reserve m,n for Nat;
reserve i,j for Integer;
reserve S for non empty addMagma;
reserve r,r1,r2,s,s1,s2,t,t1,t2 for Element of S;
reserve G for addGroup-like non empty addMagma;
reserve e,h for Element of G;
reserve G for addGroup;
reserve f,g,h for Element of G;
reserve u for UnOp of G;

theorem
  g + h = h + g implies g + ( i * h) = i * h + g
proof
  assume
A1: g + h = h + g;
  thus g + ( i * h) = 1 * g + ( i * h) by Th25
    .= i * h + ( 1 * g) by A1,Th38
    .= i * h + g by Th25;
end;
