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Commit 2021-06-10 16:03 49f5a159

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feat(algebra/ordered_ring): more granular typeclasses for with_top α 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.

Estimated changes

added theorem with_bot.bot_lt_mul
added theorem with_bot.bot_mul
added theorem with_bot.bot_mul_bot
added theorem with_bot.coe_mul
added theorem with_bot.mul_bot
added theorem with_bot.mul_coe
added theorem with_bot.mul_def
modified theorem with_top.mul_lt_top
deleted theorem ereal.ad_eq_top_iff
added theorem ereal.add_eq_top_iff
added theorem ereal.bot_mul_bot
added theorem ereal.bot_mul_coe
added theorem ereal.bot_sub_coe
added theorem ereal.bot_sub_top
added theorem ereal.coe_mul
added theorem ereal.coe_mul_bot
added theorem ereal.coe_one
added theorem ereal.coe_sub_bot
added theorem ereal.mul_top
added theorem ereal.sub_bot
added theorem ereal.to_real_mul
added theorem ereal.to_real_one
added theorem ereal.top_mul
added theorem ereal.top_sub