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/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | 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 | no goals | 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:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | intro kw w | α : Type
n m l : ℕ
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
ss : l = m
sf : FinSeq l α = FinSeq m α
d : ℕ
seq : FinSeq d α
s : zero + d = d
⊢ ∀ (kw : k < d) (w : zero + k < d), concatSeqAux s seq1 seq (zero + k) w = seq k kw | α : Type
n m l : ℕ
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
ss : l = m
sf : FinSeq l α = FinSeq m α
d : ℕ
seq : FinSeq d α
s : zero + d = d
kw : k < d
w : zero + k < d
⊢ concatSeqAux s seq1 seq (zero + k) w = seq k kw | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l : ℕ
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
ss : l = m
sf : FinSeq l α = FinSeq m α
d : ℕ
seq : FinSeq d α
s : zero + d = d
⊢ ∀ (kw : k < d) (w : zero + k < d), concatSeqAux s seq1 seq (zero + k) w = seq k kw
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | apply witness_independent | α : Type
n m l : ℕ
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
ss : l = m
sf : FinSeq l α = FinSeq m α
d : ℕ
seq : FinSeq d α
s : zero + d = d
kw : k < d
w : zero + k < d
⊢ concatSeqAux s seq1 seq (zero + k) w = seq k kw | case a
α : Type
n m l : ℕ
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
ss : l = m
sf : FinSeq l α = FinSeq m α
d : ℕ
seq : FinSeq d α
s : zero + d = d
kw : k < d
w : zero + k < d
⊢ zero + k = k | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l : ℕ
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
ss : l = m
sf : FinSeq l α = FinSeq m α
d : ℕ
seq : FinSeq d α
s : zero + d = d
kw : k < d
w : zero + k < d
⊢ concatSeqAux s seq1 seq (zero + k) w = seq k kw
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | apply Nat.zero_add | case a
α : Type
n m l : ℕ
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
ss : l = m
sf : FinSeq l α = FinSeq m α
d : ℕ
seq : FinSeq d α
s : zero + d = d
kw : k < d
w : zero + k < d
⊢ zero + k = k | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type
n m l : ℕ
seq1 : FinSeq zero α
seq2 : FinSeq m α
k : ℕ
ss : l = m
sf : FinSeq l α = FinSeq m α
d : ℕ
seq : FinSeq d α
s : zero + d = d
kw : k < d
w : zero + k < d
⊢ zero + k = k
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 p : ℕ
⊢ ∀ (s : p + 1 + m = l) (seq1 : FinSeq (p + 1) α) (seq2 : FinSeq m α) (k : ℕ),
(∀ (kw : k < p + 1) (w : k < l), concatSeqAux s seq1 seq2 k w = seq1 k kw) ∧
∀ (kw : k < m) (w : p + 1 + k < l), concatSeqAux s seq1 seq2 (p + 1 + k) w = seq2 k kw | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
⊢ (∀ (kw : k < p + 1) (w : k < l), concatSeqAux s seq1 seq2 k w = seq1 k kw) ∧
∀ (kw : k < m) (w : p + 1 + k < l), concatSeqAux s seq1 seq2 (p + 1 + k) w = seq2 k kw | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l p : ℕ
⊢ ∀ (s : p + 1 + m = l) (seq1 : FinSeq (p + 1) α) (seq2 : FinSeq m α) (k : ℕ),
(∀ (kw : k < p + 1) (w : k < l), concatSeqAux s seq1 seq2 k w = seq1 k kw) ∧
∀ (kw : k < m) (w : p + 1 + k < l), concatSeqAux s seq1 seq2 (p + 1 + k)... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | let ss : p + (m + 1) = l :=
by
rw [← s]
rw [(Nat.add_comm m 1)]
rw [(Nat.add_assoc p 1 m)]
done | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
⊢ (∀ (kw : k < p + 1) (w : k < l), concatSeqAux s seq1 seq2 k w = seq1 k kw) ∧
∀ (kw : k < m) (w : p + 1 + k < l), concatSeqAux s seq1 seq2 (p + 1 + k) w = seq2 k kw | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
⊢ (∀ (kw : k < p + 1) (w : k < l), concatSeqAux s seq1 seq2 k w = seq1 k kw) ∧
∀ (kw : k < m) (w : p + 1 + k < l), concatSeqAux s seq1 seq2 (p + 1 + k) w = seq2 k kw
TA... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | let resolve : concatSeqAux s seq1 seq2=
concatSeqAux ss (seq1.init) ((seq1.last) +| seq2) := rfl | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | rw [resolve] | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | let hyp := concat_aux_eqs ss (seq1.init) ((seq1.last) +| seq2) | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | let hyp1 := (hyp k).left | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq... |
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 p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | case left
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Na... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | focus
intro kw w
match Nat.eq_or_lt_of_le kw with
| Or.inr kww => exact hyp1 (le_of_succ_le_succ kww) w
| Or.inl eql =>
match k, eql, kw, w with
| .(p), rfl, pw, w =>
let ww : p + zero < l := by
rw [(Nat.add_zero p)]
assumption
let hyp2 := (hyp... | case left
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Na... | case right
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (N... | Please generate a tactic in lean4 to solve the state.
