8000 feat: equality in grind linarith by leodemoura · Pull Request #8697 · leanprover/lean4 · GitHub
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Merged
merged 10 commits into from
Jun 10, 2025
Merged

feat: equality in grind linarith #8697

merged 10 commits into from
Jun 10, 2025

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This PR implements support for inequalities in the grind linear arithmetic procedure and simplifies its design. Some examples that can already be solved:

open Lean.Grind
example [IntModule α] [Preorder α] [IntModule.IsOrdered α] (a b c d : α)
    : a + d < c → b = a + (2:Int)*d → b - d > c → False := by
  grind

example [CommRing α] [LinearOrder α] [Ring.IsOrdered α] (a b : α)
    : a = 0 → b = 1 → a + b ≤ 2 := by
  grind

example [CommRing α] [Preorder α] [Ring.IsOrdered α] (a b c d e : α) :
    2*a + b ≥ 1 → b ≥ 0 → c ≥ 0 → d ≥ 0 → e ≥ 0
    → a ≥ 3*c → c ≥ 6*e → d - e*5 ≥ 0
    → a + b + 3*c + d + 2*e < 0 → False := by
  grind

@leodemoura leodemoura added the changelog-language Language features, tactics, and metaprograms label Jun 9, 2025
@leodemoura leodemoura enabled auto-merge June 9, 2025 23:18
@leodemoura leodemoura added this pull request to the merge queue Jun 9, 2025
@github-actions github-actions bot added the toolchain-available A toolchain is available for this PR, at leanprover/lean4-pr-releases:pr-release-NNNN label Jun 9, 2025
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Mathlib CI status (docs):

  • ❗ Batteries/Mathlib CI will not be attempted unless your PR branches off the nightly-with-mathlib branch. Try git rebase 41c41e455af8feb974f2607ea73af83563fc758b --onto 9b9dd8546a123d746580649b239f26c26d370d20. You can force Mathlib CI using the force-mathlib-ci label. (2025-06-09 23:44:10)

Merged via the queue into master with commit 2d67524 Jun 10, 2025
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algebraic-dev pushed a commit to algebraic-dev/lean4 that referenced this pull request Jun 18, 2025
@leodemoura @algebraic-dev
feat: equality in grind linarith (leanprover#8697)
7282bd9 
This PR implements support for inequalities in the `grind` linear
arithmetic procedure and simplifies its design. Some examples that can
already be solved:
```lean
open Lean.Grind
example [IntModule α] [Preorder α] [IntModule.IsOrdered α] (a b c d : α)
    : a + d < c → b = a + (2:Int)*d → b - d > c → False := by
  grind

example [CommRing α] [LinearOrder α] [Ring.IsOrdered α] (a b : α)
    : a = 0 → b = 1 → a + b ≤ 2 := by
  grind

example [CommRing α] [Preorder α] [Ring.IsOrdered α] (a b c d e : α) :
    2*a + b ≥ 1 → b ≥ 0 → c ≥ 0 → d ≥ 0 → e ≥ 0
    → a ≥ 3*c → c ≥ 6*e → d - e*5 ≥ 0
    → a + b + 3*c + d + 2*e < 0 → False := by
  grind
```
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