Theorems · Theorem · group theory

Set.injOn_iff_map_eq_one

∀ {F : Type u_3} {G : Type u_4} {H : Type u_5} {S : Type u_6} [inst : Group G] [inst_1 : Group H]
  [inst_2 : FunLike F G H] [MonoidHomClass F G H] (f : F) [inst_4 : SetLike S G] [OneMemClass S G] [MulMemClass S G]
  [InvMemClass S G] (s : S), Set.InjOn ⇑f ↑s ↔ ∀ a ∈ s, f a = 1 → a = 1

Defined in

Mathlib.Algebra.Group.Subgroup.Defs

Cited by

0 results in Mathlib

Foundations

Depth 14 from the axioms · uses propext

Assumes

GroupGroupFunLikeMonoidHomClassSetLikeOneMemClassMulMemClassInvMemClass