STATE:
case left
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | let ass := Nat.add_assoc p 1 k | case right
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (N... | case right
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (N... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1))... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | let comm := Nat.add_comm 1 k | case right
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (N... | case right
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (N... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1))... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | intro kw w | case right
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (N... | case right
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (N... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1))... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | match p + 1 + k, ass, w with
| .(p + (1 + k)), rfl, ww =>
let hypw := (hyp (1 + k)).right
let kww : 1 + k < m + 1 := by
rw [comm]
apply Nat.succ_lt_succ
assumption
let resol := hypw kww ww
rw [resol]
match 1 + k, comm, kww with
| .(k + 1), rfl, kwww => rfl | case right
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (N... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1))... |
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 p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
⊢ p + (m + 1) = l | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
⊢ p + (m + 1) = p + 1 + m | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
⊢ p + (m + 1) = l
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | rw [(Nat.add_comm m 1)] | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
⊢ p + (m + 1) = p + 1 + m | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
⊢ p + (1 + m) = p + 1 + m | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
⊢ p + (m + 1) = p + 1 + m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | rw [(Nat.add_assoc p 1 m)] | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
⊢ p + (1 + m) = p + 1 + m | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
⊢ p + (1 + m) = p + 1 + m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | intro kw w | case left
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Na... | case left
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Na... | Please generate a tactic in lean4 to solve the state.
STATE:
case left
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | match Nat.eq_or_lt_of_le kw with
| Or.inr kww => exact hyp1 (le_of_succ_le_succ kww) w
| Or.inl eql =>
match k, eql, kw, w with
| .(p), rfl, pw, w =>
let ww : p + zero < l := by
rw [(Nat.add_zero p)]
assumption
let hyp2 := (hyp zero).right (Nat.zero_lt_succ _) ww
let lem2 : con... | case left
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Na... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case left
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | exact hyp1 (le_of_succ_le_succ kww) w | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | match k, eql, kw, w with
| .(p), rfl, pw, w =>
let ww : p + zero < l := by
rw [(Nat.add_zero p)]
assumption
let hyp2 := (hyp zero).right (Nat.zero_lt_succ _) ww
let lem2 : concatSeqAux ss (seq1.init) (seq1.last+|seq2) (p + zero) ww =
concatSeqAux ss (seq1.init) (seq1.last+|seq2) p w :=
mat... | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | let ww : p + zero < l := by
rw [(Nat.add_zero p)]
assumption | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | let hyp2 := (hyp zero).right (Nat.zero_lt_succ _) ww | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | let lem2 : concatSeqAux ss (seq1.init) (seq1.last+|seq2) (p + zero) ww =
concatSeqAux ss (seq1.init) (seq1.last+|seq2) p w :=
match (p + zero), Nat.add_zero p, ww with
| .(p), rfl, ww => rfl | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | rw [← lem2] | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | rw [hyp2] | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | rfl | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | rw [(Nat.add_zero p)] | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | assumption | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | let hypw := (hyp (1 + k)).right | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | let kww : 1 + k < m + 1 := by
rw [comm]
apply Nat.succ_lt_succ
assumption | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | let resol := hypw kww ww | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | rw [resol] | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | match 1 + k, comm, kww with
| .(k + 1), rfl, kwww => rfl | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | rw [comm] | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | apply Nat.succ_lt_succ | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | case a
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.a... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | assumption | case a
