e575736cae
This PR makes `fun_induction` and `fun_cases` (try to) unfold the function application of interest in the goal. The old behavior can be enabled with `set_option tactic.fun_induction.unfolding false`. For `fun_cases` this does not work yet when the function’s result type depends on one of the arguments, see issue #8296.
204 lines
4 KiB
Text
204 lines
4 KiB
Text
set_option grind.warning false
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reset_grind_attrs%
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/--
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info: Try these:
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• simp
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• simp only [ne_eq, reduceCtorEq, not_false_eq_true]
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• grind
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• grind only
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• simp_all
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-/
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#guard_msgs (info) in
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example : [1, 2] ≠ [] := by
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try?
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/--
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info: Try these:
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• simp +arith
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• simp +arith only [ge_iff_le]
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• grind
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• grind only
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-/
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#guard_msgs (info) in
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example : 4 + x + y ≥ 1 + x := by
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try?
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/--
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info: Try these:
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• simp +arith
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• grind
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-/
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#guard_msgs (info) in
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example : 4 + x + y ≥ 1 + x := by
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try? -only
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/--
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info: Try these:
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• grind
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• grind only
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-/
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#guard_msgs (info) in
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example (f : Nat → Nat) : f a = b → a = c → f c = b := by
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try?
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def f : Nat → Nat
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| 0 => 1
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| _ => 2
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/--
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info: Try these:
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• grind [= f]
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• grind only [f]
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-/
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#guard_msgs (info) in
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example : f (f 0) > 0 := by
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try?
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/--
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info: Try these:
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• grind [= f.eq_def]
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• grind only [= f.eq_def]
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-/
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#guard_msgs (info) in
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example : f x > 0 := by
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try?
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def app : List α → List α → List α
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| [], bs => bs
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| a::as, bs => a :: app as bs
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/--
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info: Try these:
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• rfl
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• grind [= app]
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• grind only [app]
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-/
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#guard_msgs (info) in
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example : app [a, b] [c] = [a, b, c] := by
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try?
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/--
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info: Try these:
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• (fun_induction app as bs) <;> grind [= app]
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• (fun_induction app as bs) <;> grind only [app]
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-/
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#guard_msgs (info) in
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example : app (app as bs) cs = app as (app bs cs) := by
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try?
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/-- info: Try this: (fun_induction app as bs) <;> grind [= app] -/
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#guard_msgs (info) in
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example : app (app as bs) cs = app as (app bs cs) := by
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try? (max := 1)
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/--
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info: Try these:
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• · expose_names; fun_induction app as bs_1 <;> grind [= app]
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• · expose_names; fun_induction app as bs_1 <;> grind only [app]
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-/
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#guard_msgs (info) in
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example : app (app as bs) cs = app as (app bs cs) := by
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have bs := 20 -- shadow variable in the goal
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try?
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/--
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info: Try these:
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• · expose_names; fun_induction app as bs <;> grind [= app]
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• · expose_names; fun_induction app as bs <;> grind only [app]
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-/
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#guard_msgs (info) in
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example : app (app as bs) cs = app as (app bs cs) := by
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revert as bs cs
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intro _ _ _
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-- `as`, `bs`, and `cs` now have inaccessible names.
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try?
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def concat : List α → α → List α
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| .nil, b => .cons b .nil
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| .cons a as, b => .cons a (concat as b)
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attribute [simp] concat
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/--
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info: Try these:
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• (fun_induction concat) <;> simp_all
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• (fun_induction concat) <;> simp [*]
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-/
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#guard_msgs (info) in
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example (as : List α) (a : α) : concat as a = as ++ [a] := by
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try? -only
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/--
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info: Try these:
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• (fun_induction concat) <;> simp_all
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• · fun_induction concat
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· simp
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· simp [*]
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-/
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#guard_msgs (info) in
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example (as : List α) (a : α) : concat as a = as ++ [a] := by
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try? -only -merge
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def map (f : α → β) : List α → List β
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| [] => []
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| x::xs => f x :: map f xs
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/--
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info: Try these:
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• (fun_induction map f xs) <;> grind [= map]
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• (fun_induction map f xs) <;> grind only [map]
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-/
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#guard_msgs (info) in
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theorem map_map (f : α → β) (g : β → γ) xs :
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map g (map f xs) = map (fun x => g (f x)) xs := by
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try?
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def foo : Nat → Nat
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| 0 => 1
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| x+1 => foo x - 1
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/--
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info: Try these:
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• · fun_induction foo
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· simp
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· sorry
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• · fun_induction foo
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· grind
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· sorry
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• · fun_induction foo
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· simp_all
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· sorry
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-/
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#guard_msgs (info) in
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example : foo x > 0 := by
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try? +missing -only -- `try?` does not solve all subgoals.
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sorry
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/--
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error: tactic 'try?' failed, consider using `grind` manually, or `try? +missing` for partial proofs containing `sorry`
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x : Nat
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⊢ foo x > 0
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-/
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#guard_msgs (error) in
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example : foo x > 0 := by
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try?
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@[simp] def bla : List Nat → List Nat → List Nat
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| [], ys => ys.reverse
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| _::xs, ys => bla xs ys
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attribute [grind] List.length_reverse bla
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/--
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info: Try these:
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• (fun_induction bla) <;> grind
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• (fun_induction bla) <;> simp_all
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• (fun_induction bla) <;> simp [*]
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• (fun_induction bla) <;> simp only [List.length_reverse, *]
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• (fun_induction bla) <;> grind only [List.length_reverse]
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-/
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#guard_msgs (info) in
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example : (bla xs ys).length = ys.length := by
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try?
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