theorem Th58:
  k in Seg n & c1 = z1.k & c2 = z2.k implies (z1 + z2).k = c1 + c2
proof
  assume that
A1: k in Seg n and
A2: c1 = z1.k & c2 = z2.k;
  k in dom(z1+z2) by A1,Lm4;
  hence (z1 + z2).k = addcomplex.(c1,c2) by A2,FUNCOP_1:22
    .= c1 + c2 by BINOP_2:def 3;
end;
