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[Merged by Bors] - feat(data/list/min_max): maximum is a fold, bounded prod - #8543
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[Merged by Bors] - feat(data/list/min_max): maximum is a fold, bounded prod#8543pechersky wants to merge 4 commits into
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Also provide the same lemmas for multiset.
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Also provide the same lemmas for multiset.
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Take the content of * some of `Algebra.BigOperators.List.Basic` * some of `Algebra.BigOperators.List.Lemmas` * some of `Algebra.BigOperators.Multiset.Basic` * some of `Algebra.BigOperators.Multiset.Lemmas` * `Algebra.BigOperators.Multiset.Order` * `Algebra.BigOperators.Order` and sort it into six files: * `Algebra.Order.BigOperators.Group.List`. I credit Yakov for leanprover-community/mathlib3#8543. * `Algebra.Order.BigOperators.Group.Multiset`. Copyright inherited from `Algebra.BigOperators.Multiset.Order`. * `Algebra.Order.BigOperators.Group.Finset`. Copyright inherited from `Algebra.BigOperators.Order`. * `Algebra.Order.BigOperators.Ring.List`. I credit Stuart for leanprover-community/mathlib3#10184. * `Algebra.Order.BigOperators.Ring.Multiset`. I credit Ruben for leanprover-community/mathlib3#8787. * `Algebra.Order.BigOperators.Ring.Finset`. I credit Floris for leanprover-community/mathlib3#1294. Here are the design decisions at play: * Pure algebra and big operators algebra shouldn't import (algebraic) order theory. This PR makes that better, but not perfect because we still import `Data.Nat.Order.Basic` in a few `List` files. * It's `Algebra.Order.BigOperators` instead of `Algebra.BigOperators.Order` because algebraic order theory is more of a theory than big operators algebra. Another reason is that algebraic order theory is the only way to mix pure order and pure algebra, while there are more ways to mix pure finiteness and pure algebra than just big operators. * There are separate files for group/monoid lemmas vs ring lemmas. Groups/monoids are the natural setup for big operators, so their lemmas shouldn't be mixed with ring lemmas that involves both addition and multiplication. As a result, everything under `Algebra.Order.BigOperators.Group` should be additivisable (except a few `Nat`- or `Int`-specific lemmas). In contrast, things under `Algebra.Order.BigOperators.Ring` are more prone to having heavy imports. * Lemmas are separated according to `List` vs `Multiset` vs `Finset`. This is not strictly necessary, and can be relaxed in cases where there aren't that many lemmas to be had. As an example, I could split out the `AbsoluteValue` lemmas from `Algebra.Order.BigOperators.Ring.Finset` to a file `Algebra.Order.BigOperators.Ring.AbsoluteValue` and it could stay this way until too many lemmas are in this file (or a split is needed for import reasons), in which case we would need files `Algebra.Order.BigOperators.Ring.AbsoluteValue.Finset`, `Algebra.Order.BigOperators.Ring.AbsoluteValue.Multiset`, etc... * `Finsupp` big operator and `finprod`/`finsum` order lemmas also belong in `Algebra.Order.BigOperators`. I haven't done so in this PR because the diff is big enough like that.
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Take the content of * some of `Algebra.BigOperators.List.Basic` * some of `Algebra.BigOperators.List.Lemmas` * some of `Algebra.BigOperators.Multiset.Basic` * some of `Algebra.BigOperators.Multiset.Lemmas` * `Algebra.BigOperators.Multiset.Order` * `Algebra.BigOperators.Order` and sort it into six files: * `Algebra.Order.BigOperators.Group.List`. I credit Yakov for leanprover-community/mathlib3#8543. * `Algebra.Order.BigOperators.Group.Multiset`. Copyright inherited from `Algebra.BigOperators.Multiset.Order`. * `Algebra.Order.BigOperators.Group.Finset`. Copyright inherited from `Algebra.BigOperators.Order`. * `Algebra.Order.BigOperators.Ring.List`. I credit Stuart for leanprover-community/mathlib3#10184. * `Algebra.Order.BigOperators.Ring.Multiset`. I credit Ruben for leanprover-community/mathlib3#8787. * `Algebra.Order.BigOperators.Ring.Finset`. I credit Floris for leanprover-community/mathlib3#1294. Here are the design decisions at play: * Pure algebra and big operators algebra shouldn't import (algebraic) order theory. This PR makes that better, but not perfect because we still import `Data.Nat.Order.Basic` in a few `List` files. * It's `Algebra.Order.BigOperators` instead of `Algebra.BigOperators.Order` because algebraic order theory is more of a theory than big operators algebra. Another reason is that algebraic order theory is the only way to mix pure order and pure algebra, while there are more ways to mix pure finiteness and pure algebra than just big operators. * There are separate files for group/monoid lemmas vs ring lemmas. Groups/monoids are the natural setup for big operators, so their lemmas shouldn't be mixed with ring lemmas that involves both addition and multiplication. As a result, everything under `Algebra.Order.BigOperators.Group` should be additivisable (except a few `Nat`- or `Int`-specific lemmas). In contrast, things under `Algebra.Order.BigOperators.Ring` are more prone to having heavy imports. * Lemmas are separated according to `List` vs `Multiset` vs `Finset`. This is not strictly necessary, and can be relaxed in cases where there aren't that many lemmas to be had. As an example, I could split out the `AbsoluteValue` lemmas from `Algebra.Order.BigOperators.Ring.Finset` to a file `Algebra.Order.BigOperators.Ring.AbsoluteValue` and it could stay this way until too many lemmas are in this file (or a split is needed for import reasons), in which case we would need files `Algebra.Order.BigOperators.Ring.AbsoluteValue.Finset`, `Algebra.Order.BigOperators.Ring.AbsoluteValue.Multiset`, etc... * `Finsupp` big operator and `finprod`/`finsum` order lemmas also belong in `Algebra.Order.BigOperators`. I haven't done so in this PR because the diff is big enough like that.
