reserve p,q,r for FinSequence;
reserve u,v,x,y,y1,y2,z for object, A,D,X,Y for set;
reserve i,j,k,l,m,n for Nat;

theorem Th96:
  p is one-to-one & rng p = {x,y} & x <> y implies len p = 2
proof
  assume that
A1: p is one-to-one and
A2: rng p = {x,y} and
A3: x <> y;
  set q = <* x,y *>;
A4: rng q = {x,y} by FINSEQ_2:127;
A5: len q = 2 by FINSEQ_1:44;
  q is one-to-one by A3,Th92;
  hence thesis by A1,A2,A4,A5,FINSEQ_1:48;
end;
