Theorems · Theorem · algebraic topology
Path.Homotopic.Quotient.ind
∀ {X : Type u} [inst : TopologicalSpace X] {x y : X} {motive : Path.Homotopic.Quotient x y → Prop},
(∀ (a : Path x y), motive (Path.Homotopic.Quotient.mk a)) → ∀ (q : Path.Homotopic.Quotient x y), motive qA reasoning principle for quotients that allows proofs about quotients to assume that all values are
constructed with Quotient.mk.
- Defined in
- Mathlib.Topology.Homotopy.Path
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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 · cited by 318
- Path.Homotopic.Quotientstatement and proof · cited by 55
- Path.Homotopic.Quotient.mkstatement · cited by 28
Cited by8
Results whose statement or proof uses this declaration.
- Path.Homotopic.Quotient.cast_rfl_rflproof · cited by 3
- Path.Homotopic.Quotient.symm_transproof · cited by 1
- Path.Homotopic.Quotient.trans_assocproof · cited by 1
- Path.Homotopic.Quotient.trans_reflproof · cited by 1
- Path.Homotopic.Quotient.cast_castproof · cited by 1
- Path.Homotopic.Quotient.trans_symmproof · cited by 0
- Path.Homotopic.Quotient.refl_transproof · cited by 0
- Path.Homotopic.prod_projLeft_projRightproof · cited by 0