Theorems · Theorem · group theory
AddSubgroup.addCommutator_le_map_addCommutator
∀ {G : Type u_1} {G' : Type u_2} [inst : AddGroup G] [inst_1 : AddGroup G'] {H₁ H₂ : AddSubgroup G} {f : G →+ G'}
{K₁ K₂ : AddSubgroup G'},
K₁ ≤ AddSubgroup.map f H₁ → K₂ ≤ AddSubgroup.map f H₂ → ⁅K₁, K₂⁆ ≤ AddSubgroup.map f ⁅H₁, H₂⁆- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
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- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- LE.le.transproof · cited by 3,151
- Bracket.bracketstatement · cited by 642
- AddSubgroup.mapstatement and proof · cited by 189
- ge_of_eqproof · cited by 67
- AddSubgroup.addCommutator_monoproof · cited by 7
- AddSubgroup.map_addCommutatorproof · cited by 6
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