Theorems · Theorem · global analysis
isImmersionOfComplement_subtypeVal_Icc
∀ {x y : ℝ} [h : Fact (x < y)] {n : WithTop ℕ∞},
Manifold.IsImmersionOfComplement Unit (modelWithCornersEuclideanHalfSpace 1) (modelWithCornersSelf ℝ ℝ) n fun z => ↑zThe inclusion map from a closed segment to ℝ is a smooth immersion
- Defined in
- Mathlib.Geometry.Manifold.Instances.Icc
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 229 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.
Cites81
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- RingHom.idproof · cited by 18,349
- ENNRealstatement · cited by 9,879
- Set.Elemstatement and proof · cited by 7,166
- ENatstatement and proof · cited by 4,985
- Set.preimageproof · cited by 4,946
- Set.rangeproof · cited by 4,705
- Set.univproof · cited by 3,945
- WithTopstatement and proof · cited by 3,754
- Factstatement and proof · cited by 2,726
Cited by3
Results whose statement or proof uses this declaration.
- contMDiff_subtypeVal_Iccproof · cited by 4
- contMDiff_iff_comp_subtypeVal_Iccproof · cited by 0
- isSmoothEmbedding_subtypeVal_Iccproof · cited by 0