[Merged by Bors] - feat(Analysis/Convex): lemmas about low-dimensional stdSimplexes
#10325
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Thank you so much for working on this Yury! |
eric-wieser
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eric-wieser
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eric-wieser
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Feb 7, 2024
| variable (𝕜) [OrderedRing 𝕜] | ||
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| /-- The standard one-dimensional simplex in `Fin 2 → 𝕜` is equivalent to the unit interval. -/ | ||
| def stdSimplexEquivIcc : stdSimplex 𝕜 (Fin 2) ≃ Icc (0 : 𝕜) 1 where |
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Can you add the more general
Suggested change
| def stdSimplexEquivIcc : stdSimplex 𝕜 (Fin 2) ≃ Icc (0 : 𝕜) 1 where | |
| def stdSimplexEquivIcc : stdSimplex 𝕜 (Fin (n + 1)) ≃ stdSimplex 𝕜 (Fin n) × Icc (0 : 𝕜) 1 where |
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Ah, I guess that's not quite true
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I think the true version is
Suggested change
| def stdSimplexEquivIcc : stdSimplex 𝕜 (Fin 2) ≃ Icc (0 : 𝕜) 1 where | |
| def stdSimplexEquivIcc : stdSimplex 𝕜 (Fin 2) ≃ Σ c : Icc (0 : 𝕜) 1, c • stdSimplex 𝕜 (Fin n) where |
but it seems inconvenient to use
eric-wieser
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Feb 7, 2024
eric-wieser
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Feb 7, 2024
Co-authored-by: Eric Wieser <[email protected]>
Co-authored-by: Eric Wieser <[email protected]>
Co-authored-by: Eric Wieser <[email protected]>
Co-authored-by: Eric Wieser <[email protected]>
urkud
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Feb 8, 2024
jcommelin
approved these changes
Feb 8, 2024
| variable (𝕜) [OrderedRing 𝕜] | ||
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| /-- The standard one-dimensional simplex in `Fin 2 → 𝕜` is equivalent to the unit interval. -/ | ||
| def stdSimplexEquivIcc : stdSimplex 𝕜 (Fin 2) ≃ Icc (0 : 𝕜) 1 where |
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…10325) Forward-port of leanprover-community/mathlib3#19101 Motivated by https://github.com/Shamrock-Frost/BrouwerFixedPoint Co-authored-by: @Shamrock-Frost
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…10325) Forward-port of leanprover-community/mathlib3#19101 Motivated by https://github.com/Shamrock-Frost/BrouwerFixedPoint Co-authored-by: @Shamrock-Frost
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…10325) Forward-port of leanprover-community/mathlib3#19101 Motivated by https://github.com/Shamrock-Frost/BrouwerFixedPoint Co-authored-by: @Shamrock-Frost
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Forward-port of leanprover-community/mathlib3#19101
Motivated by https://github.com/Shamrock-Frost/BrouwerFixedPoint
Co-authored-by: @Shamrock-Frost