Theorems · Theorem · general topology
Metric.toInductiveLimit_commute
∀ {X : ℕ → Type u} [inst : (n : ℕ) → MetricSpace (X n)] {f : (n : ℕ) → X n → X (n + 1)} (I : ∀ (n : ℕ), Isometry (f n))
(n : ℕ), Metric.toInductiveLimit I n.succ ∘ f n = Metric.toInductiveLimit I nThe maps toInductiveLimit n are compatible with the maps f n.
- Defined in
- Mathlib.Topology.MetricSpace.Gluing
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- TopologicalSpaceproof · cited by 24,529
- le_reflproof · cited by 2,061
- MetricSpacestatement and proof · cited by 1,684
- PseudoMetricSpaceproof · cited by 1,550
- Dist.distproof · cited by 1,539
- Isometrystatement and proof · cited by 230
- dist_selfproof · cited by 116
- Nat.leRecOnproof · cited by 13
- SeparationQuotient.mk_eq_mkproof · cited by 7
- Metric.inseparable_iffproof · cited by 6
- Nat.leRecOn_selfproof · cited by 5
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.