Theorems · Theorem · general algebraic systems
one_apply_eq_self
∀ {F : Type u_1} {α : outParam (Type u_2)} {inst : FunLike F α α} {inst_1 : One F} [self : IsOneApplyEqSelf F α]
(x : α), 1 x = xAlias of IsOneApplyEqSelf.one_apply_eq_self.
- Defined in
- Mathlib.Data.FunLike.IsApply
- Cited by
- 34 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- IsOneApplyEqSelf
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
- IsOneApplyEqSelfstatement · cited by 12
- IsOneApplyEqSelf.one_apply_eq_selfproof · cited by 1
Cited by34
Results whose statement or proof uses this declaration.
- HasDerivAt.real_of_complexproof · cited by 7
- HasStrictDerivAt.real_of_complexproof · cited by 6
- IsMIntegralCurveOn.comp_mulproof · cited by 3
- FunLike.coe_one_eq_idproof · cited by 3
- MeasureTheory.lintegral_image_eq_lintegral_deriv_mul_of_monotoneOnproof · cited by 3
- hasFDerivAt_exp_smul_const_of_mem_ballproof · cited by 3
- ContinuousLinearMap.toSpanSingleton_powproof · cited by 3
- hasStrictDerivAt_exp_of_mem_ballproof · cited by 2
- hasStrictDerivAt_exp_smul_const_of_mem_ballproof · cited by 2
- hasStrictDerivAt_exp_smul_const_of_mem_ball'proof · cited by 2
- Complex.one_div_one_sub_cpow_hasFPowerSeriesOnBall_zeroproof · cited by 2