Theorems · Theorem · functional analysis
ContinuousLinearMap.inverse_comp_equiv
∀ {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] {e : M₃ ≃L[R] M} {f : M →L[R] M₂}, (f ∘SL ↑e).inverse = ↑e.symm ∘SL f.inverse- Defined in
- Mathlib.Topology.Algebra.Module.Equiv
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- ContinuousLinearMapstatement and proof · cited by 5,352
- ContinuousLinearEquivstatement and proof · cited by 743
- ContinuousLinearMap.compstatement and proof · cited by 709
- ContinuousLinearEquiv.toContinuousLinearMapstatement and proof · cited by 448
- ContinuousLinearEquiv.symmstatement and proof · cited by 368
- ContinuousLinearMap.IsInvertibleproof · cited by 104
- ContinuousLinearMap.inversestatement and proof · cited by 82
Cited by3
Results whose statement or proof uses this declaration.
- ContMDiffWithinAt.mpullbackWithin_vectorField_interproof · cited by 4
- MDifferentiableWithinAt.mpullbackWithin_vectorField_interproof · cited by 3
- ContinuousLinearMap.IsInvertible.inverse_comp_of_rightproof · cited by 1