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Theorems · Theorem · algebraic topology

Path.Homotopic.Quotient.symm_trans

∀ {X : Type u_1} [inst : TopologicalSpace X] {x₀ x₁ : X} (γ : Path.Homotopic.Quotient x₀ x₁),
  γ.symm.trans γ = Path.Homotopic.Quotient.refl x₁
Defined in
Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic
Cited by
1 results in Mathlib
Foundations
Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

simply_connected_iff_loops_nullhomotopic · cited by 1simply_connected_iff_loop…TopologicalSpace · cited by 24529TopologicalSpacePath · cited by 318PathPath.Homotopic.Quotient · cited by 55Homotopic.QuotientPath.Homotopic.Quotient.trans · cited by 12Quotient.transPath.Homotopic.Quotient.refl · cited by 9Quotient.reflPath.Homotopic.Quotient.ind · cited by 8Quotient.indPath.Homotopic.Quotient.symm · cited by 5Quotient.symmPath.Homotopic.symm_trans · cited by 1Homotopic.symm_transQuotient.symm_transCITED BYCITES

Cites8

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Cited by1

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