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/PrependClause.lean | PrependClause.forwardResolve | [140, 1] | [153, 60] | rw [Vector.get_cons_succ, Vector.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✝ : ¬get' head focus focusLt = some branch
l : ℕ
w : l + 1 < num_clauses + 1
s : { val := l + 1, isLt := w } = Fin.succ { val := l, ... | 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✝ : ¬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] | 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
⊢ { val := l + 1, isLt := w } = Fin.succ { val := l, is... | 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✝ : ¬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.reverseResolve | [250, 1] | [261, 57] | 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 < rc.num_reducedClauses + 1),
ReductionClauses.revers... | 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 < rc.num_reducedClauses + 1
⊢ ReductionClauses.reverse (prependClause bra... | 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.reverseResolve | [250, 1] | [261, 57] | simp [ReductionClauses.reverse, ReductionClauses.reverseVec, prependClause, Vector.get', 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✝ : ¬get' head focus focusLt = some branch
l : ℕ
w : l + 1 < rc.num_reducedClauses + 1
⊢ ReductionClauses.reverse (prependClause bra... | 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 < rc.num_reducedClauses + 1
⊢ Vector.get (0 ::ᵥ map (fun x => x + 1) rc.r... | 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 < rc.num_red... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | PrependClause.reverseResolve | [250, 1] | [261, 57] | 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 < rc.num_reducedClauses + 1
⊢ Vector.get (0 ::ᵥ map (fun x => x + 1) rc.r... | 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 < rc.num_reducedClauses + 1
s : { val := l + 1, isLt := w } = Fin.succ { ... | 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 < rc.num_red... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | PrependClause.reverseResolve | [250, 1] | [261, 57] | rw [s, Vector.get_cons_succ, Vector.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✝ : ¬get' head focus focusLt = some branch
l : ℕ
w : l + 1 < rc.num_reducedClauses + 1
s : { val := l + 1, isLt := w } = Fin.succ { ... | 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✝ : ¬get' head focus focusLt = some branch
l : ℕ
w : l + 1 < rc.num_red... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | PrependClause.reverseResolve | [250, 1] | [261, 57] | 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 < rc.num_reducedClauses + 1
⊢ { val := l + 1, isLt := w } = Fin.succ { va... | 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✝ : ¬get' head focus focusLt = some branch
l : ℕ
w : l + 1 < rc.num_red... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | PrependClause.revrelAux | [263, 1] | [292, 20] | have l : Vector.get (0 ::ᵥ map (fun x ↦ x + 1) v) (Fin.succ { val := l, isLt := w }) = v.get ⟨l, w⟩ + 1 := by
rw [Vector.get_cons_succ]
rw [Vector.get_map] | num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
⊢ Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.succ { val := l, isLt := w }) < succ num_clau... | num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l✝ : ℕ
w : l✝ < num_reducedClauses
bd : Vector.get v { val := l✝, isLt := w } < num_clauses
l :
Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.succ { val := l✝, isLt := w }) =
V... | Please generate a tactic in lean4 to solve the state.
STATE:
num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
⊢ Vector.get (0 ::ᵥ map (fun x =>... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | PrependClause.revrelAux | [263, 1] | [292, 20] | rw [l] | num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l✝ : ℕ
w : l✝ < num_reducedClauses
bd : Vector.get v { val := l✝, isLt := w } < num_clauses
l :
Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.succ { val := l✝, isLt := w }) =
V... | num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l✝ : ℕ
w : l✝ < num_reducedClauses
bd : Vector.get v { val := l✝, isLt := w } < num_clauses
l :
Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.succ { val := l✝, isLt := w }) =
V... | Please generate a tactic in lean4 to solve the state.
STATE:
num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l✝ : ℕ
w : l✝ < num_reducedClauses
bd : Vector.get v { val := l✝, isLt := w } < num_clauses
l :
Vector.get (0 ::ᵥ map (f... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | PrependClause.revrelAux | [263, 1] | [292, 20] | apply Nat.succ_lt_succ | num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l✝ : ℕ
w : l✝ < num_reducedClauses
bd : Vector.get v { val := l✝, isLt := w } < num_clauses
l :
Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.succ { val := l✝, isLt := w }) =
V... | case a
num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l✝ : ℕ
w : l✝ < num_reducedClauses
bd : Vector.get v { val := l✝, isLt := w } < num_clauses
l :
Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.succ { val := l✝, isLt := w }) ... | Please generate a tactic in lean4 to solve the state.
STATE:
num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l✝ : ℕ
w : l✝ < num_reducedClauses
bd : Vector.get v { val := l✝, isLt := w } < num_clauses
l :
Vector.get (0 ::ᵥ map (f... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | PrependClause.revrelAux | [263, 1] | [292, 20] | exact bd | case a
num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l✝ : ℕ
w : l✝ < num_reducedClauses
bd : Vector.get v { val := l✝, isLt := w } < num_clauses
l :
Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.succ { val := l✝, isLt := w }) ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l✝ : ℕ
w : l✝ < num_reducedClauses
bd : Vector.get v { val := l✝, isLt := w } < num_clauses
l :
Vector.get (0 ::ᵥ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | PrependClause.revrelAux | [263, 1] | [292, 20] | rw [Vector.get_cons_succ] | num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
⊢ Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.succ { val := l, isLt := w }) =
Vector.ge... | num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
⊢ Vector.get (map (fun x => x + 1) v) { val := l, isLt := w } = Vector.get v { val := l, isLt ... | Please generate a tactic in lean4 to solve the state.
STATE:
num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
⊢ Vector.get (0 ::ᵥ map (fun x =>... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | PrependClause.revrelAux | [263, 1] | [292, 20] | rw [Vector.get_map] | num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
⊢ Vector.get (map (fun x => x + 1) v) { val := l, isLt := w } = Vector.get v { val := l, isLt ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
⊢ Vector.get (map (fun x => x + 1... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | PrependClause.revrelAux | [263, 1] | [292, 20] | symm | num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
⊢ Vector.get clauses { val := Vector.get v { val := l, isLt := w }, isLt := bd } =
Vector.... | num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
⊢ Vector.get (head ::ᵥ clauses)
{ val := Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.... | Please generate a tactic in lean4 to solve the state.
STATE:
num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
⊢ Vector.get clauses { val := Vec... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | PrependClause.revrelAux | [263, 1] | [292, 20] | let lem :=
Vector.get_cons_succ 0 (map (fun x ↦ x + 1) v) ⟨l, w⟩ | num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
⊢ Vector.get (head ::ᵥ clauses)
{ val := Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.... | num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem : Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.succ { val := l, isLt := w }) =
Vector.... | Please generate a tactic in lean4 to solve the state.