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.a... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_aux_eqs | [77, 1] | [144, 41] | rfl | α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq.mpr (id (congrArg (fun _a => p + (1 + m) = _a) (Nat.add_asso... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n m l p : ℕ
s : p + 1 + m = l
seq1 : FinSeq (p + 1) α
seq2 : FinSeq m α
k : ℕ
ss : p + (m + 1) = l :=
Eq.mpr (id (congrArg (fun _a => p + (m + 1) = _a) s.symm))
(Eq.mpr (id (congrArg (fun _a => p + _a = p + 1 + m) (Nat.add_comm m 1)))
(Eq... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_empty_seq_id | [148, 1] | [155, 63] | intro seq | α : Type
n : ℕ
⊢ ∀ (seq : FinSeq n α), seq++|FinSeq.empty = seq | α : Type
n : ℕ
seq : FinSeq n α
⊢ seq++|FinSeq.empty = seq | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n : ℕ
⊢ ∀ (seq : FinSeq n α), seq++|FinSeq.empty = seq
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_empty_seq_id | [148, 1] | [155, 63] | apply funext | α : Type
n : ℕ
seq : FinSeq n α
⊢ seq++|FinSeq.empty = seq | case h
α : Type
n : ℕ
seq : FinSeq n α
⊢ ∀ (x : ℕ), (seq++|FinSeq.empty) x = seq x | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n : ℕ
seq : FinSeq n α
⊢ seq++|FinSeq.empty = seq
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_empty_seq_id | [148, 1] | [155, 63] | intro k | case h
α : Type
n : ℕ
seq : FinSeq n α
⊢ ∀ (x : ℕ), (seq++|FinSeq.empty) x = seq x | case h
α : Type
n : ℕ
seq : FinSeq n α
k : ℕ
⊢ (seq++|FinSeq.empty) 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), (seq++|FinSeq.empty) x = seq x
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_empty_seq_id | [148, 1] | [155, 63] | apply funext | case h
α : Type
n : ℕ
seq : FinSeq n α
k : ℕ
⊢ (seq++|FinSeq.empty) k = seq k | case h.h
α : Type
n : ℕ
seq : FinSeq n α
k : ℕ
⊢ ∀ (x : k < n + zero), (seq++|FinSeq.empty) 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
⊢ (seq++|FinSeq.empty) k = seq k
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_empty_seq_id | [148, 1] | [155, 63] | intro kw | case h.h
α : Type
n : ℕ
seq : FinSeq n α
k : ℕ
⊢ ∀ (x : k < n + zero), (seq++|FinSeq.empty) k x = seq k x | case h.h
α : Type
n : ℕ
seq : FinSeq n α
k : ℕ
kw : k < n + zero
⊢ (seq++|FinSeq.empty) 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 + zero), (seq++|FinSeq.empty) k x = seq k x
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | concat_empty_seq_id | [148, 1] | [155, 63] | apply (concat_aux_eqs rfl seq FinSeq.empty k).left | case h.h
α : Type
n : ℕ
seq : FinSeq n α
k : ℕ
kw : k < n + zero
⊢ (seq++|FinSeq.empty) 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 + zero
⊢ (seq++|FinSeq.empty) k kw = seq k kw
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | insert_delete_id | [214, 1] | [238, 20] | match j, jw, c with
| .(k), .(kw), rfl => apply insert_at_focus | α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : j = k
⊢ FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw = seq j jw | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : j = k
⊢ FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw = seq j jw
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | insert_delete_id | [214, 1] | [238, 20] | apply insert_at_focus | α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : j = k
⊢ FinSeq.insert (seq k kw) n k kw (delete k kw seq) k kw = seq k kw | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : j = k
⊢ FinSeq.insert (seq k kw) n k kw (delete k kw seq) k kw = seq k kw
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | insert_delete_id | [214, 1] | [238, 20] | let i := skipInverse k j c | α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
⊢ FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw = seq j jw | α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
⊢ FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw = seq j jw | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
⊢ FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw = seq j jw
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | insert_delete_id | [214, 1] | [238, 20] | let eqn : skip k i = j := skipInverse_eq k j c | α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
⊢ FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw = seq j jw | α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
⊢ FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw = seq j jw | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
⊢ FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw = seq j jw
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | insert_delete_id | [214, 1] | [238, 20] | let iw : i < n := skip_preimage_lt kw jw eqn | α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
⊢ FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw = seq j jw | α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
