f8cdb03352
This PR add constructors `.intCast k` and `.natCast k` to
`CommRing.Expr`. We need them because terms such as `Nat.cast (R := α)
1` and `(1 : α)` are not definitionally equal. This is pervaise in
Mathlib for the numerals `0` and `1`.
```lean
import Mathlib
example {α : Type} [AddMonoidWithOne α] : Nat.cast (R := α) 0 = (0 : α) := rfl -- not defeq
example {α : Type} [AddMonoidWithOne α] : Nat.cast (R := α) 1 = (1 : α) := rfl -- not defeq
example {α : Type} [AddMonoidWithOne α] : Nat.cast (R := α) 2 = (2 : α) := rfl -- defeq from here
-- Similarly for everything past `AddMonoidWithOne` in the Mathlib hierarchy, e.g. `Ring`.
```
15 lines
458 B
Text
15 lines
458 B
Text
open Lean Grind
|
||
|
||
attribute [local instance] Semiring.natCast Ring.intCast
|
||
|
||
example [CommRing α] (a : α) : Int.cast (R := α) (-2) = a → a + 2 = 0 := by
|
||
grind
|
||
|
||
example [CommRing α] (a : α) : Nat.cast (R := α) 2 = a → a - 2 = 0 := by
|
||
grind
|
||
|
||
example [CommRing α] [IsCharP α 4] (a : α) : Int.cast (R := α) (-2) = a → a + 2 = 0 := by
|
||
grind
|
||
|
||
example [CommRing α] [IsCharP α 4] (a : α) : Nat.cast (R := α) 2 = a → a - 2 = 0 := by
|
||
grind
|