Theorems · Theorem · functional analysis

ContinuousLinearMap.IsInvertible.inverse_comp_of_right

∀ {R : Type u_1} {M : Type u_2} {M₂ : Type u_3} {M₃ : Type u_4} [inst : TopologicalSpace M]
  [inst_1 : TopologicalSpace M₂] [inst_2 : TopologicalSpace M₃] [inst_3 : Semiring R] [inst_4 : AddCommMonoid M]
  [inst_5 : Module R M] [inst_6 : AddCommMonoid M₂] [inst_7 : Module R M₂] [inst_8 : AddCommMonoid M₃]
  [inst_9 : Module R M₃] {g : M₂ →L[R] M₃} {f : M →L[R] M₂},
  f.IsInvertible → (g ∘SL f).inverse = f.inverse ∘SL g.inverse

Defined in

Mathlib.Topology.Algebra.Module.Equiv

Cited by

1 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpaceSemiringAddCommMonoidModuleAddCommMonoidModuleAddCommMonoidModule