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rcases can't use rfl on 0 = a in some circumstances. #62

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kim-em opened this issue Dec 8, 2022 · 6 comments
Open

rcases can't use rfl on 0 = a in some circumstances. #62

kim-em opened this issue Dec 8, 2022 · 6 comments

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@kim-em
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kim-em commented Dec 8, 2022

import Std.Tactic.RCases

variable {α : Type _} [LT α] (a : α)

theorem lt_trichotomy (a b : α) : a < b ∨ a = b ∨ b < a := sorry

example : True := by
  rcases lt_trichotomy 0 a with (ha | rfl | ha)

Fails with
tactic 'subst' failed, 'a' occurs at 0

This breaks a proof from Algebra.Order.Ring.Defs, leanprover-community/mathlib4#905.

@digama0
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digama0 commented Dec 8, 2022

This should be fixed in subst; both versions of rcases are just calling the subst tactic so probably you can make a repro that uses only that.

@kim-em
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kim-em commented Apr 3, 2023

I guess this is a repro:

theorem foo [OfNat α 0] (a : α) : a = 0 := sorry

example (a : α) [OfNat α 0] : True := by
  let t := @foo _ ?_ a
  subst t -- fails with `'a' occurs at 0`
  
example (a : α) [OfNat α 0] : True := by
  let t := foo a
  subst t  

@kim-em
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kim-em commented Apr 3, 2023

The problem here is that substCore calls exprDependsOn, which is conservative, and looks for any metavariables which could possibly result in a dependency.

@kim-em
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kim-em commented Apr 3, 2023

@kim-em
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kim-em commented Apr 3, 2023

Per mathlib porting meeting discussion, it seems rcases should be synthesizing instances here.

@fgdorais
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Is this still an issue?

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