Theorems · Theorem · functional analysis
ContinuousLinearMap.IsInvertible.inverse_apply_eq
∀ {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} {x : M} {y : M₂}, f.IsInvertible → (f.inverse y = x ↔ y = f x)- Defined in
- Mathlib.Topology.Algebra.Module.Equiv
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · 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
- 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
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