STATE:
num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
⊢ Vector.get (head ::ᵥ clauses)
... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | PrependClause.revrelAux | [263, 1] | [292, 20] | rw [Vector.get_map] at lem | num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem : Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.succ { val := l, isLt := w }) =
Vector.... | num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.succ { val := l, isLt := w }) =
Vec... | Please generate a tactic in lean4 to solve the state.
STATE:
num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem : Vector.get (0 ::ᵥ map (fun ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | PrependClause.revrelAux | [263, 1] | [292, 20] | let lem' : Fin.succ { val := Vector.get v { val := l, isLt := w }, isLt := bd } =
⟨ Vector.get (0 ::ᵥ map (fun x ↦ x + 1) v) (Fin.succ { val := l, isLt := w }), by
rw [lem]
apply Nat.succ_lt_succ
exact bd
⟩ := by
apply Fin.eq_of_veq
simp
symm
exact lem | num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.succ { val := l, isLt := w }) =
Vec... | num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.succ { val := l, isLt := w }) =
Vec... | Please generate a tactic in lean4 to solve the state.
STATE:
num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ map (fu... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | PrependClause.revrelAux | [263, 1] | [292, 20] | let lem'' :=
Vector.get_cons_succ head clauses ⟨Vector.get v { val := l, isLt := w }, bd⟩ | num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.succ { val := l, isLt := w }) =
Vec... | num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.succ { val := l, isLt := w }) =
Vec... | Please generate a tactic in lean4 to solve the state.
STATE:
num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ map (fu... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | PrependClause.revrelAux | [263, 1] | [292, 20] | rw [lem'] at lem'' | num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.succ { val := l, isLt := w }) =
Vec... | num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.succ { val := l, isLt := w }) =
Vec... | Please generate a tactic in lean4 to solve the state.
STATE:
num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ map (fu... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | PrependClause.revrelAux | [263, 1] | [292, 20] | exact lem'' | num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.succ { val := l, isLt := w }) =
Vec... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ map (fu... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | PrependClause.revrelAux | [263, 1] | [292, 20] | rw [lem] | num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.succ { val := l, isLt := w }) =
Vec... | num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.succ { val := l, isLt := w }) =
Vec... | Please generate a tactic in lean4 to solve the state.
STATE:
num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ map (fu... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | PrependClause.revrelAux | [263, 1] | [292, 20] | apply Nat.succ_lt_succ | num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.succ { val := l, isLt := w }) =
Vec... | case a
num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.succ { val := l, isLt := w }) =
... | Please generate a tactic in lean4 to solve the state.
STATE:
num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ map (fu... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | PrependClause.revrelAux | [263, 1] | [292, 20] | exact bd | case a
num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.succ { val := l, isLt := w }) =
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | PrependClause.revrelAux | [263, 1] | [292, 20] | apply Fin.eq_of_veq | num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.succ { val := l, isLt := w }) =
Vec... | case a
num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.succ { val := l, isLt := w }) =
... | Please generate a tactic in lean4 to solve the state.
STATE:
num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ map (fu... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | PrependClause.revrelAux | [263, 1] | [292, 20] | simp | case a
num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.succ { val := l, isLt := w }) =
... | case a
num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.succ { val := l, isLt := w }) =
... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | PrependClause.revrelAux | [263, 1] | [292, 20] | symm | case a
num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.succ { val := l, isLt := w }) =
... | case a
num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.succ { val := l, isLt := w }) =
... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/PrependClause.lean | PrependClause.revrelAux | [263, 1] | [292, 20] | exact lem | case a
num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ map (fun x => x + 1) v) (Fin.succ { val := l, isLt := w }) =
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
num_reducedClauses n num_clauses : ℕ
v : Vector ℕ num_reducedClauses
clauses : Vector (Clause (n + 1)) num_clauses
head : Clause (n + 1)
l : ℕ
w : l < num_reducedClauses
bd : Vector.get v { val := l, isLt := w } < num_clauses
lem :
Vector.get (0 ::ᵥ ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_below_eq | [16, 1] | [21, 18] | intro hyp | n m : Nat
⊢ m < n → skip n m = m | n m : Nat
hyp : m < n
⊢ skip n m = m | Please generate a tactic in lean4 to solve the state.
STATE:
n m : Nat
⊢ m < n → skip n m = m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_below_eq | [16, 1] | [21, 18] | rw [skip] | n m : Nat
hyp : m < n
⊢ skip n m = m | n m : Nat
hyp : m < n
⊢ (match n, m with
| n, m => if m < n then m else m + 1) =
m | Please generate a tactic in lean4 to solve the state.
STATE:
n m : Nat
hyp : m < n
⊢ skip n m = m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_below_eq | [16, 1] | [21, 18] | by_cases c: m < n | n m : Nat
hyp : m < n
⊢ (match n, m with
| n, m => if m < n then m else m + 1) =
m | case inl
n m : Nat
hyp c : m < n
⊢ (match n, m with
| n, m => if m < n then m else m + 1) =
m
case inr
n m : Nat
hyp : m < n
c : ¬m < n
⊢ (match n, m with
| n, m => if m < n then m else m + 1) =
m | Please generate a tactic in lean4 to solve the state.
STATE:
n m : Nat
hyp : m < n
⊢ (match n, m with
| n, m => if m < n then m else m + 1) =
m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_below_eq | [16, 1] | [21, 18] | simp [c] | case inl
n m : Nat
hyp c : m < n
⊢ (match n, m with
| n, m => if m < n then m else m + 1) =
m | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
n m : Nat
hyp c : m < n
⊢ (match n, m with
| n, m => if m < n then m else m + 1) =
m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_below_eq | [16, 1] | [21, 18] | contradiction | case inr
n m : Nat
hyp : m < n
c : ¬m < n
⊢ (match n, m with
| n, m => if m < n then m else m + 1) =
m | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
n m : Nat
hyp : m < n
c : ¬m < n
⊢ (match n, m with
| n, m => if m < n then m else m + 1) =
m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_above_eq | [24, 1] | [30, 13] | intro hyp | n m : Nat
⊢ n ≤ m → skip n m = m + 1 | n m : Nat
hyp : n ≤ m
⊢ skip n m = m + 1 | Please generate a tactic in lean4 to solve the state.
STATE:
n m : Nat
⊢ n ≤ m → skip n m = m + 1
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_above_eq | [24, 1] | [30, 13] | rw [skip] | n m : Nat
hyp : n ≤ m
⊢ skip n m = m + 1 | n m : Nat
hyp : n ≤ m
⊢ (match n, m with
| n, m => if m < n then m else m + 1) =
m + 1 | Please generate a tactic in lean4 to solve the state.
