Theorems · Theorem · general topology
Path.segment_apply
∀ {E : Type u_1} [inst : AddCommGroup E] [inst_1 : Module ℝ E] [inst_2 : TopologicalSpace E] [inst_3 : ContinuousAdd E]
[inst_4 : ContinuousSMul ℝ E] (a b : E) (t : ↑unitInterval), (Path.segment a b) t = (AffineMap.lineMap a b) ↑t- Defined in
- Mathlib.Analysis.Convex.PathConnected
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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 · 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
- Set.Elemstatement and proof · cited by 7,166
- ContinuousSMulstatement and proof · cited by 1,016
- ContinuousAddstatement and proof · cited by 777
- AffineMapstatement · cited by 674
- unitIntervalstatement and proof · cited by 607
- Pathstatement · cited by 318
Cited by8
Results whose statement or proof uses this declaration.
- Path.segment_sameproof · cited by 2
- Circle.path_selfproof · cited by 2
- segment_image_Icoproof · cited by 1
- segment_image_Iocproof · cited by 1
- Circle.path_applyproof · cited by 1
- Path.eqOn_extend_segmentproof · cited by 1
- Path.segment_add_segmentproof · cited by 0
- Path.segment_symmproof · cited by 0