54a88e941f
This PR adds additional test coverage for #11758 (fix for #11745: nonstandard instances in grind and simp +arith). The existing test `grind_11745.lean` only covers Int LE with `grind -order` and `lia -order`. This adds tests for: - LT instances (Int and Nat) - Nat LE instances - Mixed canonical and non-canonical instances in the same goal - Equality derived from two LE constraints - `simp +arith` with non-canonical instances 🤖 Prepared with Claude Code Co-authored-by: Claude <noreply@anthropic.com>
70 lines
2.1 KiB
Text
70 lines
2.1 KiB
Text
/-
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Additional tests for #11745: nonstandard instances in grind and simp +arith
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These extend the basic tests in grind_11745.lean
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-/
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-- Setup: non-canonical LE and LT instances via class extension
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class Preorder (α : Type u) extends LE α
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class StrictPreorder (α : Type u) extends LT α
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instance instPreorderInt : Preorder Int where
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instance instStrictPreorderInt : StrictPreorder Int where
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instance instPreorderNat : Preorder Nat where
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instance instStrictPreorderNat : StrictPreorder Nat where
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-- LT instances (Int)
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example (x y : Int) (h : @LT.lt Int instStrictPreorderInt.toLT x y) : x < y := by
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grind -order
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example (x y : Int) (h : @LT.lt Int instStrictPreorderInt.toLT x y) : x < y := by
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lia -order
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-- Nat LE instances
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example (x y : Nat) (h : @LE.le Nat instPreorderNat.toLE x y) : x ≤ y := by
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grind -order
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example (x y : Nat) (h : @LE.le Nat instPreorderNat.toLE x y) : x ≤ y := by
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lia -order
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-- Nat LT instances
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example (x y : Nat) (h : @LT.lt Nat instStrictPreorderNat.toLT x y) : x < y := by
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grind -order
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example (x y : Nat) (h : @LT.lt Nat instStrictPreorderNat.toLT x y) : x < y := by
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lia -order
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-- Mixed canonical and non-canonical instances
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example (x y z : Int)
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(h1 : @LE.le Int instPreorderInt.toLE x y) -- non-canonical
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(h2 : y ≤ z) -- canonical
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: x ≤ z := by
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grind -order
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example (x y z : Int)
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(h1 : @LE.le Int instPreorderInt.toLE x y)
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(h2 : y ≤ z)
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: x ≤ z := by
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lia -order
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-- Equality derived from two LE constraints
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example (x y : Int)
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(h1 : @LE.le Int instPreorderInt.toLE x y)
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(h2 : @LE.le Int instPreorderInt.toLE y x)
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: x = y := by
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grind -order
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example (x y : Int)
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(h1 : @LE.le Int instPreorderInt.toLE x y)
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(h2 : @LE.le Int instPreorderInt.toLE y x)
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: x = y := by
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lia -order
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-- simp +arith with non-canonical instances
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example (c x : Int) (mx : @LE.le Int instPreorderInt.toLE x c) : x ≤ c := by
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simp +arith [mx]
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example (c x : Int) (mx : @LT.lt Int instStrictPreorderInt.toLT x c) : x < c := by
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simp +arith [mx]
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example (c x : Nat) (mx : @LE.le Nat instPreorderNat.toLE x c) : x ≤ c := by
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simp +arith [mx]
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