theorem
  the carrier of S1 = the carrier of S2 & the carrier of T1 = the
  carrier of T2 implies [:R1,R2:] is Refinement of [:S1,T1:], [:S2,T2:]
proof
  set R = the strict Refinement of [:S1,T1:], [:S2,T2:];
  assume
A1: the carrier of S1 = the carrier of S2 & the carrier of T1 = the
  carrier of T2;
  then the carrier of [:R1,R2:] = the carrier of R by Th49;
  hence thesis by A1,Th49;
end;