STATE:
n m : Nat
hyp : n ≤ m
⊢ skip n m = m + 1
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_above_eq | [24, 1] | [30, 13] | by_cases c: m < n | n m : Nat
hyp : n ≤ m
⊢ (match n, m with
| n, m => if m < n then m else m + 1) =
m + 1 | case inl
n m : Nat
hyp : n ≤ m
c : m < n
⊢ (match n, m with
| n, m => if m < n then m else m + 1) =
m + 1
case inr
n m : Nat
hyp : n ≤ m
c : ¬m < n
⊢ (match n, m with
| n, m => if m < n then m else m + 1) =
m + 1 | Please generate a tactic in lean4 to solve the state.
STATE:
n m : Nat
hyp : n ≤ m
⊢ (match n, m with
| n, m => if m < n then m else m + 1) =
m + 1
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_above_eq | [24, 1] | [30, 13] | have c' : ¬(n ≤ m) := Nat.not_le_of_gt c | case inl
n m : Nat
hyp : n ≤ m
c : m < n
⊢ (match n, m with
| n, m => if m < n then m else m + 1) =
m + 1 | case inl
n m : Nat
hyp : n ≤ m
c : m < n
c' : ¬n ≤ m
⊢ (match n, m with
| n, m => if m < n then m else m + 1) =
m + 1 | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
n m : Nat
hyp : n ≤ m
c : m < n
⊢ (match n, m with
| n, m => if m < n then m else m + 1) =
m + 1
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_above_eq | [24, 1] | [30, 13] | contradiction | case inl
n m : Nat
hyp : n ≤ m
c : m < n
c' : ¬n ≤ m
⊢ (match n, m with
| n, m => if m < n then m else m + 1) =
m + 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
n m : Nat
hyp : n ≤ m
c : m < n
c' : ¬n ≤ m
⊢ (match n, m with
| n, m => if m < n then m else m + 1) =
m + 1
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_above_eq | [24, 1] | [30, 13] | simp [c] | case inr
n m : Nat
hyp : n ≤ m
c : ¬m < n
⊢ (match n, m with
| n, m => if m < n then m else m + 1) =
m + 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
n m : Nat
hyp : n ≤ m
c : ¬m < n
⊢ (match n, m with
| n, m => if m < n then m else m + 1) =
m + 1
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skipInverse_eq | [62, 1] | [90, 17] | by_cases c : m < n | n m : Nat
eqn : m ≠ n
⊢ skip n (skipInverse n m eqn) = m | case inl
n m : Nat
eqn : m ≠ n
c : m < n
⊢ skip n (skipInverse n m eqn) = m
case inr
n m : Nat
eqn : m ≠ n
c : ¬m < n
⊢ skip n (skipInverse n m eqn) = m | Please generate a tactic in lean4 to solve the state.
STATE:
n m : Nat
eqn : m ≠ n
⊢ skip n (skipInverse n m eqn) = m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skipInverse_eq | [62, 1] | [90, 17] | rw [skipInverse] | case inl
n m : Nat
eqn : m ≠ n
c : m < n
⊢ skip n (skipInverse n m eqn) = m | case inl
n m : Nat
eqn : m ≠ n
c : m < n
⊢ skip n
(if x : n < m then
match m, eqn, x with
| zero, x, x_1 =>
let_fun x := (_ : 0 ≤ n);
False.elim (_ : False)
| succ p, x, x_1 => p
else m) =
m | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
n m : Nat
eqn : m ≠ n
c : m < n
⊢ skip n (skipInverse n m eqn) = m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skipInverse_eq | [62, 1] | [90, 17] | simp [eqn, c] | case inl
n m : Nat
eqn : m ≠ n
c : m < n
⊢ skip n
(if x : n < m then
match m, eqn, x with
| zero, x, x_1 =>
let_fun x := (_ : 0 ≤ n);
False.elim (_ : False)
| succ p, x, x_1 => p
else m) =
m | case inl
n m : Nat
eqn : m ≠ n
c : m < n
⊢ skip n
(if h : n < m then
match m, eqn, (_ : n < m) with
| zero, x, x_1 => False.elim (_ : False)
| succ p, x, x_1 => p
else m) =
m | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
n m : Nat
eqn : m ≠ n
c : m < n
⊢ skip n
(if x : n < m then
match m, eqn, x with
| zero, x, x_1 =>
let_fun x := (_ : 0 ≤ n);
False.elim (_ : False)
| succ p, x, x_1 => p
else m) =
m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skipInverse_eq | [62, 1] | [90, 17] | have h' : ¬ (n < m) := by
apply Nat.not_le_of_gt
apply Nat.le_trans c
apply Nat.le_succ | case inl
n m : Nat
eqn : m ≠ n
c : m < n
⊢ skip n
(if h : n < m then
match m, eqn, (_ : n < m) with
| zero, x, x_1 => False.elim (_ : False)
| succ p, x, x_1 => p
else m) =
m | case inl
n m : Nat
eqn : m ≠ n
c : m < n
h' : ¬n < m
⊢ skip n
(if h : n < m then
match m, eqn, (_ : n < m) with
| zero, x, x_1 => False.elim (_ : False)
| succ p, x, x_1 => p
else m) =
m | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
n m : Nat
eqn : m ≠ n
c : m < n
⊢ skip n
(if h : n < m then
match m, eqn, (_ : n < m) with
| zero, x, x_1 => False.elim (_ : False)
| succ p, x, x_1 => p
else m) =
m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skipInverse_eq | [62, 1] | [90, 17] | simp [h'] | case inl
n m : Nat
eqn : m ≠ n
c : m < n
h' : ¬n < m
⊢ skip n
(if h : n < m then
match m, eqn, (_ : n < m) with
| zero, x, x_1 => False.elim (_ : False)
| succ p, x, x_1 => p
else m) =
m | case inl
n m : Nat
eqn : m ≠ n
c : m < n
h' : ¬n < m
⊢ skip n m = m | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
n m : Nat
eqn : m ≠ n
c : m < n
h' : ¬n < m
⊢ skip n
(if h : n < m then
match m, eqn, (_ : n < m) with
| zero, x, x_1 => False.elim (_ : False)
| succ p, x, x_1 => p
else m) =
m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skipInverse_eq | [62, 1] | [90, 17] | exact skip_below_eq c | case inl
n m : Nat
eqn : m ≠ n
c : m < n
h' : ¬n < m
⊢ skip n m = m | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
n m : Nat
eqn : m ≠ n
c : m < n
h' : ¬n < m
⊢ skip n m = m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skipInverse_eq | [62, 1] | [90, 17] | apply Nat.not_le_of_gt | n m : Nat
eqn : m ≠ n
c : m < n
⊢ ¬n < m | case h
n m : Nat
eqn : m ≠ n
c : m < n
⊢ succ n > m | Please generate a tactic in lean4 to solve the state.
