Theorems · Theorem · group theory
AddSubgroup.map_subtype_le_map_subtype
∀ {G : Type u_1} [inst : AddGroup G] {G' : AddSubgroup G} {H K : AddSubgroup ↥G'},
AddSubgroup.map G'.subtype H ≤ AddSubgroup.map G'.subtype K ↔ H ≤ K- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddSubgroup.mapstatement · cited by 189
- AddSubgroup.subtypestatement · cited by 82
- AddSubgroup.subtype_injectiveproof · cited by 10
- AddSubgroup.map_le_map_iff_of_injectiveproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.closure_add_image_eq_topproof · cited by 1