Theorems · Theorem · general algebraic systems
zero_apply
∀ {F : Type u_1} {α : outParam (Type u_2)} {β : outParam (Type u_3)} {inst : FunLike F α β} {inst_1 : Zero β}
{inst_2 : Zero F} [self : IsZeroApply F α β] (x : α), 0 x = 0Alias of IsZeroApply.zero_apply.
- Defined in
- Mathlib.Data.FunLike.IsApply
- Cited by
- 251 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 12 definitions · uses no axioms
- Assumes
- IsZeroApply
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
- IsZeroApplystatement · cited by 72
- IsZeroApply.zero_applyproof · cited by 1
Cited by251
Results whose statement or proof uses this declaration.
- sum_applyproof · cited by 83
- FunLike.coe_zeroproof · cited by 40
- deriv_zero_of_not_differentiableAtproof · cited by 34
- ContinuousLinearMap.comp_zeroproof · cited by 18
- derivWithin_zero_of_not_differentiableWithinAtproof · cited by 12
- iteratedDerivWithin_succproof · cited by 11
- ProbabilityTheory.Kernel.zero_compproof · cited by 10
- hasFDerivAtFilter_constproof · cited by 10
- MeasureTheory.Measure.compProd_of_not_isSFiniteKernelproof · cited by 10
- ContinuousLinearMap.zero_compproof · cited by 9
- MeasureTheory.VectorMeasure.variation_zeroproof · cited by 9
- MeasureTheory.VectorMeasure.restrict_emptyproof · cited by 8
Showing the 200 most cited of 251.