[Merged by Bors] - refactor(algebra/*): small API fixes #3157
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…ally_ordered_comm_semiring` * merge `associates.mk_zero_eq` and `associates.mk_eq_zero_iff_eq_zero` into `associates.mk_eq_zero`; * drop `associates.mul_zero`, `associates.zero_mul`, `associates.zero_ne_one`, and `associates.mul_eq_zero_iff` in favor of typeclass instances; * use `to_additive` for `with_top.has_one`, `with_top.coe_one` etc; * move `with_top.coe_ne_zero` to `algebra.ordered_group`; * add `with_top.has_add`, make `coe_add`, `coe_bit*` require only `[has_add α]`; * in the definition of `canonically_ordered_comm_semiring` replace `mul_eq_zero_iff` with `eq_zero_or_eq_zero_of_mul_eq_zero`; the other implication is always true because of `[semiring]`; * add instance `canonically_ordered_comm_semiring.to_no_zero_divisors`; * use proper instances for lemmas about multiplication in `with_top`, not just `canonically_ordered_comm_semiring` for everything; * drop `mul_eq_zero_iff_eq_zero_or_eq_zero` in favor of `mul_eq_zero`; * drop `ennreal.mul_eq_zero` in favor of `mul_eq_zero` from instance.
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## Changes to `canonically_ordered_comm_semiring` * in the definition of `canonically_ordered_comm_semiring` replace `mul_eq_zero_iff` with `eq_zero_or_eq_zero_of_mul_eq_zero`; the other implication is always true because of `[semiring]`; * add instance `canonically_ordered_comm_semiring.to_no_zero_divisors`; ## Changes to `with_top` * use `to_additive` for `with_top.has_one`, `with_top.coe_one` etc; * move `with_top.coe_ne_zero` to `algebra.ordered_group`; * add `with_top.has_add`, make `coe_add`, `coe_bit*` require only `[has_add α]`; * use proper instances for lemmas about multiplication in `with_top`, not just `canonically_ordered_comm_semiring` for everything; ## Changes to `associates` * merge `associates.mk_zero_eq` and `associates.mk_eq_zero_iff_eq_zero` into `associates.mk_eq_zero`; * drop `associates.mul_zero`, `associates.zero_mul`, `associates.zero_ne_one`, and `associates.mul_eq_zero_iff` in favor of typeclass instances; ## Misc changes * drop `mul_eq_zero_iff_eq_zero_or_eq_zero` in favor of `mul_eq_zero`; * drop `ennreal.mul_eq_zero` in favor of `mul_eq_zero` from instance.
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## Changes to `canonically_ordered_comm_semiring` * in the definition of `canonically_ordered_comm_semiring` replace `mul_eq_zero_iff` with `eq_zero_or_eq_zero_of_mul_eq_zero`; the other implication is always true because of `[semiring]`; * add instance `canonically_ordered_comm_semiring.to_no_zero_divisors`; ## Changes to `with_top` * use `to_additive` for `with_top.has_one`, `with_top.coe_one` etc; * move `with_top.coe_ne_zero` to `algebra.ordered_group`; * add `with_top.has_add`, make `coe_add`, `coe_bit*` require only `[has_add α]`; * use proper instances for lemmas about multiplication in `with_top`, not just `canonically_ordered_comm_semiring` for everything; ## Changes to `associates` * merge `associates.mk_zero_eq` and `associates.mk_eq_zero_iff_eq_zero` into `associates.mk_eq_zero`; * drop `associates.mul_zero`, `associates.zero_mul`, `associates.zero_ne_one`, and `associates.mul_eq_zero_iff` in favor of typeclass instances; ## Misc changes * drop `mul_eq_zero_iff_eq_zero_or_eq_zero` in favor of `mul_eq_zero`; * drop `ennreal.mul_eq_zero` in favor of `mul_eq_zero` from instance.
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Changes to
canonically_ordered_comm_semiringcanonically_ordered_comm_semiringreplacemul_eq_zero_iffwitheq_zero_or_eq_zero_of_mul_eq_zero; the otherimplication is always true because of
[semiring];canonically_ordered_comm_semiring.to_no_zero_divisors;Changes to
with_topto_additiveforwith_top.has_one,with_top.coe_oneetc;with_top.coe_ne_zerotoalgebra.ordered_group;with_top.has_add, makecoe_add,coe_bit*require only[has_add α];with_top, notjust
canonically_ordered_comm_semiringfor everything;Changes to
associatesassociates.mk_zero_eqandassociates.mk_eq_zero_iff_eq_zerointoassociates.mk_eq_zero;associates.mul_zero,associates.zero_mul,associates.zero_ne_one,and
associates.mul_eq_zero_iffin favor of typeclass instances;Misc changes
mul_eq_zero_iff_eq_zero_or_eq_zeroin favor ofmul_eq_zero;ennreal.mul_eq_zeroin favor ofmul_eq_zerofrom instance.Waiting for CI to see if I broke something.