STATE:
n m : Nat
eqn : m ≠ n
c : m < n
⊢ ¬n < m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skipInverse_eq | [62, 1] | [90, 17] | apply Nat.le_trans c | case h
n m : Nat
eqn : m ≠ n
c : m < n
⊢ succ n > m | case h
n m : Nat
eqn : m ≠ n
c : m < n
⊢ n ≤ succ n | Please generate a tactic in lean4 to solve the state.
STATE:
case h
n m : Nat
eqn : m ≠ n
c : m < n
⊢ succ n > m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skipInverse_eq | [62, 1] | [90, 17] | apply Nat.le_succ | case h
n m : Nat
eqn : m ≠ n
c : m < n
⊢ n ≤ succ n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
n m : Nat
eqn : m ≠ n
c : m < n
⊢ n ≤ succ n
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skipInverse_eq | [62, 1] | [90, 17] | rw [skipInverse] | case inr
n m : Nat
eqn : m ≠ n
c : ¬m < n
⊢ skip n (skipInverse n m eqn) = m | case inr
n m : Nat
eqn : m ≠ n
c : ¬m < n
⊢ skip n
(if x : n < m then
match m, eqn, x with
| zero, x, x_1 =>
let_fun x := (_ : 0 ≤ n);
False.elim (_ : False)
| succ p, x, x_1 => p
else m) =
m | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
n m : Nat
eqn : m ≠ n
c : ¬m < n
⊢ skip n (skipInverse n m eqn) = m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skipInverse_eq | [62, 1] | [90, 17] | simp [h'] | case inr
n m : Nat
eqn : m ≠ n
c : ¬m < n
h' : n < m
⊢ skip n
(if x : n < m then
match m, eqn, x with
| zero, x, x_1 =>
let_fun x := (_ : 0 ≤ n);
False.elim (_ : False)
| succ p, x, x_1 => p
else m) =
m | case inr
n m : Nat
eqn : m ≠ n
c : ¬m < n
h' : n < m
⊢ skip n
(match m, eqn, (_ : n < m) with
| zero, x, x_1 => False.elim (_ : False)
| succ p, x, x_1 => p) =
m | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
n m : Nat
eqn : m ≠ n
c : ¬m < n
h' : n < m
⊢ skip n
(if x : n < m then
match m, eqn, x with
| zero, x, x_1 =>
let_fun x := (_ : 0 ≤ n);
False.elim (_ : False)
| succ p, x, x_1 => p
else m) =
... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skipInverse_eq | [62, 1] | [90, 17] | match m with
| zero =>
have _ := Nat.zero_le n
contradiction
| succ p =>
apply skip_above_eq n p
apply Nat.le_of_succ_le_succ
apply Nat.le_trans h'
simp | case inr
n m : Nat
eqn : m ≠ n
c : ¬m < n
h' : n < m
⊢ skip n
(match m, eqn, (_ : n < m) with
| zero, x, x_1 => False.elim (_ : False)
| succ p, x, x_1 => p) =
m | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
n m : Nat
eqn : m ≠ n
c : ¬m < n
h' : n < m
⊢ skip n
(match m, eqn, (_ : n < m) with
| zero, x, x_1 => False.elim (_ : False)
| succ p, x, x_1 => p) =
m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skipInverse_eq | [62, 1] | [90, 17] | apply Nat.lt_of_le_of_ne | n m : Nat
eqn : m ≠ n
c : ¬m < n
⊢ n < m | case h₁
n m : Nat
eqn : m ≠ n
c : ¬m < n
⊢ n ≤ m
case h₂
n m : Nat
eqn : m ≠ n
c : ¬m < n
⊢ ¬n = m | Please generate a tactic in lean4 to solve the state.
STATE:
n m : Nat
eqn : m ≠ n
c : ¬m < n
⊢ n < m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skipInverse_eq | [62, 1] | [90, 17] | by_cases h'' : n ≤ m | case h₁
n m : Nat
eqn : m ≠ n
c : ¬m < n
⊢ n ≤ m | case h₁.inl
n m : Nat
eqn : m ≠ n
c : ¬m < n
h'' : n ≤ m
⊢ n ≤ m
case h₁.inr
n m : Nat
eqn : m ≠ n
c : ¬m < n
h'' : ¬n ≤ m
⊢ n ≤ m | Please generate a tactic in lean4 to solve the state.
STATE:
case h₁
n m : Nat
eqn : m ≠ n
c : ¬m < n
⊢ n ≤ m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skipInverse_eq | [62, 1] | [90, 17] | assumption | case h₁.inl
n m : Nat
eqn : m ≠ n
c : ¬m < n
h'' : n ≤ m
⊢ n ≤ m | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h₁.inl
n m : Nat
eqn : m ≠ n
c : ¬m < n
h'' : n ≤ m
⊢ n ≤ m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skipInverse_eq | [62, 1] | [90, 17] | let h''' := Nat.gt_of_not_le h'' | case h₁.inr
n m : Nat
eqn : m ≠ n
c : ¬m < n
h'' : ¬n ≤ m
⊢ n ≤ m | case h₁.inr
n m : Nat
eqn : m ≠ n
c : ¬m < n
h'' : ¬n ≤ m
h''' : n > m := gt_of_not_le h''
⊢ n ≤ m | Please generate a tactic in lean4 to solve the state.
