feat(algebra/order_operation_defs): introduce new typeclasses for mixing orders and binary operations #7396
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sgouezel
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Apr 28, 2021
eric-wieser
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Apr 28, 2021
following Sébastien's and Eric's suggestions
eric-wieser
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Apr 28, 2021
adomani
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Vierkantor
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May 4, 2021
eric-wieser
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May 4, 2021
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| -- TODO: convert `has_exists_mul_of_le`, `has_exists_add_of_le`? | ||
| -- TODO: relationship with add_con | ||
| -- include equivalence of `left_cancel_semigroup` with | ||
| -- `semigroup partial_order contravariant_class α α (*) (≤)`? | ||
| -- use ⇒, as per Eric's suggestion? |
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Are these TODOs for a later PR, or for iterations of this one?
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I am planning to take these on, though I had been experimenting with a newer PR. I will get back to working on this next week.
eric-wieser
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May 4, 2021
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| lemma is_symm_op.swap_eq {α β} (op) [is_symm_op α β op] : flip op = op := | ||
| funext $ λ a, funext $ λ b, (is_symm_op.symm_op a b).symm |
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This belongs somewhere way more basic; perhaps function.basic or even logic.basic.
eric-wieser
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May 4, 2021
Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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Dear Anne and Eric, Thank you for your comments! I will take a look at this PR again next week and will get back to you! |
Vierkantor
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This can be closed now, right? |
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This PR revises and splits off the definitions of PR #7371.
I introduce two definitions, like in the other PR:
covariantandcontravariant. They are definitions instead of classes since, if I understood correctly, Sébastien said that they would burden the typeclass search system.Using these definitions, I then introduce 16 new classes, each one saying that addition/multiplication is left/right monotone in various convenient ways. They system is heavily based on the original
ordered_[...]hierarchy, except that now it is possible to mix-and-match assumptions on the algebraic side and on the order side.I also provide instances to show that
(≤)assumptions imply(<)assumptions, if the order is linear.Zulip discussion:
https://leanprover.zulipchat.com/#narrow/stream/116395-maths/topic/ordered.20stuff