⊢ FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw = seq j jw | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
⊢ FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw = seq j jw
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | insert_delete_id | [214, 1] | [238, 20] | let lem1 : insert (seq k kw) n k kw (delete k kw seq) j jw
= insert (seq k kw) n k kw (delete k kw seq) (skip k i) (skip_le_succ iw) :=
by
apply witness_independent
rw [← eqn] | α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
⊢ FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw = seq j jw | α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
lem1 : FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw =
FinSeq.insert (seq k kw) n k kw (delete k kw seq) (skip... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
⊢ FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw = s... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | insert_delete_id | [214, 1] | [238, 20] | let lem2 : insert (seq k kw) n k kw (delete k kw seq) (skip k i) (_ : skip k i < n + 1) =
delete k kw seq i iw := by apply insert_at_image | α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
lem1 : FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw =
FinSeq.insert (seq k kw) n k kw (delete k kw seq) (skip... | α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
lem1 : FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw =
FinSeq.insert (seq k kw) n k kw (delete k kw seq) (skip... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
lem1 : FinSeq.insert (seq k kw) n k kw (delete k kw seq) j j... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | insert_delete_id | [214, 1] | [238, 20] | let resolve : delete k kw seq i iw = seq (skip k i) (skip_le_succ iw) := by rfl | α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
lem1 : FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw =
FinSeq.insert (seq k kw) n k kw (delete k kw seq) (skip... | α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
lem1 : FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw =
FinSeq.insert (seq k kw) n k kw (delete k kw seq) (skip... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
lem1 : FinSeq.insert (seq k kw) n k kw (delete k kw seq) j j... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | insert_delete_id | [214, 1] | [238, 20] | rw [lem1] | α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
lem1 : FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw =
FinSeq.insert (seq k kw) n k kw (delete k kw seq) (skip... | α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
lem1 : FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw =
FinSeq.insert (seq k kw) n k kw (delete k kw seq) (skip... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
lem1 : FinSeq.insert (seq k kw) n k kw (delete k kw seq) j j... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | insert_delete_id | [214, 1] | [238, 20] | rw [lem2] | α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
lem1 : FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw =
FinSeq.insert (seq k kw) n k kw (delete k kw seq) (skip... | α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
lem1 : FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw =
FinSeq.insert (seq k kw) n k kw (delete k kw seq) (skip... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
lem1 : FinSeq.insert (seq k kw) n k kw (delete k kw seq) j j... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | insert_delete_id | [214, 1] | [238, 20] | rw [resolve] | α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
lem1 : FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw =
FinSeq.insert (seq k kw) n k kw (delete k kw seq) (skip... | α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
lem1 : FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw =
FinSeq.insert (seq k kw) n k kw (delete k kw seq) (skip... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
lem1 : FinSeq.insert (seq k kw) n k kw (delete k kw seq) j j... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | insert_delete_id | [214, 1] | [238, 20] | apply witness_independent | α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
lem1 : FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw =
FinSeq.insert (seq k kw) n k kw (delete k kw seq) (skip... | case a
α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
lem1 : FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw =
FinSeq.insert (seq k kw) n k kw (delete k kw seq... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
lem1 : FinSeq.insert (seq k kw) n k kw (delete k kw seq) j j... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | insert_delete_id | [214, 1] | [238, 20] | exact eqn | case a
α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
lem1 : FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw =
FinSeq.insert (seq k kw) n k kw (delete k kw seq... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
