feat: Field support in grind ring
#8777
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algebraic-dev
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to algebraic-dev/lean4
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Jun 18, 2025
This PR implements basic `Field` support in the commutative ring module
in `grind`. It is just division by numerals for now. Examples:
```lean
open Lean Grind
example [Field α] [IsCharP α 0] (a b c : α) : a/3 = b → c = a/3 → a/2 + a/2 = b + 2*c := by
grind
example [Field α] (a b : α) : b = 0 → (a + a) / 0 = b := by
grind
example [Field α] [IsCharP α 3] (a b : α) : a/3 = b → b = 0 := by
grind
example [Field α] [IsCharP α 7] (a b c : α) : a/3 = b → c = a/3 → a/2 + a/2 = b + 2*c + 7 := by
grind
example [Field R] [IsCharP R 0] (x : R) (cos : R → R) :
(cos x ^ 2 + (2 * cos x ^ 2 - 1) ^ 2 + (4 * cos x ^ 3 - 3 * cos x) ^ 2 - 1) / 4 =
cos x * (cos x ^ 2 - 1 / 2) * (4 * cos x ^ 3 - 3 * cos x) := by
grind
```
wkrozowski
pushed a commit
to wkrozowski/lean4
that referenced
this pull request
Jun 24, 2025
This PR implements basic `Field` support in the commutative ring module
in `grind`. It is just division by numerals for now. Examples:
```lean
open Lean Grind
example [Field α] [IsCharP α 0] (a b c : α) : a/3 = b → c = a/3 → a/2 + a/2 = b + 2*c := by
grind
example [Field α] (a b : α) : b = 0 → (a + a) / 0 = b := by
grind
example [Field α] [IsCharP α 3] (a b : α) : a/3 = b → b = 0 := by
grind
example [Field α] [IsCharP α 7] (a b c : α) : a/3 = b → c = a/3 → a/2 + a/2 = b + 2*c + 7 := by
grind
example [Field R] [IsCharP R 0] (x : R) (cos : R → R) :
(cos x ^ 2 + (2 * cos x ^ 2 - 1) ^ 2 + (4 * cos x ^ 3 - 3 * cos x) ^ 2 - 1) / 4 =
cos x * (cos x ^ 2 - 1 / 2) * (4 * cos x ^ 3 - 3 * cos x) := by
grind
```
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This PR implements basic
Fieldsupport in the commutative ring module ingrind. It is just division by numerals for now. Examples: