Theorems · Definition · group theory
AddEquiv.addSubmonoidCongr
{M : Type u_1} → [inst : AddZeroClass M] → {S T : AddSubmonoid M} → S = T → ↥S ≃+ ↥TMakes the identity additive isomorphism from a proof two submonoids of an additive monoid are equal.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
- Assumes
- AddZeroClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivproof · cited by 8,337
- SetLike.coeproof · cited by 8,199
- Set.Elemproof · cited by 7,166
- AddZeroClassstatement and proof · cited by 1,237
- AddSubmonoidstatement and proof · cited by 1,178
- AddEquivstatement · cited by 1,087
- Equiv.setCongrproof · cited by 13
Cited by5
Results whose statement or proof uses this declaration.
- IsAddTorsion.torsionAddEquivproof · cited by 4
- IsAddTorsion.torsionAddEquiv_applystatement · cited by 1
- AddMonoid.IsTorsion.torsionAddEquiv_applystatement · cited by 0
- AddCon.quotientKerEquivRangeproof · cited by 0
- AddEquiv.addSubmonoidCongr.congr_simpstatement and proof · cited by 0