Theorems · Theorem · general algebraic systems
neg_apply
∀ {F : Type u_1} {α : outParam (Type u_2)} {β : outParam (Type u_3)} {inst : FunLike F α β} {inst_1 : Neg β}
{inst_2 : Neg F} [self : IsNegApply F α β] (f : F) (x : α), (-f) x = -f xAlias of IsNegApply.neg_apply.
- Defined in
- Mathlib.Data.FunLike.IsApply
- Cited by
- 96 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 8 definitions · uses no axioms
- Assumes
- IsNegApply
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- FunLikestatement · cited by 2,560
- IsNegApplystatement · cited by 21
- IsNegApply.neg_applyproof · cited by 1
Cited by96
Results whose statement or proof uses this declaration.
- FunLike.coe_negproof · cited by 13
- HasDerivAtFilter.negproof · cited by 7
- MeasureTheory.VectorMeasure.neg_le_negproof · cited by 6
- hasFDerivAt_ringInverseproof · cited by 5
- MeasureTheory.SignedMeasure.toMeasureOfLEZero_applystatement and proof · cited by 5
- ContinuousLinearMap.comp_negproof · cited by 4
- ConvexOn.exists_affine_le_of_ltproof · cited by 4
- spectrum.hasDerivAt_resolvent_const_leftproof · cited by 3
- VectorField.pullbackWithin_lieBracketWithin_of_isSymmSndFDerivWithinAtproof · cited by 3
- iteratedFDerivWithin_neg_applyproof · cited by 3
- MeasureTheory.VectorMeasure.variation_negproof · cited by 3
- MeasureTheory.withDensityᵥ_negproof · cited by 3