STATE:
case h₁.inr
n m : Nat
eqn : m ≠ n
c : ¬m < n
h'' : ¬n ≤ m
⊢ n ≤ m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skipInverse_eq | [62, 1] | [90, 17] | contradiction | case h₁.inr
n m : Nat
eqn : m ≠ n
c : ¬m < n
h'' : ¬n ≤ m
h''' : n > m := gt_of_not_le h''
⊢ n ≤ m | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h₁.inr
n m : Nat
eqn : m ≠ n
c : ¬m < n
h'' : ¬n ≤ m
h''' : n > m := gt_of_not_le h''
⊢ n ≤ m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skipInverse_eq | [62, 1] | [90, 17] | intro contra | case h₂
n m : Nat
eqn : m ≠ n
c : ¬m < n
⊢ ¬n = m | case h₂
n m : Nat
eqn : m ≠ n
c : ¬m < n
contra : n = m
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
case h₂
n m : Nat
eqn : m ≠ n
c : ¬m < n
⊢ ¬n = m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skipInverse_eq | [62, 1] | [90, 17] | simp [contra] at eqn | case h₂
n m : Nat
eqn : m ≠ n
c : ¬m < n
contra : n = m
⊢ False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h₂
n m : Nat
eqn : m ≠ n
c : ¬m < n
contra : n = m
⊢ False
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skipInverse_eq | [62, 1] | [90, 17] | have _ := Nat.zero_le n | n m : Nat
eqn : zero ≠ n
c : ¬zero < n
h' : n < zero
⊢ skip n
(match zero, eqn, (_ : n < zero) with
| zero, x, x_1 => False.elim (_ : False)
| succ p, x, x_1 => p) =
zero | n m : Nat
eqn : zero ≠ n
c : ¬zero < n
h' : n < zero
x✝ : 0 ≤ n
⊢ skip n
(match zero, eqn, (_ : n < zero) with
| zero, x, x_1 => False.elim (_ : False)
| succ p, x, x_1 => p) =
zero | Please generate a tactic in lean4 to solve the state.
STATE:
n m : Nat
eqn : zero ≠ n
c : ¬zero < n
h' : n < zero
⊢ skip n
(match zero, eqn, (_ : n < zero) with
| zero, x, x_1 => False.elim (_ : False)
| succ p, x, x_1 => p) =
zero
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skipInverse_eq | [62, 1] | [90, 17] | contradiction | n m : Nat
eqn : zero ≠ n
c : ¬zero < n
h' : n < zero
x✝ : 0 ≤ n
⊢ skip n
(match zero, eqn, (_ : n < zero) with
| zero, x, x_1 => False.elim (_ : False)
| succ p, x, x_1 => p) =
zero | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n m : Nat
eqn : zero ≠ n
c : ¬zero < n
h' : n < zero
x✝ : 0 ≤ n
⊢ skip n
(match zero, eqn, (_ : n < zero) with
| zero, x, x_1 => False.elim (_ : False)
| succ p, x, x_1 => p) =
zero
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skipInverse_eq | [62, 1] | [90, 17] | apply skip_above_eq n p | n m p : Nat
eqn : succ p ≠ n
c : ¬succ p < n
h' : n < succ p
⊢ skip n
(match succ p, eqn, (_ : n < succ p) with
| zero, x, x_1 => False.elim (_ : False)
| succ p, x, x_1 => p) =
succ p | n m p : Nat
eqn : succ p ≠ n
c : ¬succ p < n
h' : n < succ p
⊢ n ≤ p | Please generate a tactic in lean4 to solve the state.
STATE:
n m p : Nat
eqn : succ p ≠ n
c : ¬succ p < n
h' : n < succ p
⊢ skip n
(match succ p, eqn, (_ : n < succ p) with
| zero, x, x_1 => False.elim (_ : False)
| succ p, x, x_1 => p) =
succ p
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skipInverse_eq | [62, 1] | [90, 17] | apply Nat.le_of_succ_le_succ | n m p : Nat
eqn : succ p ≠ n
c : ¬succ p < n
h' : n < succ p
⊢ n ≤ p | case a
n m p : Nat
eqn : succ p ≠ n
c : ¬succ p < n
h' : n < succ p
⊢ succ n ≤ succ p | Please generate a tactic in lean4 to solve the state.
STATE:
n m p : Nat
eqn : succ p ≠ n
c : ¬succ p < n
h' : n < succ p
⊢ n ≤ p
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skipInverse_eq | [62, 1] | [90, 17] | apply Nat.le_trans h' | case a
n m p : Nat
eqn : succ p ≠ n
c : ¬succ p < n
h' : n < succ p
⊢ succ n ≤ succ p | case a
n m p : Nat
eqn : succ p ≠ n
c : ¬succ p < n
h' : n < succ p
⊢ succ p ≤ succ p | Please generate a tactic in lean4 to solve the state.
STATE:
case a
n m p : Nat
eqn : succ p ≠ n
c : ¬succ p < n
h' : n < succ p
⊢ succ n ≤ succ p
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skipInverse_eq | [62, 1] | [90, 17] | simp | case a
n m p : Nat
eqn : succ p ≠ n
c : ¬succ p < n
h' : n < succ p
⊢ succ p ≤ succ p | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
n m p : Nat
eqn : succ p ≠ n
c : ¬succ p < n
h' : n < succ p
⊢ succ p ≤ succ p
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_lt | [93, 1] | [105, 28] | rw [eqn] | k j : Nat
c : j < k
eqn : skip k j = j := skip_below_eq c
⊢ skip k j < j + 2 | k j : Nat
c : j < k
eqn : skip k j = j := skip_below_eq c
⊢ j < j + 2 | Please generate a tactic in lean4 to solve the state.
STATE:
k j : Nat
c : j < k
eqn : skip k j = j := skip_below_eq c
⊢ skip k j < j + 2
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_lt | [93, 1] | [105, 28] | apply Nat.le_step | k j : Nat
c : j < k
eqn : skip k j = j := skip_below_eq c
⊢ j < j + 2 | case h
k j : Nat
c : j < k
eqn : skip k j = j := skip_below_eq c
⊢ succ j ≤ j + 1 | Please generate a tactic in lean4 to solve the state.
STATE:
k j : Nat
c : j < k
eqn : skip k j = j := skip_below_eq c
⊢ j < j + 2
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_lt | [93, 1] | [105, 28] | apply Nat.le_refl | case h
k j : Nat
c : j < k
eqn : skip k j = j := skip_below_eq c
⊢ succ j ≤ j + 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
k j : Nat
c : j < k
eqn : skip k j = j := skip_below_eq c
⊢ succ j ≤ j + 1
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_lt | [93, 1] | [105, 28] | rw [eqn] | k j : Nat
c : ¬j < k
eqn : skip k j = j + 1 := skip_not_below_eq k j c
⊢ skip k j < j + 2 | k j : Nat
c : ¬j < k
eqn : skip k j = j + 1 := skip_not_below_eq k j c
⊢ j + 1 < j + 2 | Please generate a tactic in lean4 to solve the state.
