Theorems · Theorem · functional analysis
ContinuousLinearMap.IsInvertible.inverse
∀ {R : Type u_1} {M : Type u_2} {M₂ : Type u_3} [inst : TopologicalSpace M] [inst_1 : TopologicalSpace M₂]
[inst_2 : Semiring R] [inst_3 : AddCommMonoid M] [inst_4 : Module R M] [inst_5 : AddCommMonoid M₂]
[inst_6 : Module R M₂] {f : M →L[R] M₂}, f.IsInvertible → f.inverse.IsInvertible- Defined in
- Mathlib.Topology.Algebra.Module.Equiv
- Cited by
- 1 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.
Cites11
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
- ContinuousLinearEquivproof · cited by 743
- ContinuousLinearEquiv.toContinuousLinearMapproof · cited by 448
- ContinuousLinearMap.IsInvertiblestatement and proof · cited by 104
- ContinuousLinearMap.inversestatement · cited by 82
- ContinuousLinearMap.inverse_equivproof · cited by 19
Cited by1
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.isInvertible_inverse_iffproof · cited by 0