lem1 : FinSeq.insert (seq k kw) n k kw (delete k kw s... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | insert_delete_id | [214, 1] | [238, 20] | apply witness_independent | α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
⊢ FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw =
FinSeq.insert (seq k kw) n k kw (delete k kw seq) (skip k ... | case a
α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
⊢ j = skip k i | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
⊢ FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw =
... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | insert_delete_id | [214, 1] | [238, 20] | rw [← eqn] | case a
α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
⊢ j = skip k i | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
⊢ j = skip k i
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | insert_delete_id | [214, 1] | [238, 20] | apply insert_at_image | α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
lem1 : FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw =
FinSeq.insert (seq k kw) n k kw (delete k kw seq) (skip... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
lem1 : FinSeq.insert (seq k kw) n k kw (delete k kw seq) j j... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | insert_delete_id | [214, 1] | [238, 20] | rfl | α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
lem1 : FinSeq.insert (seq k kw) n k kw (delete k kw seq) j jw =
FinSeq.insert (seq k kw) n k kw (delete k kw seq) (skip... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n k : ℕ
kw : k < n + 1
seq : FinSeq (n + 1) α
j : ℕ
jw : j < succ n
c : ¬j = k
i : ℕ := skipInverse k j c
eqn : skip k i = j := skipInverse_eq k j c
iw : i < n := skip_preimage_lt kw jw eqn
lem1 : FinSeq.insert (seq k kw) n k kw (delete k kw seq) j j... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | elem_not_beyond_vacuously | [350, 1] | [355, 48] | intro hyp k kw ineq | α : Type
n : ℕ
seq : FinSeq n α
elem : α
m : ℕ
⊢ n ≤ m → elemNotBeyond seq elem m | α : Type
n : ℕ
seq : FinSeq n α
elem : α
m : ℕ
hyp : n ≤ m
k : ℕ
kw : k < n
ineq : m ≤ k
⊢ ¬seq k kw = elem | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n : ℕ
seq : FinSeq n α
elem : α
m : ℕ
⊢ n ≤ m → elemNotBeyond seq elem m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | elem_not_beyond_vacuously | [350, 1] | [355, 48] | let inq := Nat.le_trans hyp ineq | α : Type
n : ℕ
seq : FinSeq n α
elem : α
m : ℕ
hyp : n ≤ m
k : ℕ
kw : k < n
ineq : m ≤ k
⊢ ¬seq k kw = elem | α : Type
n : ℕ
seq : FinSeq n α
elem : α
m : ℕ
hyp : n ≤ m
k : ℕ
kw : k < n
ineq : m ≤ k
inq : n ≤ k := Nat.le_trans hyp ineq
⊢ ¬seq k kw = elem | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n : ℕ
seq : FinSeq n α
elem : α
m : ℕ
hyp : n ≤ m
k : ℕ
kw : k < n
ineq : m ≤ k
⊢ ¬seq k kw = elem
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | elem_not_beyond_vacuously | [350, 1] | [355, 48] | let inq2 := Nat.lt_of_lt_of_le kw inq | α : Type
n : ℕ
seq : FinSeq n α
elem : α
m : ℕ
hyp : n ≤ m
k : ℕ
kw : k < n
ineq : m ≤ k
inq : n ≤ k := Nat.le_trans hyp ineq
⊢ ¬seq k kw = elem | α : Type
n : ℕ
seq : FinSeq n α
elem : α
m : ℕ
hyp : n ≤ m
k : ℕ
kw : k < n
ineq : m ≤ k
inq : n ≤ k := Nat.le_trans hyp ineq
inq2 : k < k := Nat.lt_of_lt_of_le kw inq
⊢ ¬seq k kw = elem | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n : ℕ
seq : FinSeq n α
elem : α
m : ℕ
hyp : n ≤ m
k : ℕ
kw : k < n
ineq : m ≤ k
inq : n ≤ k := Nat.le_trans hyp ineq
⊢ ¬seq k kw = elem
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/FinSeq.lean | elem_not_beyond_vacuously | [350, 1] | [355, 48] | exact (False.elim (Nat.lt_irrefl k inq2)) | α : Type
n : ℕ
seq : FinSeq n α
elem : α
m : ℕ
hyp : n ≤ m
k : ℕ
kw : k < n
ineq : m ≤ k
inq : n ≤ k := Nat.le_trans hyp ineq
inq2 : k < k := Nat.lt_of_lt_of_le kw inq
⊢ ¬seq k kw = elem | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
n : ℕ
seq : FinSeq n α
elem : α
m : ℕ
hyp : n ≤ m
k : ℕ
kw : k < n
ineq : m ≤ k
inq : n ≤ k := Nat.le_trans hyp ineq
inq2 : k < k := Nat.lt_of_lt_of_le kw inq
⊢ ¬seq k kw = elem
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/DPLL.lean | notpure_cases | [234, 1] | [247, 35] | match b, eqn with
| true, Or.inr pf =>
intro hyp
simp [pf] at hyp
| false, Or.inr pf =>
intro hyp
simp [pf] at hyp
| _ , Or.inl pf =>
intro hyp
let w := Eq.trans (Eq.symm pf) hyp
exact Option.noConfusion w | b : Bool
x : Option Bool
eqn : x = none ∨ x = some b
⊢ ¬x = some !b | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
b : Bool
x : Option Bool
eqn : x = none ∨ x = some b
⊢ ¬x = some !b
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/DPLL.lean | notpure_cases | [234, 1] | [247, 35] | intro hyp | b : Bool
x : Option Bool
eqn : x = none ∨ x = some b
pf : x = some true
⊢ ¬x = some !true | b : Bool
x : Option Bool
eqn : x = none ∨ x = some b
pf : x = some true
hyp : x = some !true
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
b : Bool
x : Option Bool
eqn : x = none ∨ x = some b
