reserve k,m,n for Element of NAT,
  a,X,Y for set,
  D,D1,D2 for non empty set;
reserve p,q for FinSequence of NAT;
reserve x,y,z,t for Variable;

theorem Th3:
  All(x,p) = All(y,q) implies x = y & p = q
proof
A1: <*4*>^<*x*>^p = <*4*>^(<*x*>^p) & <*4*>^<*y*>^q = <*4*>^(<*y*>^q) by
FINSEQ_1:32;
A2: (<*x*>^p).1 = x & (<*y*>^q).1 = y by FINSEQ_1:41;
  assume
A3: All(x,p) = All(y,q);
  hence x = y by A1,A2,FINSEQ_1:33;
  <*x*>^p = <*y*>^q by A3,A1,FINSEQ_1:33;
  hence thesis by A2,FINSEQ_1:33;
end;
