[Merged by Bors] - feat: add basic API lemmas for BddAbove (range f) and BddBelow (range f)
#9472
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Mathlib/Order/Bounds/Basic.lean
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| rw [bddBelow_def] at hf ⊢ | ||
| obtain ⟨C, hC⟩ := hf | ||
| refine ⟨g C, fun y hy => ?_⟩ | ||
| rw [Set.mem_range] at hy | ||
| obtain ⟨y', hy'⟩ := hy | ||
| calc y = g (f y') := hy'.symm | ||
| _ ≥ g C := hg <| hC (f y') <| Set.mem_range_self _ |
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Can't this also be golfed using OrderDual?
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Not easily. We need to take the dual of both β and γ, and I think the Monotone g hypothesis needs to be adapted. Maybe it's possible but it's easier to copy/paste.
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Co-authored-by: Anatole Dedecker <anatolededecker@gmail.com>
Co-authored-by: Anatole Dedecker <anatolededecker@gmail.com>
Co-authored-by: Anatole Dedecker <anatolededecker@gmail.com>
Co-authored-by: Anatole Dedecker <anatolededecker@gmail.com>
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…nge f)` (#9472) This PR adds some basic API lemmas for `BddAbove (range f)` (resp `BddBelow`). This is a ubiquitous side condition when working with `iInf`/`iSup` in conditionally complete lattices, so I think it's worth having. Co-authored-by: Frédéric Dupuis <31101893+dupuisf@users.noreply.github.com>
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bors r- Sorry, I thought you were done... bors d+ |
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…nge f)` (#9472) This PR adds some basic API lemmas for `BddAbove (range f)` (resp `BddBelow`). This is a ubiquitous side condition when working with `iInf`/`iSup` in conditionally complete lattices, so I think it's worth having. Co-authored-by: Frédéric Dupuis <31101893+dupuisf@users.noreply.github.com>
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Pull request successfully merged into master. Build succeeded: |
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BddAbove (range f) and BddBelow (range f)BddAbove (range f) and BddBelow (range f)
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…nge f)` (#9472) This PR adds some basic API lemmas for `BddAbove (range f)` (resp `BddBelow`). This is a ubiquitous side condition when working with `iInf`/`iSup` in conditionally complete lattices, so I think it's worth having. Co-authored-by: Frédéric Dupuis <31101893+dupuisf@users.noreply.github.com>
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This PR adds some basic API lemmas for
BddAbove (range f)(respBddBelow). This is a ubiquitous side condition when working withiInf/iSupin conditionally complete lattices, so I think it's worth having.