STATE:
k j : Nat
c : ¬j < k
eqn : skip k j = j + 1 := skip_not_below_eq k j c
⊢ skip k j < j + 2
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_lt | [93, 1] | [105, 28] | apply Nat.le_refl | k j : Nat
c : ¬j < k
eqn : skip k j = j + 1 := skip_not_below_eq k j c
⊢ j + 1 < j + 2 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
k j : Nat
c : ¬j < k
eqn : skip k j = j + 1 := skip_not_below_eq k j c
⊢ j + 1 < j + 2
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_ge | [107, 1] | [119, 28] | rw [eqn] | k j : Nat
c : j < k
eqn : skip k j = j := skip_below_eq c
⊢ j ≤ skip k j | k j : Nat
c : j < k
eqn : skip k j = j := skip_below_eq c
⊢ j ≤ j | Please generate a tactic in lean4 to solve the state.
STATE:
k j : Nat
c : j < k
eqn : skip k j = j := skip_below_eq c
⊢ j ≤ skip k j
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_ge | [107, 1] | [119, 28] | apply Nat.le_refl | k j : Nat
c : j < k
eqn : skip k j = j := skip_below_eq c
⊢ j ≤ j | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
k j : Nat
c : j < k
eqn : skip k j = j := skip_below_eq c
⊢ j ≤ j
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_ge | [107, 1] | [119, 28] | rw [eqn] | k j : Nat
c : ¬j < k
eqn : skip k j = j + 1 := skip_not_below_eq k j c
⊢ j ≤ skip k j | k j : Nat
c : ¬j < k
eqn : skip k j = j + 1 := skip_not_below_eq k j c
⊢ j ≤ j + 1 | Please generate a tactic in lean4 to solve the state.
STATE:
k j : Nat
c : ¬j < k
eqn : skip k j = j + 1 := skip_not_below_eq k j c
⊢ j ≤ skip k j
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_ge | [107, 1] | [119, 28] | apply Nat.le_step | k j : Nat
c : ¬j < k
eqn : skip k j = j + 1 := skip_not_below_eq k j c
⊢ j ≤ j + 1 | case h
k j : Nat
c : ¬j < k
eqn : skip k j = j + 1 := skip_not_below_eq k j c
⊢ j ≤ j | Please generate a tactic in lean4 to solve the state.
STATE:
k j : Nat
c : ¬j < k
eqn : skip k j = j + 1 := skip_not_below_eq k j c
⊢ j ≤ j + 1
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_ge | [107, 1] | [119, 28] | apply Nat.le_refl | case h
k j : Nat
c : ¬j < k
eqn : skip k j = j + 1 := skip_not_below_eq k j c
⊢ j ≤ j | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
k j : Nat
c : ¬j < k
eqn : skip k j = j + 1 := skip_not_below_eq k j c
⊢ j ≤ j
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_gt_or_arg_below | [121, 1] | [128, 39] | rw [eqn] | k j : Nat
c : ¬j < k
eqn : skip k j = j + 1 := skip_not_below_eq k j c
⊢ j + 1 ≤ skip k j | k j : Nat
c : ¬j < k
eqn : skip k j = j + 1 := skip_not_below_eq k j c
⊢ j + 1 ≤ j + 1 | Please generate a tactic in lean4 to solve the state.
STATE:
k j : Nat
c : ¬j < k
eqn : skip k j = j + 1 := skip_not_below_eq k j c
⊢ j + 1 ≤ skip k j
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_gt_or_arg_below | [121, 1] | [128, 39] | apply Nat.le_refl | k j : Nat
c : ¬j < k
eqn : skip k j = j + 1 := skip_not_below_eq k j c
⊢ j + 1 ≤ j + 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
k j : Nat
c : ¬j < k
eqn : skip k j = j + 1 := skip_not_below_eq k j c
⊢ j + 1 ≤ j + 1
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_le_succ | [130, 1] | [135, 14] | intro hyp | n k j : Nat
⊢ j < n → skip k j < n + 1 | n k j : Nat
hyp : j < n
⊢ skip k j < n + 1 | Please generate a tactic in lean4 to solve the state.
STATE:
n k j : Nat
⊢ j < n → skip k j < n + 1
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_le_succ | [130, 1] | [135, 14] | apply Nat.le_trans (skip_lt k j) | n k j : Nat
hyp : j < n
⊢ skip k j < n + 1 | n k j : Nat
hyp : j < n
⊢ j + 2 ≤ n + 1 | Please generate a tactic in lean4 to solve the state.
STATE:
n k j : Nat
hyp : j < n
⊢ skip k j < n + 1
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_le_succ | [130, 1] | [135, 14] | apply Nat.succ_lt_succ | n k j : Nat
hyp : j < n
⊢ j + 2 ≤ n + 1 | case a
n k j : Nat
hyp : j < n
⊢ j < n | Please generate a tactic in lean4 to solve the state.
STATE:
n k j : Nat
hyp : j < n
⊢ j + 2 ≤ n + 1
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_le_succ | [130, 1] | [135, 14] | exact hyp | case a
n k j : Nat
hyp : j < n
⊢ j < n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
n k j : Nat
hyp : j < n
⊢ j < n
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_preimage_lt | [137, 1] | [153, 27] | have lem1 : i < j :=
by
rw [← eqn]
exact ineq | i j k n : Nat
kw : k < n + 1
jw : j < n + 1
eqn : skip k i = j
ineq : i + 1 ≤ skip k i
⊢ i < n | i j k n : Nat
kw : k < n + 1
jw : j < n + 1
eqn : skip k i = j
ineq : i + 1 ≤ skip k i
lem1 : i < j
⊢ i < n | Please generate a tactic in lean4 to solve the state.
STATE:
i j k n : Nat
kw : k < n + 1
jw : j < n + 1
eqn : skip k i = j
ineq : i + 1 ≤ skip k i
⊢ i < n
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_preimage_lt | [137, 1] | [153, 27] | apply Nat.lt_of_lt_of_le lem1 | i j k n : Nat
kw : k < n + 1
jw : j < n + 1
eqn : skip k i = j
ineq : i + 1 ≤ skip k i
lem1 : i < j
⊢ i < n | i j k n : Nat
kw : k < n + 1
jw : j < n + 1
eqn : skip k i = j
ineq : i + 1 ≤ skip k i
lem1 : i < j
⊢ j ≤ n | Please generate a tactic in lean4 to solve the state.
STATE:
i j k n : Nat
kw : k < n + 1
jw : j < n + 1
eqn : skip k i = j
ineq : i + 1 ≤ skip k i
lem1 : i < j
⊢ i < n
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_preimage_lt | [137, 1] | [153, 27] | apply Nat.le_of_succ_le_succ | i j k n : Nat
kw : k < n + 1
jw : j < n + 1
eqn : skip k i = j
ineq : i + 1 ≤ skip k i
lem1 : i < j
⊢ j ≤ n | case a
i j k n : Nat
kw : k < n + 1
jw : j < n + 1
eqn : skip k i = j
ineq : i + 1 ≤ skip k i
lem1 : i < j
⊢ succ j ≤ succ n | Please generate a tactic in lean4 to solve the state.
