Theorems · Inductive type · general algebraic systems
IsOneApplyEqSelf
(F : Type u_1) → (α : outParam (Type u_2)) → [FunLike F α α] → [One F] → Prop
IsOneApplyEqSelf F α α states for all x : α, (1 : F) x = x.
- Defined in
- Mathlib.Data.FunLike.IsApply
- Cited by
- 12 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 by17
Results whose statement or proof uses this declaration.
- one_apply_eq_selfstatement · cited by 34
- FunLike.coe_one_eq_idstatement and proof · cited by 3
- FunLike.coe_pow_eq_iteratestatement and proof · cited by 2
- IsOneApplyEqSelf.one_apply_eq_selfstatement and proof · cited by 1
- FunLike.natCast_eq_nsmul_onestatement and proof · cited by 1
- pow_apply_eq_iteratestatement and proof · cited by 1
- FunLike.intCast_eq_zsmul_onestatement and proof · cited by 1
- FunLike.monoidWithZerostatement and proof · cited by 0
- IsOneApplyEqSelf.casesOnstatement and proof · cited by 0
- IsOneApplyEqSelf.recOnstatement and proof · cited by 0
- ContinuousLinearMap.coe_pow'statement · cited by 0
- FunLike.ringstatement and proof · cited by 0