atarnoam
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Take the content of * some of `Algebra.BigOperators.List.Basic` * some of `Algebra.BigOperators.List.Lemmas` * some of `Algebra.BigOperators.Multiset.Basic` * some of `Algebra.BigOperators.Multiset.Lemmas` * `Algebra.BigOperators.Multiset.Order` * `Algebra.BigOperators.Order` and sort it into six files: * `Algebra.Order.BigOperators.Group.List`. I credit Yakov for leanprover-community/mathlib3#8543. * `Algebra.Order.BigOperators.Group.Multiset`. Copyright inherited from `Algebra.BigOperators.Multiset.Order`. * `Algebra.Order.BigOperators.Group.Finset`. Copyright inherited from `Algebra.BigOperators.Order`. * `Algebra.Order.BigOperators.Ring.List`. I credit Stuart for leanprover-community/mathlib3#10184. * `Algebra.Order.BigOperators.Ring.Multiset`. I credit Ruben for leanprover-community/mathlib3#8787. * `Algebra.Order.BigOperators.Ring.Finset`. I credit Floris for leanprover-community/mathlib3#1294. Here are the design decisions at play: * Pure algebra and big operators algebra shouldn't import (algebraic) order theory. This PR makes that better, but not perfect because we still import `Data.Nat.Order.Basic` in a few `List` files. * It's `Algebra.Order.BigOperators` instead of `Algebra.BigOperators.Order` because algebraic order theory is more of a theory than big operators algebra. Another reason is that algebraic order theory is the only way to mix pure order and pure algebra, while there are more ways to mix pure finiteness and pure algebra than just big operators. * There are separate files for group/monoid lemmas vs ring lemmas. Groups/monoids are the natural setup for big operators, so their lemmas shouldn't be mixed with ring lemmas that involves both addition and multiplication. As a result, everything under `Algebra.Order.BigOperators.Group` should be additivisable (except a few `Nat`- or `Int`-specific lemmas). In contrast, things under `Algebra.Order.BigOperators.Ring` are more prone to having heavy imports. * Lemmas are separated according to `List` vs `Multiset` vs `Finset`. This is not strictly necessary, and can be relaxed in cases where there aren't that many lemmas to be had. As an example, I could split out the `AbsoluteValue` lemmas from `Algebra.Order.BigOperators.Ring.Finset` to a file `Algebra.Order.BigOperators.Ring.AbsoluteValue` and it could stay this way until too many lemmas are in this file (or a split is needed for import reasons), in which case we would need files `Algebra.Order.BigOperators.Ring.AbsoluteValue.Finset`, `Algebra.Order.BigOperators.Ring.AbsoluteValue.Multiset`, etc... * `Finsupp` big operator and `finprod`/`finsum` order lemmas also belong in `Algebra.Order.BigOperators`. I haven't done so in this PR because the diff is big enough like that.
