[Merged by Bors] - chore(*): don't assume sub_eq_add_neg and div_eq_mul_inv are defeq
#5302
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This commit prepares for a follow-up that makes `div` and `sub` fields in (`add_`)`group`(`_with_zero`).
Vierkantor
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(Because fields don't extend `div_inv_monoid` yet.)
Vierkantor
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Since the PR is still getting errors, I'm marking it as WIP until it compiles again. |
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I have fixed |
sgouezel
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Great, thank you so much! |
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The linter complains. I'll let you fix it, then I'll review your changes (and you will have to review mine!) |
Vierkantor
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Dec 11, 2020
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Let's merge this. Thanks a lot! |
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#5302) This PR prepares for a follow-up PR (#5303) that adds `div` and `sub` fields to (`add_`)`group`(`_with_zero`). That follow-up PR is intended to fix the following kind of diamonds: Let `foo X` be a type with a `∀ X, has_div (foo X)` instance but no `∀ X, has_inv (foo X)`, e.g. when `foo X` is a `euclidean_domain`. Suppose we also have an instance `∀ X [cromulent X], group_with_zero (foo X)`. Then the `(/)` coming from `group_with_zero_has_div` cannot be defeq to the `(/)` coming from `foo.has_div`. As a consequence of making the `has_div` instances defeq, we can no longer assume that `(div_eq_mul_inv a b : a / b = a * b⁻¹) = rfl` for all groups. This preparation PR should have changed all places in mathlib that assumed defeqness, to rewrite explicitly instead. Zulip thread: https://leanprover.zulipchat.com/#narrow/stream/113488-general/topic/.60div.60.20as.20a.20field.20in.20.60group(_with_zero).60 Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr>
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Pull request successfully merged into master. Build succeeded: |
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sub_eq_add_neg and div_eq_mul_inv are defeqsub_eq_add_neg and div_eq_mul_inv are defeq
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…5303) This PR is intended to fix the following kind of diamonds: Let `foo X` be a type with a `∀ X, has_div (foo X)` instance but no `∀ X, has_inv (foo X)`, e.g. when `foo X` is a `euclidean_domain`. Suppose we also have an instance `∀ X [cromulent X], group_with_zero (foo X)`. Then the `(/)` coming from `group_with_zero_has_div` cannot be defeq to the `(/)` coming from `foo.has_div`. As a consequence of making the `has_div` instances defeq, we can no longer assume that `(div_eq_mul_inv a b : a / b = a * b⁻¹) = rfl` for all groups. The previous preparation PR #5302 should have changed all places in mathlib that assumed defeqness, to rewrite explicitly instead. Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>
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This PR prepares for a follow-up PR (#5303) that adds
divandsubfields to (add_)group(_with_zero). That follow-up PR is intended to fix the following kind of diamonds:Let
foo Xbe a type with a∀ X, has_div (foo X)instance but no∀ X, has_inv (foo X), e.g. whenfoo Xis aeuclidean_domain. Suppose we also have an instance∀ X [cromulent X], group_with_zero (foo X). Then the(/)coming fromgroup_with_zero_has_divcannot be defeq to the(/)coming fromfoo.has_div.As a consequence of making the
has_divinstances defeq, we can no longer assume that(div_eq_mul_inv a b : a / b = a * b⁻¹) = rflfor all groups. This preparation PR should have changed all places in mathlib that assumed defeqness, to rewrite explicitly instead.Zulip thread: https://leanprover.zulipchat.com/#narrow/stream/113488-general/topic/.60div.60.20as.20a.20field.20in.20.60group(_with_zero).60