b6399e18c3
This PR adds support for decidable equality of empty lists and empty arrays. Decidable equality for lists and arrays is suitably modified so that all diamonds are definitionally equal. Following #9302, the strong condition of definitionally equal under `with_reducible_and_instances` is tested. This also moves some of the comments added in #9302 out of docstrings. --------- Co-authored-by: Aaron Liu <aaronliu2008@outlook.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
42 lines
1.4 KiB
Text
42 lines
1.4 KiB
Text
/--
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info: Option.map.fun_cases.{u_1} {α : Type u_1} (motive : Option α → Prop) (case1 : ∀ (x : α), motive (some x))
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(case2 : motive none) (x✝ : Option α) : motive x✝
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-/
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#guard_msgs(pass trace, all) 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 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_1} {α : Type u_1} (motive : List α → Prop) (case1 : motive [])
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(case2 : ∀ (head : α) (tail : List α), motive (head :: tail)) (x✝ : List α) : motive 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} {α : Type u} (p : α → Bool) (motive : List α → Prop) (case1 : motive [])
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(case2 : ∀ (a : α) (as : List α), p a = true → motive (a :: as))
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(case3 : ∀ (a : α) (as : List α), p a = false → motive (a :: as)) (x✝ : List α) : motive 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 (x y : Nat) (motive : Prop) (case1 : x = y → motive) (case2 : ¬x = y → motive) :
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motive
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-/
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#guard_msgs in
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#check areTheseTargetsUnchanged.fun_cases
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