uniwuni
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Apr 19, 2024
Take the content of * some of `Algebra.BigOperators.List.Basic` * some of `Algebra.BigOperators.List.Lemmas` * some of `Algebra.BigOperators.Multiset.Basic` * some of `Algebra.BigOperators.Multiset.Lemmas` * `Algebra.BigOperators.Multiset.Order` * `Algebra.BigOperators.Order` and sort it into six files: * `Algebra.Order.BigOperators.Group.List`. I credit Yakov for leanprover-community/mathlib3#8543. * `Algebra.Order.BigOperators.Group.Multiset`. Copyright inherited from `Algebra.BigOperators.Multiset.Order`. * `Algebra.Order.BigOperators.Group.Finset`. Copyright inherited from `Algebra.BigOperators.Order`. * `Algebra.Order.BigOperators.Ring.List`. I credit Stuart for leanprover-community/mathlib3#10184. * `Algebra.Order.BigOperators.Ring.Multiset`. I credit Ruben for leanprover-community/mathlib3#8787. * `Algebra.Order.BigOperators.Ring.Finset`. I credit Floris for leanprover-community/mathlib3#1294. Here are the design decisions at play: * Pure algebra and big operators algebra shouldn't import (algebraic) order theory. This PR makes that better, but not perfect because we still import `Data.Nat.Order.Basic` in a few `List` files. * It's `Algebra.Order.BigOperators` instead of `Algebra.BigOperators.Order` because algebraic order theory is more of a theory than big operators algebra. Another reason is that algebraic order theory is the only way to mix pure order and pure algebra, while there are more ways to mix pure finiteness and pure algebra than just big operators. * There are separate files for group/monoid lemmas vs ring lemmas. Groups/monoids are the natural setup for big operators, so their lemmas shouldn't be mixed with ring lemmas that involves both addition and multiplication. As a result, everything under `Algebra.Order.BigOperators.Group` should be additivisable (except a few `Nat`- or `Int`-specific lemmas). In contrast, things under `Algebra.Order.BigOperators.Ring` are more prone to having heavy imports. * Lemmas are separated according to `List` vs `Multiset` vs `Finset`. This is not strictly necessary, and can be relaxed in cases where there aren't that many lemmas to be had. As an example, I could split out the `AbsoluteValue` lemmas from `Algebra.Order.BigOperators.Ring.Finset` to a file `Algebra.Order.BigOperators.Ring.AbsoluteValue` and it could stay this way until too many lemmas are in this file (or a split is needed for import reasons), in which case we would need files `Algebra.Order.BigOperators.Ring.AbsoluteValue.Finset`, `Algebra.Order.BigOperators.Ring.AbsoluteValue.Multiset`, etc... * `Finsupp` big operator and `finprod`/`finsum` order lemmas also belong in `Algebra.Order.BigOperators`. I haven't done so in this PR because the diff is big enough like that.
callesonne
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Apr 22, 2024
Take the content of * some of `Algebra.BigOperators.List.Basic` * some of `Algebra.BigOperators.List.Lemmas` * some of `Algebra.BigOperators.Multiset.Basic` * some of `Algebra.BigOperators.Multiset.Lemmas` * `Algebra.BigOperators.Multiset.Order` * `Algebra.BigOperators.Order` and sort it into six files: * `Algebra.Order.BigOperators.Group.List`. I credit Yakov for leanprover-community/mathlib3#8543. * `Algebra.Order.BigOperators.Group.Multiset`. Copyright inherited from `Algebra.BigOperators.Multiset.Order`. * `Algebra.Order.BigOperators.Group.Finset`. Copyright inherited from `Algebra.BigOperators.Order`. * `Algebra.Order.BigOperators.Ring.List`. I credit Stuart for leanprover-community/mathlib3#10184. * `Algebra.Order.BigOperators.Ring.Multiset`. I credit Ruben for leanprover-community/mathlib3#8787. * `Algebra.Order.BigOperators.Ring.Finset`. I credit Floris for leanprover-community/mathlib3#1294. Here are the design decisions at play: * Pure algebra and big operators algebra shouldn't import (algebraic) order theory. This PR makes that better, but not perfect because we still import `Data.Nat.Order.Basic` in a few `List` files. * It's `Algebra.Order.BigOperators` instead of `Algebra.BigOperators.Order` because algebraic order theory is more of a theory than big operators algebra. Another reason is that algebraic order theory is the only way to mix pure order and pure algebra, while there are more ways to mix pure finiteness and pure algebra than just big operators. * There are separate files for group/monoid lemmas vs ring lemmas. Groups/monoids are the natural setup for big operators, so their lemmas shouldn't be mixed with ring lemmas that involves both addition and multiplication. As a result, everything under `Algebra.Order.BigOperators.Group` should be additivisable (except a few `Nat`- or `Int`-specific lemmas). In contrast, things under `Algebra.Order.BigOperators.Ring` are more prone to having heavy imports. * Lemmas are separated according to `List` vs `Multiset` vs `Finset`. This is not strictly necessary, and can be relaxed in cases where there aren't that many lemmas to be had. As an example, I could split out the `AbsoluteValue` lemmas from `Algebra.Order.BigOperators.Ring.Finset` to a file `Algebra.Order.BigOperators.Ring.AbsoluteValue` and it could stay this way until too many lemmas are in this file (or a split is needed for import reasons), in which case we would need files `Algebra.Order.BigOperators.Ring.AbsoluteValue.Finset`, `Algebra.Order.BigOperators.Ring.AbsoluteValue.Multiset`, etc... * `Finsupp` big operator and `finprod`/`finsum` order lemmas also belong in `Algebra.Order.BigOperators`. I haven't done so in this PR because the diff is big enough like that.
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Also provide the same lemmas for multiset.