Theorems · Theorem · group theory
map_one
∀ {M : Type u_4} {N : Type u_5} {F : Type u_9} [inst : One M] [inst_1 : One N] [inst_2 : FunLike F M N]
[OneHomClass F M N] (f : F), f 1 = 1See note [hom simp lemma priority]
- Defined in
- Mathlib.Algebra.Group.Hom.Defs
- Cited by
- 861 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 12 definitions · uses no axioms
- Assumes
- OneOneFunLikeOneHomClass
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 and proof · cited by 2,560
- OneHomClassstatement and proof · cited by 38
- OneHomClass.map_oneproof · cited by 3
Cited by861
Results whose statement or proof uses this declaration.
- map_natCastproof · cited by 134
- eq_intCastproof · cited by 127
- map_inv₀proof · cited by 106
- eq_natCastproof · cited by 104
- RingHom.map_oneproof · cited by 76
- Polynomial.coeff_X_powproof · cited by 50
- MvPolynomial.map_Xproof · cited by 42
- Polynomial.derivative_Xproof · cited by 34
- Polynomial.eval₂_Xproof · cited by 34
- inner_neg_leftproof · cited by 33
- Function.Injective.isDomainproof · cited by 27
- Polynomial.Monic.natDegree_mapproof · cited by 21
Showing the 200 most cited of 861.