Commit graph

9 commits

Author SHA1 Message Date
Kim Morrison
6970d77ae4
feat: the grothendieck envelope of an ordered semiring is an ordered ring (#8959)
This PR add instances showing that the Grothendieck (i.e. additive)
envelope of a semiring is an ordered ring if the original semiring is
ordered (and satisfies ExistsAddOfLE), and in this case the embedding is
monotone.
2025-06-24 03:23:18 +00:00
Kim Morrison
8f4b2909de
chore: cleanup of grind's order typeclasses (#8913)
This PR cleans up `grind`'s internal order typeclasses, removing
unnecessary duplication.
2025-06-22 23:36:48 +00:00
Leonardo de Moura
7531d16112
feat: (commutative) semiring support in grind (#8921)
This PR implements support for (commutative) semirings in `grind`. It
uses the Grothendieck completion to construct a (commutative) ring
`Lean.Grind.Ring.OfSemiring.Q α` from a (commutative) semiring `α`. This
construction is mostly useful for semirings that implement
`AddRightCancel α`. Otherwise, the function `toQ` is not injective.
Examples:
```lean
example (x y : Nat) : x^2*y = 1 → x*y^2 = y → y*x = 1 := by
  grind 

example [CommSemiring α] [AddRightCancel α] (x y : α) : x^2*y = 1 → x*y^2 = y → y*x = 1 := by
  grind

example (a b : Nat) : 3 * a * b = a * b * 3 := by grind

example (k z : Nat) : k * (z * 2 * (z * 2 + 1)) = z * (k * (2 * (z * 2 + 1))) := by grind

example [CommSemiring α] [AddRightCancel α] [IsCharP α 0] (x y : α) 
    : x^2*y = 1 → x*y^2 = y → x + y = 1 → False := by
  grind
```
2025-06-21 23:00:16 +00:00
Joachim Breitner
61518e4357
chore: remove more unused simp args (#8920)
This PR uses the linter from #8901 to clean up more simp arguments,
completing #8905.
2025-06-21 18:34:17 +00:00
Leonardo de Moura
9ece4e463a
refactor: NoNatZeroDivisors (#8909)
This PR refactors the `NoNatZeroDivisors` to make sure it will work with
the new `Semiring` support.
2025-06-21 03:01:05 +00:00
Joachim Breitner
be80a23281
chore: remove unused simp args (#8905)
This PR uses the linter from
https://github.com/leanprover/lean4/pull/8901 to clean up simp
arguments.
2025-06-20 22:34:30 +00:00
Kim Morrison
827c69e46e
feat: generalize Lean.Grind.IsCharP to semirings (#8847)
This PR relaxes the assumptions for `Lean.Grind.IsCharP` from `Ring` to
`Semiring`, and provides an alternative constructor for rings.
2025-06-19 04:39:53 +00:00
Kim Morrison
259e2ec3e8
feat: define the CommRing envelope of a CommSemiring (#8835)
This PR defines the embedding of a `CommSemiring` into its `CommRing`
envelope, injective when the `CommSemiring` is cancellative. This will
be used by `grind` to prove results in `Nat`.
2025-06-17 05:39:14 +00:00
Kim Morrison
f557bf6024
chore: move grind algebra instances into Init.GrindInstances (#8830)
This PR rearranges files under `Init.Grind`, moving out instances for
concrete algebraic types in `Init.GrindInstances`.
2025-06-17 03:59:15 +00:00