Theorems · Definition · group theory
ofAddUnits_addUnits_gci
{M : Type u_1} → [inst : AddMonoid M] → GaloisCoinsertion AddSubgroup.ofAddUnits AddSubmonoid.addUnitsA Galois coinsertion exists between the coercion from an additive subgroup of additive units to an additive submonoid and the reduction from an additive submonoid to its unit group.
- Defined in
- Mathlib.Algebra.Group.Submonoid.Units
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
- Assumes
- AddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddSubgroupstatement · cited by 3,232
- AddMonoidstatement and proof · cited by 2,864
- AddSubmonoidstatement · cited by 1,178
- AddUnitsstatement · cited by 325
- GaloisCoinsertionstatement · cited by 35
- AddSubmonoid.addUnitsstatement · cited by 32
- AddSubgroup.ofAddUnitsstatement · cited by 30
- AddSubgroup.ofAddUnits_monoproof · cited by 0
- AddSubgroup.addUnits_ofAddUnits_eqproof · cited by 0
- AddSubmonoid.addUnits_monoproof · cited by 0
- GaloisCoinsertion.monotoneIntroproof · cited by 0
- AddSubmonoid.ofAddUnits_addUnits_leproof · cited by 0
Cited by9
Results whose statement or proof uses this declaration.
- ofAddUnits_addUnits_gcproof · cited by 11
- AddSubgroup.ofAddUnits_injectiveproof · cited by 0
- AddSubgroup.ofAddUnits_right_inverseproof · cited by 0
- AddSubgroup.ofAddUnits_strictMonoproof · cited by 0
- AddSubgroup.ofAddUnits_sup_addUnitsproof · cited by 0
- AddSubmonoid.addUnits_botproof · cited by 0
- AddSubmonoid.addUnits_left_inverseproof · cited by 0
- AddSubmonoid.addUnits_surjectiveproof · cited by 0
- AddSubgroup.ofAddUnits_inf_addUnitsproof · cited by 0