Theorems · Definition · group theory
QuotientAddGroup.quotientBot
{G : Type u} → [inst : AddGroup G] → G ⧸ ⊥ ≃+ GThe canonical isomorphism G/⊥ ≃+ G.
- Defined in
- Mathlib.GroupTheory.QuotientGroup.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 84 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botstatement · cited by 4,720
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- HasQuotient.Quotientstatement · cited by 2,301
- AddEquivstatement · cited by 1,087
- AddMonoidHom.idproof · cited by 107
- QuotientAddGroup.quotientKerEquivOfRightInverseproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- AddSubgroup.index_botproof · cited by 4
- QuotientAddGroup.quotientBotIsometryEquivproof · cited by 0
- QuotientAddGroup.quotientBot_applystatement and proof · cited by 0
- QuotientAddGroup.quotientBot_symm_applystatement and proof · cited by 0