Theorems · Theorem · general topology

BoundedContinuousFunction.comp_apply

∀ {α : Type u} {β : Type v} {γ : Type w} [inst : TopologicalSpace α] [inst_1 : PseudoMetricSpace β]
  [inst_2 : PseudoMetricSpace γ] (G : β → γ) {C : NNReal} (H : LipschitzWith C G) (f : BoundedContinuousFunction α β)
  (a : α), (BoundedContinuousFunction.comp G H f) a = G (f a)

Defined in: Mathlib.Topology.ContinuousMap.Bounded.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace PseudoMetricSpace PseudoMetricSpace

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DFunLike.coestatement · cited by 62,936
TopologicalSpacestatement and proof · cited by 24,529
NNRealstatement and proof · cited by 4,310
PseudoMetricSpacestatement and proof · cited by 1,550
BoundedContinuousFunctionstatement and proof · cited by 511
LipschitzWithstatement and proof · cited by 316
BoundedContinuousFunction.compstatement · cited by 12

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