
theorem Th44:
  for x,y,z,f being object holds x in the carrier of 1GateCircStr(<*x
,y,z*>,f) & y in the carrier of 1GateCircStr(<*x,y,z*>,f) & z in the carrier of
  1GateCircStr(<*x,y,z*>,f)
proof
  let x,y,z,f be object;
  set p = <*x,y,z*>;
  set A = the carrier of 1GateCircStr(p,f);
  y in {x,y,z} by ENUMSET1:def 1;
  then
A1: y in rng p by FINSEQ_2:128;
  z in {x,y,z} by ENUMSET1:def 1;
  then
A2: z in rng p by FINSEQ_2:128;
  x in {x,y,z} by ENUMSET1:def 1;
  then A = rng p \/ {[p,f]} & x in rng p by CIRCCOMB:def 6,FINSEQ_2:128;
  hence thesis by A1,A2,XBOOLE_0:def 3;
end;