STATE:
i j k n : Nat
kw : k < n + 1
jw : j < n + 1
eqn : skip k i = j
ineq : i + 1 ≤ skip k i
lem1 : i < j
⊢ j ≤ n
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_preimage_lt | [137, 1] | [153, 27] | apply jw | case a
i j k n : Nat
kw : k < n + 1
jw : j < n + 1
eqn : skip k i = j
ineq : i + 1 ≤ skip k i
lem1 : i < j
⊢ succ j ≤ succ n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
i j k n : Nat
kw : k < n + 1
jw : j < n + 1
eqn : skip k i = j
ineq : i + 1 ≤ skip k i
lem1 : i < j
⊢ succ j ≤ succ n
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_preimage_lt | [137, 1] | [153, 27] | rw [← eqn] | i j k n : Nat
kw : k < n + 1
jw : j < n + 1
eqn : skip k i = j
ineq : i + 1 ≤ skip k i
⊢ i < j | i j k n : Nat
kw : k < n + 1
jw : j < n + 1
eqn : skip k i = j
ineq : i + 1 ≤ skip k i
⊢ i < skip k i | Please generate a tactic in lean4 to solve the state.
STATE:
i j k n : Nat
kw : k < n + 1
jw : j < n + 1
eqn : skip k i = j
ineq : i + 1 ≤ skip k i
⊢ i < j
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_preimage_lt | [137, 1] | [153, 27] | exact ineq | i j k n : Nat
kw : k < n + 1
jw : j < n + 1
eqn : skip k i = j
ineq : i + 1 ≤ skip k i
⊢ i < skip k i | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i j k n : Nat
kw : k < n + 1
jw : j < n + 1
eqn : skip k i = j
ineq : i + 1 ≤ skip k i
⊢ i < skip k i
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_preimage_lt | [137, 1] | [153, 27] | apply Nat.lt_of_lt_of_le ineqn | i j k n : Nat
kw : k < n + 1
jw : j < n + 1
eqn : skip k i = j
ineqn : i < k
⊢ i < n | i j k n : Nat
kw : k < n + 1
jw : j < n + 1
eqn : skip k i = j
ineqn : i < k
⊢ k ≤ n | Please generate a tactic in lean4 to solve the state.
STATE:
i j k n : Nat
kw : k < n + 1
jw : j < n + 1
eqn : skip k i = j
ineqn : i < k
⊢ i < n
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_preimage_lt | [137, 1] | [153, 27] | apply Nat.le_of_succ_le_succ | i j k n : Nat
kw : k < n + 1
jw : j < n + 1
eqn : skip k i = j
ineqn : i < k
⊢ k ≤ n | case a
i j k n : Nat
kw : k < n + 1
jw : j < n + 1
eqn : skip k i = j
ineqn : i < k
⊢ succ k ≤ succ n | Please generate a tactic in lean4 to solve the state.
STATE:
i j k n : Nat
kw : k < n + 1
jw : j < n + 1
eqn : skip k i = j
ineqn : i < k
⊢ k ≤ n
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_preimage_lt | [137, 1] | [153, 27] | apply kw | case a
i j k n : Nat
kw : k < n + 1
jw : j < n + 1
eqn : skip k i = j
ineqn : i < k
⊢ succ k ≤ succ n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
i j k n : Nat
kw : k < n + 1
jw : j < n + 1
eqn : skip k i = j
ineqn : i < k
⊢ succ k ≤ succ n
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_injective | [156, 1] | [194, 28] | rw [← eq1] | n j1 j2 : Nat
hyp : skip n j1 = skip n j2
p1 : j1 < n
eq1 : skip n j1 = j1 := skip_below_eq p1
p2 : j2 < n
eq2 : skip n j2 = j2 := skip_below_eq p2
⊢ j1 = j2 | n j1 j2 : Nat
hyp : skip n j1 = skip n j2
p1 : j1 < n
eq1 : skip n j1 = j1 := skip_below_eq p1
p2 : j2 < n
eq2 : skip n j2 = j2 := skip_below_eq p2
⊢ skip n j1 = j2 | Please generate a tactic in lean4 to solve the state.
STATE:
n j1 j2 : Nat
hyp : skip n j1 = skip n j2
p1 : j1 < n
eq1 : skip n j1 = j1 := skip_below_eq p1
p2 : j2 < n
eq2 : skip n j2 = j2 := skip_below_eq p2
⊢ j1 = j2
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_injective | [156, 1] | [194, 28] | rw [← eq2] | n j1 j2 : Nat
hyp : skip n j1 = skip n j2
p1 : j1 < n
eq1 : skip n j1 = j1 := skip_below_eq p1
p2 : j2 < n
eq2 : skip n j2 = j2 := skip_below_eq p2
⊢ skip n j1 = j2 | n j1 j2 : Nat
hyp : skip n j1 = skip n j2
p1 : j1 < n
eq1 : skip n j1 = j1 := skip_below_eq p1
p2 : j2 < n
eq2 : skip n j2 = j2 := skip_below_eq p2
⊢ skip n j1 = skip n j2 | Please generate a tactic in lean4 to solve the state.
STATE:
n j1 j2 : Nat
hyp : skip n j1 = skip n j2
p1 : j1 < n
eq1 : skip n j1 = j1 := skip_below_eq p1
p2 : j2 < n
eq2 : skip n j2 = j2 := skip_below_eq p2
⊢ skip n j1 = j2
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_injective | [156, 1] | [194, 28] | exact hyp | n j1 j2 : Nat
hyp : skip n j1 = skip n j2
p1 : j1 < n
eq1 : skip n j1 = j1 := skip_below_eq p1
p2 : j2 < n
eq2 : skip n j2 = j2 := skip_below_eq p2
⊢ skip n j1 = skip n j2 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n j1 j2 : Nat
hyp : skip n j1 = skip n j2
p1 : j1 < n
eq1 : skip n j1 = j1 := skip_below_eq p1
p2 : j2 < n
eq2 : skip n j2 = j2 := skip_below_eq p2
⊢ skip n j1 = skip n j2
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_injective | [156, 1] | [194, 28] | rw [← eq1] | n j1 j2 : Nat
hyp : skip n j1 = skip n j2
p1 : j1 ≥ n
eq1 : skip n j1 = succ j1 := skip_above_eq n j1 p1
p2 : j2 ≥ n
eq2 : skip n j2 = succ j2 := skip_above_eq n j2 p2
⊢ succ j1 = succ j2 | n j1 j2 : Nat
hyp : skip n j1 = skip n j2
p1 : j1 ≥ n
eq1 : skip n j1 = succ j1 := skip_above_eq n j1 p1
p2 : j2 ≥ n
eq2 : skip n j2 = succ j2 := skip_above_eq n j2 p2
⊢ skip n j1 = succ j2 | Please generate a tactic in lean4 to solve the state.
