a31eb94e5a
This PR implements `NatModule` normalization when the `AddRightCancel`
instance is not available. Note that in this case, the embedding into
`IntModule` is not injective. Therefore, we use a custom normalizer,
similar to the `CommSemiring` normalizer used in the `grind ring`
module. Example:
```lean
open Lean Grind
example [NatModule α] (a b c : α)
: 2•a + 2•(b + 2•c) + 3•a = 4•a + c + 2•b + 3•c + a := by
grind
```
14 lines
656 B
Text
14 lines
656 B
Text
open Lean.Grind
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variable (R : Type u) [NatModule R]
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example (a b : R) : a + b = b + a := by grind
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example (a : R) : a + 0 = a := by grind
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example (a : R) : 0 + a = a := by grind
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example (a b c : R) : a + b + c = a + (b + c) := by grind
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example (a : R) : 2 • a = a + a := by grind
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example (b c : R) : 2 • (b + c) = c + 2 • b + c := by grind
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example (a b c : R) : 2•a + 2•(b + 2•c) + 3•a = 4•a + c + 2•b + 3•c + a := by grind
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example (a : R) : 2 • a = a + 0 + a + 2•0 := by grind
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example (a : R) : 2 • (a + 0) = a + 0 + a + 2•Zero.zero := by grind
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example (a : R) : 2 • (a + Zero.zero) = a + 0 + a + 2•Zero.zero := by grind
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