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Theorems · Theorem · group theory

map_ne_one_iff

∀ {R : Type u_10} {S : Type u_11} {F : Type u_12} [inst : One R] [inst_1 : One S] [inst_2 : FunLike F R S]
  [OneHomClass F R S] (f : F), Function.Injective ⇑f → ∀ {x : R}, f x ≠ 1 ↔ x ≠ 1
Defined in
Mathlib.Algebra.Group.Hom.Defs
Cited by
1 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
OneOneFunLikeOneHomClass
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

riemannZeta_conj · cited by 0riemannZeta_conjDFunLike.coe · cited by 62936DFunLike.coeFunLike · cited by 2560FunLikeIff.not · cited by 489Iff.notOneHomClass · cited by 38OneHomClassmap_eq_one_iff · cited by 15map_eq_one_iffmap_ne_one_iffCITED BYCITES

Cites5

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Cited by1

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