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[Merged by Bors] - feat(Order/OmegaCompletePartialOrder): Show that Scott Continuity implies OmegaCompletePartialOrder.Continuous'#6831

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[Merged by Bors] - feat(Order/OmegaCompletePartialOrder): Show that Scott Continuity implies OmegaCompletePartialOrder.Continuous'#6831
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@mans0954 mans0954 commented Aug 28, 2023

In leanprover-community/mathlib3#18517 we introduced the notion of a Scott Continuous function between preorders. This PR shows that a Scott Continuous function between OmegaCompletePartialOrders is necessarily OmegaCompletePartialOrder.Continuous'.

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Some stylistic remarks.

Note that on L303 the name is also wrong. It should simply be .monotone instead of .to_monotone. But I don't claim this should be fixed in this PR.

@jcommelin jcommelin added awaiting-author A reviewer has asked the author a question or requested changes. and removed awaiting-review labels Sep 14, 2023
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mans0954 commented Sep 14, 2023 

No space left on device : '/home/lean/actions-runner/_work/_actions/dcarbone/install-jq-action/v1.0.1'

Not sure there's anything I can do about this @jcommelin ?

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mans0954 commented Sep 15, 2023 

No space left on device : '/home/lean/actions-runner/_work/_actions/dcarbone/install-jq-action/v1.0.1'

Possibly fixed by #7166?

@mans0954 mans0954 added awaiting-review and removed awaiting-author A reviewer has asked the author a question or requested changes. labels Sep 15, 2023
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Thanks 🎉

bors merge

@ghost ghost added ready-to-merge This PR has been sent to bors. and removed awaiting-review labels Sep 15, 2023
bors bot pushed a commit that referenced this pull request Sep 15, 2023
@mans0954
feat(Order/OmegaCompletePartialOrder): Show that Scott Continuity imp…
b0e5bef 
…lies OmegaCompletePartialOrder.Continuous' (#6831)

In leanprover-community/mathlib3#18517 we introduced the notion of a Scott Continuous function between preorders. This PR shows that a Scott Continuous function between OmegaCompletePartialOrders is necessarily `OmegaCompletePartialOrder.Continuous'`.



Co-authored-by: Christopher Hoskin <mans0954@users.noreply.github.com>
Co-authored-by: Christopher Hoskin <christopher.hoskin@overleaf.com>
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@bors bors bot changed the title feat(Order/OmegaCompletePartialOrder): Show that Scott Continuity implies OmegaCompletePartialOrder.Continuous' [Merged by Bors] - feat(Order/OmegaCompletePartialOrder): Show that Scott Continuity implies OmegaCompletePartialOrder.Continuous' Sep 15, 2023
@bors bors bot closed this Sep 15, 2023
@bors bors bot deleted the mans0954/scott-continuity branch September 15, 2023 09:18
@mans0954 mans0954 mentioned this pull request Sep 20, 2023
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kodyvajjha pushed a commit that referenced this pull request Sep 22, 2023
@mans0954 @kodyvajjha
feat(Order/OmegaCompletePartialOrder): Show that Scott Continuity imp…
5d926dd 
…lies OmegaCompletePartialOrder.Continuous' (#6831)

In leanprover-community/mathlib3#18517 we introduced the notion of a Scott Continuous function between preorders. This PR shows that a Scott Continuous function between OmegaCompletePartialOrders is necessarily `OmegaCompletePartialOrder.Continuous'`.



Co-authored-by: Christopher Hoskin <mans0954@users.noreply.github.com>
Co-authored-by: Christopher Hoskin <christopher.hoskin@overleaf.com>
@mans0954 mans0954 mentioned this pull request May 26, 2024
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mathlib-bors bot pushed a commit that referenced this pull request Sep 5, 2024
@mans0954
refactor(Order/OmegaCompletePartialOrder): Unify concepts of Scott Co…
d6ca7ae 
…ntinuity (#13201)

We currently have two related but different concepts of Scott Continuity in Mathlib - `ScottContinuous` in `Order/Bounds/Basic` and `OmegaCompletePartialOrder.Continuous'` in `Order/OmegaCompletePartialOrder`. We previously showed (#6831) that `ScottContinuous` implies `OmegaCompletePartialOrder.Continuous'` (in general the converse isn't true).

