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Theorems · Theorem · group theory

OneHomClass.map_one

∀ {F : Type u_10} {M : outParam (Type u_11)} {N : outParam (Type u_12)} {inst : One M} {inst_1 : One N}
  {inst_2 : FunLike F M N} [self : OneHomClass F M N] (f : F), f 1 = 1

The proposition that the function preserves 1

Defined in
Mathlib.Algebra.Group.Hom.Defs
Cited by
3 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
OneHomClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

map_one · cited by 861map_oneOneHomClass.toOneHom · cited by 2OneHomClass.toOneHomOneHomClass.bound_of_antilipschitz · cited by 0OneHomClass.bound_of_anti…PontryaginDual.map_one · cited by 0PontryaginDual.map_oneDFunLike.coe · cited by 62936DFunLike.coeFunLike · cited by 2560FunLikeOneHomClass · cited by 38OneHomClassOneHomClass.map_oneCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by4

Results whose statement or proof uses this declaration.