Theorems · Theorem · general topology
Path.segment_same
∀ {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 : E), Path.segment a a = Path.refl a- Defined in
- Mathlib.Analysis.Convex.PathConnected
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- 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.Elemproof · cited by 7,166
- ContinuousSMulstatement and proof · cited by 1,016
- ContinuousAddstatement and proof · cited by 777
- unitIntervalproof · cited by 607
- Pathstatement · cited by 318
- Path.reflstatement · cited by 36
- Path.segmentstatement · cited by 31
Cited by2
Results whose statement or proof uses this declaration.
- HasFDerivWithinAt.curveIntegral_segment_source'proof · cited by 2
- Convex.curveIntegral_segment_add_eq_of_hasFDerivWithinAt_symmetricproof · cited by 1