[Merged by Bors] - feat(algebra/ordered_ring): more granular typeclasses for with_top α and with_bot α
#7845
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`with_top α` now inherits the following typeclasses from `α` with suitable assumptions: * `mul_zero_one_class` * `semigroup_with_zero` * `monoid_with_zero` * `comm_monoid_with_zero` These were all split out of the existing `canonically_ordered_comm_semiring`, with their proofs unchanged. It is not possible to split further, as `distrib'` requires `add_eq_zero_iff`, and `canonically_ordered_comm_semiring` is the smallest typeclass that provides both this lemma and `mul_zero_class`.
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| with_top.coe_mul.symm.trans $ | ||
| with_bot.coe_eq_coe.mpr $ with_bot.mul_bot $ function.injective.ne (@option.some.inj _) h | ||
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| lemma to_real_mul : ∀ {x y : ereal} (hx : x ≠ ⊤) (h'x : x ≠ ⊥) (hy : y ≠ ⊤) (h'y : y ≠ ⊥), |
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I think this holds without any assumptions on x or y.
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I copied this lemma from the one about add, but maybe you're right
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Good catch, I was able to remove all the assumptions.
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Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr>
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…` and `with_bot α` (#7845) `with_top α` and `with_bot α` now inherit the following typeclasses from `α` with suitable assumptions: * `mul_zero_one_class` * `semigroup_with_zero` * `monoid_with_zero` * `comm_monoid_with_zero` These were all split out of the existing `canonically_ordered_comm_semiring`, with their proofs unchanged. The same instances are added for `with_bot`. It is not possible to split further, as `distrib'` requires `add_eq_zero_iff`, and `canonically_ordered_comm_semiring` is the smallest typeclass that provides both this lemma and `mul_zero_class`. With these instances in place, we can now show `comm_monoid_with_zero ereal`.
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with_top αandwith_bot αnow inherit the following typeclasses fromαwith suitable assumptions:mul_zero_one_classsemigroup_with_zeromonoid_with_zerocomm_monoid_with_zeroThese were all split out of the existing
canonically_ordered_comm_semiring, with their proofs unchanged.The same instances are added for
with_bot.It is not possible to split further, as
distrib'requiresadd_eq_zero_iff, andcanonically_ordered_comm_semiringis the smallest typeclass that provides both this lemma andmul_zero_class.With these instances in place, we can now show
comm_monoid_with_zero ereal.