Theorems · Theorem · functional analysis
ContinuousLinearMap.inverse_equiv
∀ {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] (e : M ≃L[R] M₂), (↑e).inverse = ↑e.symmBy definition, if f is invertible then inverse f = f.symm.
- Defined in
- Mathlib.Topology.Algebra.Module.Equiv
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 73 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 · cited by 5,352
- ContinuousLinearEquivstatement and proof · cited by 743
- ContinuousLinearEquiv.toContinuousLinearMapstatement and proof · cited by 448
- ContinuousLinearEquiv.symmstatement and proof · cited by 368
- ContinuousLinearMap.inversestatement · cited by 82
- Classical.choose_eqproof · cited by 15
Cited by19
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.inverse_comp_equivproof · cited by 3
- OpenPartialHomeomorph.contDiffAt_symmproof · cited by 3
- ContinuousLinearMap.inverse_equiv_compproof · cited by 3
- exists_continuousLinearEquiv_fderivWithin_symm_eqproof · cited by 3
- ContinuousLinearMap.inverse_eqproof · cited by 2
- ContinuousLinearMap.inverse_eq_ringInverseproof · cited by 2
- ContinuousLinearMap.IsInvertible.inverse_comp_of_leftproof · cited by 2
- VectorField.pullbackWithin_eq_of_fderivWithin_eqproof · cited by 2
- ContinuousLinearMap.IsInvertible.inverseproof · cited by 1
- ContinuousLinearMap.IsInvertible.inverse_comp_of_rightproof · cited by 1
- ContinuousLinearMap.IsInvertible.self_apply_inverseproof · cited by 1
- ContinuousLinearMap.ringInverse_equivproof · cited by 1