This PR resolves a defeq diamond, which caused a problem in Mathlib:
```
import Mathlib
example (R : Type) [I : Ring R] :
@AddCommGroup.toGrindIntModule R (@Ring.toAddCommGroup R I) =
@Lean.Grind.Ring.instIntModule R (@Ring.toGrindRing R I) := rfl -- fails
```
This PR uses the commutative ring module to normalize nonlinear
polynomials in `grind cutsat`. Examples:
```lean
example (a b : Nat) (h₁ : a + 1 ≠ a * b * a) (h₂ : a * a * b ≤ a + 1) : b * a^2 < a + 1 := by
grind
example (a b c : Int) (h₁ : a + 1 + c = b * a) (h₂ : c + 2*b*a = 0) : 6 * a * b - 2 * a ≤ 2 := by
grind
```
This PR implements support for equations `<num> = 0` in rings and fields
of unknown characteristic. Examples:
```lean
example [Field α] (a : α) : (2 * a)⁻¹ = a⁻¹ / 2 := by grind
example [Field α] (a : α) : (2 : α) ≠ 0 → 1 / a + 1 / (2 * a) = 3 / (2 * a) := by grind
example [CommRing α] (a b : α) (h₁ : a + 2 = a) (h₂ : 2*b + a = 0) : a = 0 := by
grind
example [CommRing α] (a b : α) (h₁ : a + 6 = a) (h₂ : b + 9 = b) (h₂ : 3*b + a = 0) : a = 0 := by
grind
example [CommRing α] (a b : α) (h₁ : a + 6 = a) (h₂ : b + 9 = b) (h₂ : 3*b + a = 0) : a = 0 := by
grind
example [CommRing α] (a b : α) (h₁ : a + 2 = a) (h₂ : b = 0) : 4*a + b = 0 := by
grind
example [CommRing α] (a b c : α) (h₁ : a + 6 = a) (h₂ : c = c + 9) (h : b + 3*c = 0) : 27*a + b = 0 := by
grind
```
This PR embeds a NatModule into its IntModule completion, which is
injective when we have AddLeftCancel, and monotone when the modules are
ordered. Also adds some (failing) grind test cases that can be verified
once `grind` uses this embedding.
This PR implements support for normalization for commutative semirings
that do not implement `AddRightCancel`. Examples:
```lean
variable (R : Type u) [CommSemiring R]
example (a b c : R) : a * (b + c) = a * c + b * a := by grind
example (a b : R) : (a + b)^2 = a^2 + 2 * a * b + b^2 := by grind
example (a b : R) : (a + 2 * b)^2 = a^2 + 4 * a * b + 4 * b^2 := by grind
example (a b : R) : (a + 2 * b)^2 = 4 * b^2 + b * 4 * a + a^2 := by grind
```
This PR implements equality elimination in `grind linarith`. The current
implementation supports only `IntModule` and `IntModule` +
`NoNatZeroDivisors`
This PR implements the Rabinowitsch transformation for `Field`
disequalities in `grind`. For example, this transformation is necessary
for solving:
```lean
example [Field α] (a : α) : a^2 = 0 → a = 0 := by
grind
```
