Theorems · Theorem · functional analysis
ContinuousLinearEquiv.neg_apply
∀ {R : Type u_1} [inst : Semiring R] {M : Type u_2} [inst_1 : TopologicalSpace M] [inst_2 : AddCommGroup M]
[inst_3 : Module R M] [inst_4 : ContinuousNeg M] (x : M), (ContinuousLinearEquiv.neg R) x = -x- Defined in
- Mathlib.Topology.Algebra.Module.Equiv
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommGroupstatement and proof · cited by 12,871
- ContinuousLinearEquivstatement · cited by 743
- ContinuousNegstatement and proof · cited by 119
- ContinuousLinearEquiv.negstatement · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.negAt_apply_isReal_and_memproof · cited by 5
- NumberField.mixedEmbedding.negAt_symmproof · cited by 2
- ProbabilityTheory.IsGaussian.integral_dual_conv_map_neg_eq_zeroproof · cited by 1