reserve w, w1, w2 for Element of ExtREAL;
reserve c, c1, c2 for Complex;
reserve A, B, C, D for complex-membered set;
reserve F, G, H, I for ext-real-membered set;
reserve a, b, s, t, z for Complex;
reserve f, g, h, i, j for ExtReal;
reserve r for Real;
reserve e for set;

theorem Th45:
  {f,g}++{h,i} = {f+h,f+i,g+h,g+i}
proof
  thus {f,g}++{h,i} = ({f}\/{g})++{h,i} by ENUMSET1:1
    .= ({f}++{h,i}) \/ ({g}++{h,i}) by Th41
    .= {f+h,f+i} \/ ({g}++{h,i}) by Th44
    .= {f+h,f+i} \/ {g+h,g+i} by Th44
    .= {f+h,f+i,g+h,g+i} by ENUMSET1:5;
end;
