Theorems · Theorem · group theory
QuotientAddGroup.equivQuotientZSMulOfEquiv_trans
∀ {A B C : Type u} [inst : AddCommGroup A] [inst_1 : AddCommGroup B] [inst_2 : AddCommGroup C] (e : A ≃+ B) (d : B ≃+ C)
(n : ℤ),
(QuotientAddGroup.equivQuotientZSMulOfEquiv e n).trans (QuotientAddGroup.equivQuotientZSMulOfEquiv d n) =
QuotientAddGroup.equivQuotientZSMulOfEquiv (e.trans d) n- Defined in
- Mathlib.GroupTheory.QuotientGroup.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- AddCommGroupstatement and proof · cited by 12,871
- AddSubgroupstatement · cited by 3,232
- HasQuotient.Quotientstatement and proof · cited by 2,301
- AddEquivstatement and proof · cited by 1,087
- AddMonoidHom.rangestatement and proof · cited by 142
- Quotient.outproof · cited by 141
- Quotient.mk''proof · cited by 132
- AddEquiv.transstatement and proof · cited by 53
- Quotient.out_eq'proof · cited by 35
- QuotientAddGroup.leftRelproof · cited by 34
- AddEquiv.extproof · cited by 30
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