This PR gives a more general definition of Scott Continuity, `ScottContinuousOn` which specialises to `ScottContinuous` and something equivalent to  `OmegaCompletePartialOrder.Continuous'` to give a more satisfactory unification of the concepts.



Co-authored-by: Christopher Hoskin <mans0954@users.noreply.github.com>
Co-authored-by: Christopher Hoskin <christopher.hoskin@overleaf.com>
bjoernkjoshanssen pushed a commit that referenced this pull request Sep 9, 2024
@mans0954 @bjoernkjoshanssen
refactor(Order/OmegaCompletePartialOrder): Unify concepts of Scott Co…
cba448f 
…ntinuity (#13201)

We currently have two related but different concepts of Scott Continuity in Mathlib - `ScottContinuous` in `Order/Bounds/Basic` and `OmegaCompletePartialOrder.Continuous'` in `Order/OmegaCompletePartialOrder`. We previously showed (#6831) that `ScottContinuous` implies `OmegaCompletePartialOrder.Continuous'` (in general the converse isn't true).

This PR gives a more general definition of Scott Continuity, `ScottContinuousOn` which specialises to `ScottContinuous` and something equivalent to  `OmegaCompletePartialOrder.Continuous'` to give a more satisfactory unification of the concepts.



Co-authored-by: Christopher Hoskin <mans0954@users.noreply.github.com>
Co-authored-by: Christopher Hoskin <christopher.hoskin@overleaf.com>
bjoernkjoshanssen pushed a commit that referenced this pull request Sep 9, 2024
@mans0954 @bjoernkjoshanssen
refactor(Order/OmegaCompletePartialOrder): Unify concepts of Scott Co…
5696668 
…ntinuity (#13201)

We currently have two related but different concepts of Scott Continuity in Mathlib - `ScottContinuous` in `Order/Bounds/Basic` and `OmegaCompletePartialOrder.Continuous'` in `Order/OmegaCompletePartialOrder`. We previously showed (#6831) that `ScottContinuous` implies `OmegaCompletePartialOrder.Continuous'` (in general the converse isn't true).

This PR gives a more general definition of Scott Continuity, `ScottContinuousOn` which specialises to `ScottContinuous` and something equivalent to  `OmegaCompletePartialOrder.Continuous'` to give a more satisfactory unification of the concepts.



Co-authored-by: Christopher Hoskin <mans0954@users.noreply.github.com>
Co-authored-by: Christopher Hoskin <christopher.hoskin@overleaf.com>
bjoernkjoshanssen pushed a commit that referenced this pull request Sep 12, 2024
@mans0954 @bjoernkjoshanssen
refactor(Order/OmegaCompletePartialOrder): Unify concepts of Scott Co…
21ee29a 
…ntinuity (#13201)

We currently have two related but different concepts of Scott Continuity in Mathlib - `ScottContinuous` in `Order/Bounds/Basic` and `OmegaCompletePartialOrder.Continuous'` in `Order/OmegaCompletePartialOrder`. We previously showed (#6831) that `ScottContinuous` implies `OmegaCompletePartialOrder.Continuous'` (in general the converse isn't true).

This PR gives a more general definition of Scott Continuity, `ScottContinuousOn` which specialises to `ScottContinuous` and something equivalent to  `OmegaCompletePartialOrder.Continuous'` to give a more satisfactory unification of the concepts.



Co-authored-by: Christopher Hoskin <mans0954@users.noreply.github.com>
Co-authored-by: Christopher Hoskin <christopher.hoskin@overleaf.com>
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