Theorems · Theorem · algebraic topology

Path.Homotopic.pi_lift

∀ {ι : Type u_1} {X : ι → Type u_2} [inst : (i : ι) → TopologicalSpace (X i)] {as bs : (i : ι) → X i}
  (γ : (i : ι) → Path (as i) (bs i)),
  (Path.Homotopic.pi fun i => Path.Homotopic.Quotient.mk (γ i)) = Path.Homotopic.Quotient.mk (Path.pi γ)

Defined in: Mathlib.Topology.Homotopy.Product
Cited by: 3 results in Mathlib
Foundations: Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace

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Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

TopologicalSpacestatement and proof · cited by 24,529
Pathstatement and proof · cited by 318
Path.Homotopic.Quotientstatement · cited by 55
Path.Homotopic.Quotient.mkstatement · cited by 28
Path.Homotopic.setoidproof · cited by 14
Path.pistatement and proof · cited by 8
Path.Homotopic.pistatement · cited by 5
Quotient.choiceproof · cited by 2
Quotient.map.congr_simpproof · cited by 2
Quotient.choice_eqproof · cited by 1

Cited by3

Results whose statement or proof uses this declaration.

Path.Homotopic.comp_pi_eq_pi_compproof · cited by 0
Path.Homotopic.pi_projproof · cited by 0
Path.Homotopic.proj_piproof · cited by 0