[Merged by Bors] - feat(Analysis/LocallyConvex/WithSeminorms): congr lemmas #5797
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| @@ -628,7 +627,7 @@ theorem continuous_iff_continuous_comp {q : SeminormFamily 𝕜₂ F ι'} [Topol | |||
| #align seminorm.continuous_iff_continuous_comp Seminorm.continuous_iff_continuous_comp | |||
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| theorem continuous_from_bounded {p : SeminormFamily 𝕝 E ι} {q : SeminormFamily 𝕝₂ F ι'} | |||
| [TopologicalSpace E] (hp : WithSeminorms p) [TopologicalSpace F] (hq : WithSeminorms q) | |||
| {_ : TopologicalSpace E} (hp : WithSeminorms p) {_ : TopologicalSpace F} (hq : WithSeminorms q) | |||
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With the old version this line doesn't work. More generally, I feel like everything goes way smoother when things that can be inferred from various places (these topologies can either be inferred from the expected type or from the types of the arguments) aren't also searched by the typeclass system, especially since Lean4 seems to be even more strict on that than Lean3.
| variable [NormedField 𝕜₂] [AddCommGroup F] [Module 𝕜₂ F] | ||
| variable {σ₁₂ : 𝕜 →+* 𝕜₂} [RingHomIsometric σ₁₂] | ||
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| protected theorem congr {p : SeminormFamily 𝕜 E ι} {q : SeminormFamily 𝕜 E ι'} |
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Maybe add a docstring to this one.
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This adds `WithSeminorms.congr` which allows to replace a family of seminorm by an equivalent one. We use that to prove that one can always replace the family by a directed family (and a nice one if the indexing set is a `LocallyFiniteOrderBot`).
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This adds `WithSeminorms.congr` which allows to replace a family of seminorm by an equivalent one. We use that to prove that one can always replace the family by a directed family (and a nice one if the indexing set is a `LocallyFiniteOrderBot`).
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This adds `WithSeminorms.congr` which allows to replace a family of seminorm by an equivalent one. We use that to prove that one can always replace the family by a directed family (and a nice one if the indexing set is a `LocallyFiniteOrderBot`).
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This adds
WithSeminorms.congrwhich allows to replace a family of seminorm by an equivalent one. We use that to prove that one can always replace the family by a directed family (and a nice one if the indexing set is aLocallyFiniteOrderBot).