theorem Th64:
  p in rng f1 implies (f1^f2):-p = (f1:-p)^f2
proof
  assume
A1: p in rng f1;
  rng(f1^f2) = rng f1 \/ rng f2 by FINSEQ_1:31;
  then p in rng(f1^f2) by A1,XBOOLE_0:def 3;
  hence (f1^f2):-p = <*p*>^((f1^f2)|--p) by Th41
    .= <*p*>^((f1|--p)^f2) by A1,Th8
    .= <*p*>^(f1|--p)^f2 by FINSEQ_1:32
    .= (f1:-p)^f2 by A1,Th41;
end;