pf : x = some true
⊢ ¬x = some !true
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/DPLL.lean | notpure_cases | [234, 1] | [247, 35] | simp [pf] at hyp | b : Bool
x : Option Bool
eqn : x = none ∨ x = some b
pf : x = some true
hyp : x = some !true
⊢ False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
b : Bool
x : Option Bool
eqn : x = none ∨ x = some b
pf : x = some true
hyp : x = some !true
⊢ False
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/DPLL.lean | notpure_cases | [234, 1] | [247, 35] | intro hyp | b : Bool
x : Option Bool
eqn : x = none ∨ x = some b
pf : x = some false
⊢ ¬x = some !false | b : Bool
x : Option Bool
eqn : x = none ∨ x = some b
pf : x = some false
hyp : x = some !false
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
b : Bool
x : Option Bool
eqn : x = none ∨ x = some b
pf : x = some false
⊢ ¬x = some !false
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/DPLL.lean | notpure_cases | [234, 1] | [247, 35] | simp [pf] at hyp | b : Bool
x : Option Bool
eqn : x = none ∨ x = some b
pf : x = some false
hyp : x = some !false
⊢ False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
b : Bool
x : Option Bool
eqn : x = none ∨ x = some b
pf : x = some false
hyp : x = some !false
⊢ False
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/DPLL.lean | notpure_cases | [234, 1] | [247, 35] | intro hyp | b : Bool
x : Option Bool
eqn : x = none ∨ x = some b
x✝ : Bool
pf : x = none
⊢ ¬x = some !x✝ | b : Bool
x : Option Bool
eqn : x = none ∨ x = some b
x✝ : Bool
pf : x = none
hyp : x = some !x✝
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
b : Bool
x : Option Bool
eqn : x = none ∨ x = some b
x✝ : Bool
pf : x = none
⊢ ¬x = some !x✝
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/DPLL.lean | notpure_cases | [234, 1] | [247, 35] | let w := Eq.trans (Eq.symm pf) hyp | b : Bool
x : Option Bool
eqn : x = none ∨ x = some b
x✝ : Bool
pf : x = none
hyp : x = some !x✝
⊢ False | b : Bool
x : Option Bool
eqn : x = none ∨ x = some b
x✝ : Bool
pf : x = none
hyp : x = some !x✝
w : none = some !x✝ := pf.symm.trans hyp
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
b : Bool
x : Option Bool
eqn : x = none ∨ x = some b
x✝ : Bool
pf : x = none
hyp : x = some !x✝
⊢ False
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/DPLL.lean | notpure_cases | [234, 1] | [247, 35] | exact Option.noConfusion w | b : Bool
x : Option Bool
eqn : x = none ∨ x = some b
x✝ : Bool
pf : x = none
hyp : x = some !x✝
w : none = some !x✝ := pf.symm.trans hyp
⊢ False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
b : Bool
x : Option Bool
eqn : x = none ∨ x = some b
x✝ : Bool
pf : x = none
hyp : x = some !x✝
w : none = some !x✝ := pf.symm.trans hyp
⊢ False
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PosRestClause.lean | PosResClause.reverseResolve | [111, 1] | [137, 26] | intro rc head neg l w | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
⊢ ∀ (rc : ReductionClauses branch focus focusLt clauses) (head : Clause (n + 1))
(pos : Vector.get' head focus focusLt = some branch) (l : ℕ) (w : l < rc.num_reducedClauses),
ReductionClauses.reverse ... | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_reducedClauses
⊢ ReductionClauses.reverse (addPositiveClause br... | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
⊢ ∀ (rc : ReductionClauses branch focus focusLt clauses) (head : Clause (n + 1))
(pos : Vector.get' head focus focusLt = some branch) (l : ℕ) (... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PosRestClause.lean | PosResClause.reverseResolve | [111, 1] | [137, 26] | let rcN := addPositiveClause branch focus focusLt clauses rc head neg | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_reducedClauses
⊢ ReductionClauses.reverse (addPositiveClause br... | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_reducedClauses
rcN : ReductionClauses branch focus focusLt (hea... | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_re... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PosRestClause.lean | PosResClause.reverseResolve | [111, 1] | [137, 26] | have res1 : rcN.reverse l w =
rcN.reverseVec.get' l w := by rfl | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_reducedClauses
rcN : ReductionClauses branch focus focusLt (hea... | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_reducedClauses
rcN : ReductionClauses branch focus focusLt (hea... | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_re... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PosRestClause.lean | PosResClause.reverseResolve | [111, 1] | [137, 26] | have res2 : rc.reverse l w =
rc.reverseVec.get' l w := by rfl | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_reducedClauses
rcN : ReductionClauses branch focus focusLt (hea... | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_reducedClauses
