[Merged by Bors] - feat(Order/Hom): prove disjoint from order embedding #12223
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frederic-marbach
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I golfed your proofs (I hope, without loss of readability). LGTM |
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🚀 Pull request has been placed on the maintainer queue by urkud. |
leanprover-community-mathlib4-bot
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Apr 18, 2024
This adds 3 lemmas which state that if you have an order embedding `f` such that `f a₁` and `f a₂` are disjoint/codisjoint/complements, then the same holds for `a₁` and `a₂`. *Motivation*: For a project described [here](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Derivations.20on.20Lie.20algebras), I wanted to know that if two Lie ideals are complements as submodules, then they are complements as Lie ideals too. I realized that the correct level of generality was probably in the `Order.Hom.Basic` file. *Caveats*: I am very much open to golfing/naming/redesign suggestions. Within the modified file, there was already a `Disjoint.map_orderIso` result, but it requires an `OrderIso` (not just a one-way embedding) and it requires a `SemilatticeInf` (whereas my version just uses `PartialOrder`). Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>
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Pull request successfully merged into master. Build succeeded: |
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Thank you very much for the golfing and the fast merging. The proofs indeed look much better. |
uniwuni
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Apr 19, 2024
This adds 3 lemmas which state that if you have an order embedding `f` such that `f a₁` and `f a₂` are disjoint/codisjoint/complements, then the same holds for `a₁` and `a₂`. *Motivation*: For a project described [here](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Derivations.20on.20Lie.20algebras), I wanted to know that if two Lie ideals are complements as submodules, then they are complements as Lie ideals too. I realized that the correct level of generality was probably in the `Order.Hom.Basic` file. *Caveats*: I am very much open to golfing/naming/redesign suggestions. Within the modified file, there was already a `Disjoint.map_orderIso` result, but it requires an `OrderIso` (not just a one-way embedding) and it requires a `SemilatticeInf` (whereas my version just uses `PartialOrder`). Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>
callesonne
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Apr 22, 2024
This adds 3 lemmas which state that if you have an order embedding `f` such that `f a₁` and `f a₂` are disjoint/codisjoint/complements, then the same holds for `a₁` and `a₂`. *Motivation*: For a project described [here](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Derivations.20on.20Lie.20algebras), I wanted to know that if two Lie ideals are complements as submodules, then they are complements as Lie ideals too. I realized that the correct level of generality was probably in the `Order.Hom.Basic` file. *Caveats*: I am very much open to golfing/naming/redesign suggestions. Within the modified file, there was already a `Disjoint.map_orderIso` result, but it requires an `OrderIso` (not just a one-way embedding) and it requires a `SemilatticeInf` (whereas my version just uses `PartialOrder`). Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>
Jun2M
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Apr 24, 2024
This adds 3 lemmas which state that if you have an order embedding `f` such that `f a₁` and `f a₂` are disjoint/codisjoint/complements, then the same holds for `a₁` and `a₂`. *Motivation*: For a project described [here](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Derivations.20on.20Lie.20algebras), I wanted to know that if two Lie ideals are complements as submodules, then they are complements as Lie ideals too. I realized that the correct level of generality was probably in the `Order.Hom.Basic` file. *Caveats*: I am very much open to golfing/naming/redesign suggestions. Within the modified file, there was already a `Disjoint.map_orderIso` result, but it requires an `OrderIso` (not just a one-way embedding) and it requires a `SemilatticeInf` (whereas my version just uses `PartialOrder`). Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>
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This adds 3 lemmas which state that if you have an order embedding
fsuch thatf a₁andf a₂are disjoint/codisjoint/complements, then the same holds fora₁anda₂.Motivation: For a project described here, I wanted to know that if two Lie ideals are complements as submodules, then they are complements as Lie ideals too. I realized that the correct level of generality was probably in the
Order.Hom.Basicfile.Caveats: I am very much open to golfing/naming/redesign suggestions. Within the modified file, there was already a
Disjoint.map_orderIsoresult, but it requires anOrderIso(not just a one-way embedding) and it requires aSemilatticeInf(whereas my version just usesPartialOrder).