STATE:
n j1 j2 : Nat
hyp : skip n j1 = skip n j2
p1 : j1 ≥ n
eq1 : skip n j1 = succ j1 := skip_above_eq n j1 p1
p2 : j2 ≥ n
eq2 : skip n j2 = succ j2 := skip_above_eq n j2 p2
⊢ succ j1 = succ j2
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_injective | [156, 1] | [194, 28] | rw [← eq2] | n j1 j2 : Nat
hyp : skip n j1 = skip n j2
p1 : j1 ≥ n
eq1 : skip n j1 = succ j1 := skip_above_eq n j1 p1
p2 : j2 ≥ n
eq2 : skip n j2 = succ j2 := skip_above_eq n j2 p2
⊢ skip n j1 = succ j2 | n j1 j2 : Nat
hyp : skip n j1 = skip n j2
p1 : j1 ≥ n
eq1 : skip n j1 = succ j1 := skip_above_eq n j1 p1
p2 : j2 ≥ n
eq2 : skip n j2 = succ j2 := skip_above_eq n j2 p2
⊢ skip n j1 = skip n j2 | Please generate a tactic in lean4 to solve the state.
STATE:
n j1 j2 : Nat
hyp : skip n j1 = skip n j2
p1 : j1 ≥ n
eq1 : skip n j1 = succ j1 := skip_above_eq n j1 p1
p2 : j2 ≥ n
eq2 : skip n j2 = succ j2 := skip_above_eq n j2 p2
⊢ skip n j1 = succ j2
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_injective | [156, 1] | [194, 28] | exact hyp | n j1 j2 : Nat
hyp : skip n j1 = skip n j2
p1 : j1 ≥ n
eq1 : skip n j1 = succ j1 := skip_above_eq n j1 p1
p2 : j2 ≥ n
eq2 : skip n j2 = succ j2 := skip_above_eq n j2 p2
⊢ skip n j1 = skip n j2 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n j1 j2 : Nat
hyp : skip n j1 = skip n j2
p1 : j1 ≥ n
eq1 : skip n j1 = succ j1 := skip_above_eq n j1 p1
p2 : j2 ≥ n
eq2 : skip n j2 = succ j2 := skip_above_eq n j2 p2
⊢ skip n j1 = skip n j2
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_injective | [156, 1] | [194, 28] | injection eq3 | n j1 j2 : Nat
hyp : skip n j1 = skip n j2
p1 : j1 ≥ n
eq1 : skip n j1 = succ j1 := skip_above_eq n j1 p1
p2 : j2 ≥ n
eq2 : skip n j2 = succ j2 := skip_above_eq n j2 p2
eq3 : succ j1 = succ j2 :=
Eq.mpr (id (congrArg (fun _a => _a = succ j2) (Eq.symm eq1)))
(Eq.mpr (id (congrArg (fun _a => skip n j1 = _a) (Eq.symm... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n j1 j2 : Nat
hyp : skip n j1 = skip n j2
p1 : j1 ≥ n
eq1 : skip n j1 = succ j1 := skip_above_eq n j1 p1
p2 : j2 ≥ n
eq2 : skip n j2 = succ j2 := skip_above_eq n j2 p2
eq3 : succ j1 = succ j2 :=
Eq.mpr (id (congrArg (fun _a => _a = succ j2) (Eq.symm eq1)))
... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_no_fixedpoints | [196, 1] | [217, 18] | rw [←hyp] | k j : Nat
c : j < k
eqn : skip k j = j := skip_below_eq c
hyp : skip k j = k
⊢ k ≤ j | k j : Nat
c : j < k
eqn : skip k j = j := skip_below_eq c
hyp : skip k j = k
⊢ skip k j ≤ j | Please generate a tactic in lean4 to solve the state.
STATE:
k j : Nat
c : j < k
eqn : skip k j = j := skip_below_eq c
hyp : skip k j = k
⊢ k ≤ j
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_no_fixedpoints | [196, 1] | [217, 18] | rw [eqn] | k j : Nat
c : j < k
eqn : skip k j = j := skip_below_eq c
hyp : skip k j = k
⊢ skip k j ≤ j | k j : Nat
c : j < k
eqn : skip k j = j := skip_below_eq c
hyp : skip k j = k
⊢ j ≤ j | Please generate a tactic in lean4 to solve the state.
STATE:
k j : Nat
c : j < k
eqn : skip k j = j := skip_below_eq c
hyp : skip k j = k
⊢ skip k j ≤ j
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_no_fixedpoints | [196, 1] | [217, 18] | apply Nat.le_refl | k j : Nat
c : j < k
eqn : skip k j = j := skip_below_eq c
hyp : skip k j = k
⊢ j ≤ j | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
k j : Nat
c : j < k
eqn : skip k j = j := skip_below_eq c
hyp : skip k j = k
⊢ j ≤ j
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_no_fixedpoints | [196, 1] | [217, 18] | rw [←hyp] | k j : Nat
c : ¬j < k
eqn : skip k j = j + 1 := skip_not_below_eq k j c
hyp : skip k j = k
⊢ j + 1 = k | k j : Nat
c : ¬j < k
eqn : skip k j = j + 1 := skip_not_below_eq k j c
hyp : skip k j = k
⊢ j + 1 = skip k j | Please generate a tactic in lean4 to solve the state.
STATE:
k j : Nat
c : ¬j < k
eqn : skip k j = j + 1 := skip_not_below_eq k j c
hyp : skip k j = k
⊢ j + 1 = k
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_no_fixedpoints | [196, 1] | [217, 18] | rw [eqn] | k j : Nat
c : ¬j < k
eqn : skip k j = j + 1 := skip_not_below_eq k j c
hyp : skip k j = k
⊢ j + 1 = skip k j | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
k j : Nat
c : ¬j < k
eqn : skip k j = j + 1 := skip_not_below_eq k j c
hyp : skip k j = k
⊢ j + 1 = skip k j
TACTIC:
|
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