℕ
s : zero + m = l
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
ss : l = m
sf : FinSeq... | case right
α : Type
n m l : ℕ
s : zero + m = l
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
ss : l = m
sf : FinSeq l α = FinSeq m α
⊢ ∀ (kw : k < m) (w : zero + k < l), concatSeqAux s seq1 seq2 (zero + k) w = seq2 k kw | Please generate a tactic in lean4 to solve the state.
STATE:
case left
α : Type
n m l : ℕ
s : zero + m = l
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
ss : l = m
sf : FinSeq l α = FinSeq m α
⊢ ∀ (kw : k < zero) (w : k < l), concatSeqAux s seq1 seq2 k w = seq1 k kw
case right
α : Type
n m l : ℕ
s : zero + m = l
seq1 :... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | match l, m, ss, sf, seq2 with
| d, .(d), rfl, rfl, seq =>
intro kw w
apply witness_independent
apply Nat.zero_add | case right
α : Type
n m l : ℕ
s : zero + m = l
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
ss : l = m
sf : FinSeq l α = FinSeq m α
⊢ ∀ (kw : k < m) (w : zero + k < l), concatSeqAux s seq1 seq2 (zero + k) w = seq2 k kw | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right
α : Type
n m l : ℕ
s : zero + m = l
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
ss : l = m
sf : FinSeq l α = FinSeq m α
⊢ ∀ (kw : k < m) (w : zero + k < l), concatSeqAux s seq1 seq2 (zero + k) w = seq2 k kw
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | rw [← s] | α : Type
n m l : ℕ
s : zero + m = l
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
⊢ l = m | α : Type
n m l : ℕ
s : zero + m = l
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
⊢ zero + m = m | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l : ℕ
s : zero + m = l
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
⊢ l = m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | apply Nat.zero_add | α : Type
n m l : ℕ
s : zero + m = l
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
⊢ zero + m = m | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l : ℕ
s : zero + m = l
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
⊢ zero + m = m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | rw [ss] | α : Type
n m l : ℕ
s : zero + m = l
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
ss : l = m
⊢ FinSeq l α = FinSeq m α | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l : ℕ
s : zero + m = l
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
ss : l = m
⊢ FinSeq l α = FinSeq m α
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | intro kw | case left
α : Type
n m l : ℕ
s : zero + m = l
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
ss : l = m
sf : FinSeq l α = FinSeq m α
⊢ ∀ (kw : k < zero) (w : k < l), concatSeqAux s seq1 seq2 k w = seq1 k kw | case left
α : Type
n m l : ℕ
s : zero + m = l
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
ss : l = m
sf : FinSeq l α = FinSeq m α
kw : k < zero
⊢ ∀ (w : k < l), concatSeqAux s seq1 seq2 k w = seq1 k kw | Please generate a tactic in lean4 to solve the state.
STATE:
case left
α : Type
n m l : ℕ
s : zero + m = l
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
ss : l = m
sf : FinSeq l α = FinSeq m α
⊢ ∀ (kw : k < zero) (w : k < l), concatSeqAux s seq1 seq2 k w = seq1 k kw
TACTIC:
|
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