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 Th91:
  <* x *> is one-to-one
proof
  let y1,y2 be object;
  assume that
A1: y1 in dom<* x *> and
A2: y2 in dom<* x *> and
  <* x *>.y1 = <* x *>.y2;
  y1 in {1} by A1,FINSEQ_1:2,def 8;
  then
A3: y1 = 1 by TARSKI:def 1;
  y2 in {1} by A2,FINSEQ_1:2,def 8;
  hence thesis by A3,TARSKI:def 1;
end;
