Theorems · Theorem · general algebraic systems
add_apply
∀ {F : Type u_1} {α : outParam (Type u_2)} {β : outParam (Type u_3)} {inst : FunLike F α β} {inst_1 : Add β}
{inst_2 : Add F} [self : IsAddApply F α β] (f g : F) (x : α), (f + g) x = f x + g xAlias of IsAddApply.add_apply.
- Defined in
- Mathlib.Data.FunLike.IsApply
- Cited by
- 154 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 11 definitions · uses no axioms
- Assumes
- IsAddApply
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
- IsAddApplystatement · cited by 75
- IsAddApply.add_applyproof · cited by 1
Cited by154
Results whose statement or proof uses this declaration.
- sum_applyproof · cited by 83
- FunLike.coe_addproof · cited by 30
- HasDerivWithinAt.mulproof · cited by 7
- HasDerivWithinAt.smulproof · cited by 6
- hasStrictFDerivAt_norm_sqproof · cited by 6
- HasDerivAtFilter.addproof · cited by 5
- MeasureTheory.VectorMeasure.integral_add_vectorMeasureproof · cited by 5
- ContinuousLinearMap.add_compproof · cited by 5
- iteratedDerivWithin_addproof · cited by 5
- ContinuousLinearMap.hasDerivAt_of_bilinearproof · cited by 4
- hasStrictFDerivAt_list_prod'proof · cited by 4
- MeasureTheory.withDensityᵥ_addproof · cited by 4