rcN : ReductionClauses branch focus focusLt (hea... | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_re... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PosRestClause.lean | PosResClause.reverseResolve | [111, 1] | [137, 26] | rw [res1] | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_reducedClauses
rcN : ReductionClauses branch focus focusLt (hea... | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_reducedClauses
rcN : ReductionClauses branch focus focusLt (hea... | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_re... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PosRestClause.lean | PosResClause.reverseResolve | [111, 1] | [137, 26] | rw [res2] | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_reducedClauses
rcN : ReductionClauses branch focus focusLt (hea... | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_reducedClauses
rcN : ReductionClauses branch focus focusLt (hea... | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_re... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PosRestClause.lean | PosResClause.reverseResolve | [111, 1] | [137, 26] | have res3 :rcN.reverseVec =
(rc.reverseVec.map (. + 1)) := by rfl | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_reducedClauses
rcN : ReductionClauses branch focus focusLt (hea... | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_reducedClauses
rcN : ReductionClauses branch focus focusLt (hea... | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_re... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PosRestClause.lean | PosResClause.reverseResolve | [111, 1] | [137, 26] | rw [res3] | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_reducedClauses
rcN : ReductionClauses branch focus focusLt (hea... | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_reducedClauses
rcN : ReductionClauses branch focus focusLt (hea... | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_re... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PosRestClause.lean | PosResClause.reverseResolve | [111, 1] | [137, 26] | have res4 :
( (rc.reverseVec.map (. + 1)) ).get' l w =
(zero +:
(rc.reverseVec.map (. + 1)) ).get'
(l + 1) (Nat.succ_le_succ w) := by rfl | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_reducedClauses
rcN : ReductionClauses branch focus focusLt (hea... | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_reducedClauses
rcN : ReductionClauses branch focus focusLt (hea... | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_re... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PosRestClause.lean | PosResClause.reverseResolve | [111, 1] | [137, 26] | rw [res4] | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_reducedClauses
rcN : ReductionClauses branch focus focusLt (hea... | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_reducedClauses
rcN : ReductionClauses branch focus focusLt (hea... | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_re... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PosRestClause.lean | PosResClause.reverseResolve | [111, 1] | [137, 26] | rw [(get'_cons_succ
zero (rc.reverseVec.map (. + 1)))] | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_reducedClauses
rcN : ReductionClauses branch focus focusLt (hea... | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_reducedClauses
rcN : ReductionClauses branch focus focusLt (hea... | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_re... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PosRestClause.lean | PosResClause.reverseResolve | [111, 1] | [137, 26] | rw [get'_map] | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_reducedClauses
rcN : ReductionClauses branch focus focusLt (hea... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_re... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PosRestClause.lean | PosResClause.reverseResolve | [111, 1] | [137, 26] | rfl | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_reducedClauses
rcN : ReductionClauses branch focus focusLt (hea... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_re... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PosRestClause.lean | PosResClause.reverseResolve | [111, 1] | [137, 26] | rfl | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_reducedClauses
rcN : ReductionClauses branch focus focusLt (hea... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_re... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PosRestClause.lean | PosResClause.reverseResolve | [111, 1] | [137, 26] | rfl | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_reducedClauses
rcN : ReductionClauses branch focus focusLt (hea... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_re... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PosRestClause.lean | PosResClause.reverseResolve | [111, 1] | [137, 26] | rfl | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_reducedClauses
rcN : ReductionClauses branch focus focusLt (hea... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg : Vector.get' head focus focusLt = some branch
l : ℕ
