reserve x,y,z for set;
reserve f,f1,f2,f3 for FinSequence,
  p,p1,p2,p3 for set,
  i,k for Nat;

theorem Th28:
  x <> z & y <> z implies <*x,y,z*> -| z = <*x,y*>
proof
  assume that
A1: x <> z and
A2: y <> z;
  rng<*x,y,z*> = { x,y,z } by Lm2;
  then
A3: z in rng<*x,y,z*> by ENUMSET1:def 1;
  z..<*x,y,z*> = 2+1 by A1,A2,Th23;
  then 2 = z..<*x,y,z*>-1;
  hence <*x,y,z*> -| z = <*x,y,z*>| Seg 2 by A3,FINSEQ_4:33
    .= <*x,y*> by Th5;
end;
