
theorem Th59:
  for L being RelStr, S being SubRelStr of L for a,b being Element
  of L for x,y being Element of S st x = a & y = b & x <= y holds a <= b
proof
  let L be RelStr, S be SubRelStr of L;
  let a,b be Element of L, x,y be Element of S such that
A1: x = a & y = b;
A2: the InternalRel of S c= the InternalRel of L by Def13;
  assume [x,y] in the InternalRel of S;
  hence [a,b] in the InternalRel of L by A1,A2;
end;