w : l < rc.num_re... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | none_mapsto_none | [108, 1] | [109, 24] | rfl | α β : Type
fn : α → β
⊢ none = none | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α β : Type
fn : α → β
⊢ none = none
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | map_plusone_not_somezero | [111, 1] | [120, 24] | injection hyp | n : Option ℕ
j : ℕ
hyp : some (j + 1) = some zero
⊢ j + 1 = zero | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : Option ℕ
j : ℕ
hyp : some (j + 1) = some zero
⊢ j + 1 = zero
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | map_plusone_pred | [122, 1] | [135, 23] | injection hyp | n : Option ℕ
m j : ℕ
hyp : some (j + 1) = some (m + 1)
⊢ j + 1 = m + 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : Option ℕ
m j : ℕ
hyp : some (j + 1) = some (m + 1)
⊢ j + 1 = m + 1
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | map_plusone_pred | [122, 1] | [135, 23] | injection lem1 | n : Option ℕ
m j : ℕ
hyp : some (j + 1) = some (m + 1)
lem1 : j + 1 = m + 1 := Option.noConfusion hyp fun val_eq => val_eq
⊢ j = m | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : Option ℕ
m j : ℕ
hyp : some (j + 1) = some (m + 1)
lem1 : j + 1 = m + 1 := Option.noConfusion hyp fun val_eq => val_eq
⊢ j = m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | PrependClause.forwardResolve | [140, 1] | [153, 60] | intro rc head _ l w | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
⊢ ∀ (rc : ReductionClauses branch focus focusLt clauses) (head : Clause (n + 1))
(neg : ¬get' head focus focusLt = some branch) (l : ℕ) (w : l + 1 < num_clauses + 1),
ReductionClauses.forward (prepend... | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg✝ : ¬get' head focus focusLt = some branch
l : ℕ
w : l + 1 < num_clauses + 1
⊢ ReductionClauses.forward (prependClause branch focus ... | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
⊢ ∀ (rc : ReductionClauses branch focus focusLt clauses) (head : Clause (n + 1))
(neg : ¬get' head focus focusLt = some branch) (l : ℕ) (w : l ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | PrependClause.forwardResolve | [140, 1] | [153, 60] | simp [ReductionClauses.forward, ReductionClauses.forwardVec, prependClause] | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg✝ : ¬get' head focus focusLt = some branch
l : ℕ
w : l + 1 < num_clauses + 1
⊢ ReductionClauses.forward (prependClause branch focus ... | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg✝ : ¬get' head focus focusLt = some branch
l : ℕ
w : l + 1 < num_clauses + 1
⊢ get' (some 0 ::ᵥ map (fun nop => Option.map (fun x =>... | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg✝ : ¬get' head focus focusLt = some branch
l : ℕ
w : l + 1 < num_clause... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | PrependClause.forwardResolve | [140, 1] | [153, 60] | simp [Vector.get'] | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg✝ : ¬get' head focus focusLt = some branch
l : ℕ
w : l + 1 < num_clauses + 1
⊢ get' (some 0 ::ᵥ map (fun nop => Option.map (fun x =>... | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg✝ : ¬get' head focus focusLt = some branch
l : ℕ
w : l + 1 < num_clauses + 1
⊢ Vector.get (some 0 ::ᵥ map (fun nop => Option.map (fu... | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg✝ : ¬get' head focus focusLt = some branch
l : ℕ
w : l + 1 < num_clause... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | PrependClause.forwardResolve | [140, 1] | [153, 60] | have s : { val := l + 1, isLt := w } = Fin.succ
⟨l, le_of_succ_le_succ w⟩ := by rfl | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg✝ : ¬get' head focus focusLt = some branch
l : ℕ
w : l + 1 < num_clauses + 1
⊢ Vector.get (some 0 ::ᵥ map (fun nop => Option.map (fu... | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg✝ : ¬get' head focus focusLt = some branch
l : ℕ
w : l + 1 < num_clauses + 1
s : { val := l + 1, isLt := w } = Fin.succ { val := l, ... | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg✝ : ¬get' head focus focusLt = some branch
l : ℕ
w : l + 1 < num_clause... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | PrependClause.forwardResolve | [140, 1] | [153, 60] | rw [s] | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg✝ : ¬get' head focus focusLt = some branch
l : ℕ
w : l + 1 < num_clauses + 1
s : { val := l + 1, isLt := w } = Fin.succ { val := l, ... | num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg✝ : ¬get' head focus focusLt = some branch
l : ℕ
w : l + 1 < num_clauses + 1
s : { val := l + 1, isLt := w } = Fin.succ { val := l, ... | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : ℕ
branch : Bool
focus : ℕ
focusLt : focus < n + 1
clauses : Vector (Clause (n + 1)) num_clauses
rc : ReductionClauses branch focus focusLt clauses
head : Clause (n + 1)
neg✝ : ¬get' head focus focusLt = some branch
l : ℕ
w : l + 1 < num_clause... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.