Theorems · Theorem · general algebraic systems
sub_apply
∀ {F : Type u_1} {α : outParam (Type u_2)} {β : outParam (Type u_3)} {inst : FunLike F α β} {inst_1 : Sub β}
{inst_2 : Sub F} [self : IsSubApply F α β] (f g : F) (x : α), (f - g) x = f x - g xAlias of IsSubApply.sub_apply.
- Defined in
- Mathlib.Data.FunLike.IsApply
- Cited by
- 51 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- IsSubApply
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
- IsSubApplystatement · cited by 21
- IsSubApply.sub_applyproof · cited by 1
Cited by51
Results whose statement or proof uses this declaration.
- FunLike.coe_subproof · cited by 15
- MeasureTheory.Measure.toSignedMeasure_sub_applyproof · cited by 6
- HarmonicAt.differentiableAt_complex_partialproof · cited by 3
- isClosed_setOfPred_isCompactOperatorproof · cited by 3
- MeasureTheory.SignedMeasure.null_of_totalVariation_zeroproof · cited by 3
- hasFDerivAt_of_tendstoUniformlyOnFilterproof · cited by 2
- intervalIntegral.integral_hasFDerivWithinAt_of_tendsto_aeproof · cited by 2
- intervalIntegral.integral_hasStrictFDerivAt_of_tendsto_aeproof · cited by 2
- eVariationOn_bilinear_comp_leproof · cited by 2
- Submodule.starProjection_orthogonalproof · cited by 2
- ContinuousLinearMap.IsIdempotentElem.isSelfAdjoint_iff_isStarNormalproof · cited by 2
- MeasureTheory.SignedMeasure.withDensityᵥ_rnDeriv_eqproof · cited by 2