Theorems · Theorem · functional analysis
ContinuousLinearMap.ringInverse_equiv
∀ {R : Type u_1} {M : Type u_2} [inst : TopologicalSpace M] [inst_1 : Semiring R] [inst_2 : AddCommMonoid M]
[inst_3 : Module R M] (e : M ≃L[R] M), Ring.inverse ↑e = (↑e).inverse- Defined in
- Mathlib.Topology.Algebra.Module.Equiv
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- 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
- Units.valproof · cited by 1,966
- ContinuousLinearEquivstatement and proof · cited by 743
- MulEquiv.symmproof · cited by 482
- MonoidWithZeroproof · cited by 456
- ContinuousLinearEquiv.toContinuousLinearMapstatement and proof · cited by 448
Cited by1
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.inverse_eq_ringInverseproof · cited by 2