Theorems · Theorem · general topology
JoinedIn.of_segment_subset
∀ {E : Type u_1} [inst : AddCommGroup E] [inst_1 : Module ℝ E] [inst_2 : TopologicalSpace E] [ContinuousAdd E]
[ContinuousSMul ℝ E] {x y : E} {s : Set E}, segment ℝ x y ⊆ s → JoinedIn s x y- Defined in
- Mathlib.Analysis.Convex.PathConnected
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- ContinuousSMulstatement and proof · cited by 1,016
- ContinuousAddstatement and proof · cited by 777
- segmentstatement and proof · cited by 120
- Set.range_subset_iffproof · cited by 99
- JoinedInstatement · cited by 40
- Path.segmentproof · cited by 31
- Path.range_segmentproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Set.Countable.isPathConnected_compl_of_one_lt_rankproof · cited by 2
- StarConvex.isPathConnectedproof · cited by 1