[Merged by Bors] - feat: make MulOpposite and AddOpposite structures #1036
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gebner
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Dec 15, 2022
| @@ -343,8 +351,10 @@ theorem op_div [Div α] (a b : α) : op (a / b) = op a / op b := | |||
| rfl | |||
| #align add_opposite.op_div AddOpposite.op_div | |||
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| -- porting note: this lemma looked wrong to me -- is it wrong in mathlib3? | |||
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I agree, this is wrong in mathlib3. We didn't notice this because / is the same operation on αᵃᵒᵖ and α and so it still works as a simp lemma.
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This is not linting right now; I asked at https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/possible.20linter.20bugs/near/316074640 |
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This refactor makes `αᵐᵒᵖ` and `αᵃᵒᵖ` into structures with one field, an idea more appropriate in Lean 4 than the Lean 3 approach of type synonyms.
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It turns out to be convenient to have `MulOpposite α = AddOpposite α` true by definition, in the same way that it is convenient to have `Additive α = α`; this means that we also get the defeq `AddOpposite (Additive α) = MulOpposite α`, which is convenient when working with quotients. This is a compromise between making `MulOpposite α = AddOpposite α = α` (what we had in Lean 3) and having no defeqs within those three types (which we had as of #1036). This is motivated by #3333
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It turns out to be convenient to have `MulOpposite α = AddOpposite α` true by definition, in the same way that it is convenient to have `Additive α = α`; this means that we also get the defeq `AddOpposite (Additive α) = MulOpposite α`, which is convenient when working with quotients. This is a compromise between making `MulOpposite α = AddOpposite α = α` (what we had in Lean 3) and having no defeqs within those three types (which we had as of leanprover-community#1036). This is motivated by leanprover-community#3333
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This refactor makes
αᵐᵒᵖandαᵃᵒᵖinto structures with one field, an idea more appropriate in Lean 4 than the Lean 3 approach of type synonyms.