Theorems · Theorem · general topology
Path.trans_range
∀ {X : Type u_1} [inst : TopologicalSpace X] {a b c : X} (γ₁ : Path a b) (γ₂ : Path b c),
Set.range ⇑(γ₁.trans γ₂) = Set.range ⇑γ₁ ∪ Set.range ⇑γ₂- Defined in
- Mathlib.Topology.Path
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemstatement · cited by 7,166
- Set.imageproof · cited by 5,609
- Set.rangestatement and proof · cited by 4,705
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- Set.Iicproof · cited by 1,111
- Set.Iciproof · cited by 1,070
- unitIntervalstatement · cited by 607
Cited by1
Results whose statement or proof uses this declaration.
- IsPathConnected.exists_path_through_familyproof · cited by 2