Theorems · Theorem · global analysis
contMDiff_subtypeVal_Icc
∀ {x y : ℝ} [h : Fact (x < y)] {n : WithTop ℕ∞},
ContMDiff (modelWithCornersEuclideanHalfSpace 1) (modelWithCornersSelf ℝ ℝ) n fun z => ↑zThe inclusion map from of a closed segment to ℝ is smooth in the manifold sense.
- Defined in
- Mathlib.Geometry.Manifold.Instances.Icc
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 230 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fact
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- ENNRealstatement · cited by 9,879
- Set.Elemstatement · cited by 7,166
- ENatstatement and proof · cited by 4,985
- WithTopstatement and proof · cited by 3,754
- Factstatement and proof · cited by 2,726
- Set.Iccstatement · cited by 1,702
- modelWithCornersSelfstatement · cited by 920
- EuclideanSpacestatement · cited by 307
- ContMDiffstatement · cited by 278
- EuclideanHalfSpacestatement · cited by 47
Cited by4
Results whose statement or proof uses this declaration.
- contMDiffOn_comp_projIcc_iffproof · cited by 2
- mdifferentiableWithinAt_comp_projIcc_iffproof · cited by 1
- contMDiffWithinAt_comp_projIcc_iffproof · cited by 0
- contMDiff_subtype_coe_Iccproof · cited by 0