Theorems · Definition · group theory

AddGroupExtension.Equiv.trans

{N : Type u_1} →
  {E : Type u_2} →
    {G : Type u_3} →
      [inst : AddGroup N] →
        [inst_1 : AddGroup E] →
          [inst_2 : AddGroup G] →
            {S : AddGroupExtension N E G} →
              {E' : Type u_4} →
                [inst_3 : AddGroup E'] →
                  {S' : AddGroupExtension N E' G} →
                    S.Equiv S' →
                      {E'' : Type u_5} →
                        [inst_4 : AddGroup E''] → {S'' : AddGroupExtension N E'' G} → S'.Equiv S'' → S.Equiv S''

The composition of monoid isomorphisms associated to equivalences of additive group extensions gives another equivalence.

Defined in

Mathlib.GroupTheory.GroupExtension.Defs

Cited by

2 results in Mathlib

Foundations

Depth 22 from the axioms · uses Quot.sound

Assumes

AddGroupAddGroupAddGroupAddGroupAddGroup