Theorems · Theorem · group theory
AddSubgroup.map_eq_bot_iff_of_injective
∀ {G : Type u_1} [inst : AddGroup G] {N : Type u_5} [inst_1 : AddGroup N] (H : AddSubgroup G) {f : G →+ N},
Function.Injective ⇑f → (AddSubgroup.map f H = ⊥ ↔ H = ⊥)- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Bot.botstatement and proof · cited by 4,720
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- AddSubgroup.mapstatement · cited by 189
- le_bot_iffproof · cited by 116
- AddMonoidHom.ker_eq_botproof · cited by 7
- AddSubgroup.map_eq_bot_iffproof · cited by 6
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