Theorems · Inductive type · general algebraic systems
IsZeroApply
(F : Type u_1) → (α : outParam (Type u_2)) → (β : outParam (Type u_3)) → [FunLike F α β] → [Zero β] → [Zero F] → Prop
IsZeroApply F α β states for all x : α, (0 : F) x = 0.
- Defined in
- Mathlib.Data.FunLike.IsApply
- Cited by
- 72 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- FunLikestatement · cited by 2,560
Cited by103
Results whose statement or proof uses this declaration.
- zero_applystatement · cited by 251
- sum_applystatement and proof · cited by 83
- FunLike.coe_zerostatement and proof · cited by 40
- FunLike.coeAddMonoidHomstatement and proof · cited by 19
- FunLike.coeAddMonoidHom_applystatement and proof · cited by 7
- FunLike.coe_sumstatement and proof · cited by 6
- FunLike.coe_coeAddMonoidHomstatement and proof · cited by 4
- FunLike.coeAddMonoidHom_injectivestatement and proof · cited by 3
- Seminorm.zero_applystatement · cited by 1
- FunLike.coe_zero_iffstatement and proof · cited by 1
- IsZeroApply.zero_applystatement and proof · cited by 1
- ContinuousMultilinearMap.changeOrigin_toFormalMultilinearSeriesproof · cited by 1