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.
48 lines
2 KiB
Text
48 lines
2 KiB
Text
/--
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info: Option.map.fun_cases.{u_1, u_2} (motive : {α : Type u_1} → {β : Type u_2} → (α → β) → Option α → Prop)
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(case1 : ∀ {α : Type u_1} {β : Type u_2} (f : α → β) (x : α), motive f (some x))
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(case2 : ∀ {α : Type u_1} {β : Type u_2} (f : α → β), motive f none) {α : Type u_1} {β : Type u_2} (f : α → β)
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(x✝ : Option α) : motive f x✝
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-/
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#guard_msgs in
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#check Option.map.fun_cases
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example (x : Option Nat) (f : Nat → Nat) : (x.map f).isSome = x.isSome := by
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cases f, x using Option.map.fun_cases
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case case1 x => simp
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case case2 => simp
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/--
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info: List.map.fun_cases.{u, v} (motive : {α : Type u} → {β : Type v} → (α → β) → List α → Prop)
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(case1 : ∀ {α : Type u} {β : Type v} (f : α → β), motive f [])
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(case2 : ∀ {α : Type u} {β : Type v} (f : α → β) (a : α) (as : List α), motive f (a :: as)) {α : Type u} {β : Type v}
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(f : α → β) (x✝ : List α) : motive f x✝
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-/
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#guard_msgs in
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#check List.map.fun_cases
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/--
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info: List.find?.fun_cases.{u} (motive : {α : Type u} → (α → Bool) → List α → Prop)
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(case1 : ∀ {α : Type u} (p : α → Bool), motive p [])
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(case2 : ∀ {α : Type u} (p : α → Bool) (a : α) (as : List α), p a = true → motive p (a :: as))
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(case3 : ∀ {α : Type u} (p : α → Bool) (a : α) (as : List α), p a = false → motive p (a :: as)) {α : Type u}
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(p : α → Bool) (x✝ : List α) : motive p x✝
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-/
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#guard_msgs in
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#check List.find?.fun_cases
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-- This tests shows that its not so easy to post-hoc recognize that `x` could be a parameter, but
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-- `y` should be a target of the `fun_cases` principle (or the other way around)
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def areTheseTargetsUnchanged (x y : Nat) : Bool :=
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if _ : x = y then
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true
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else
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false
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/--
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info: areTheseTargetsUnchanged.fun_cases (motive : Nat → Nat → Prop) (case1 : ∀ (y : Nat), motive y y)
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(case2 : ∀ (x y : Nat), ¬x = y → motive x y) (x y : Nat) : motive x y
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-/
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#guard_msgs in
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#check areTheseTargetsUnchanged.fun_cases
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