
theorem Th39: :: iMR1ba:
for n being Nat, R being NatRelStr of n
 holds the InternalRel of R c= the InternalRel of Mycielskian R
proof
 let n be Nat, R be NatRelStr of n;
 set iR = the InternalRel of R;
 set MR = Mycielskian R;
 set iMR = the InternalRel of MR;
 iMR = iR
   \/ { [x,y+n] where x, y is Element of NAT : [x,y] in iR }
   \/ { [x+n,y] where x, y is Element of NAT : [x,y] in iR }
   \/ [: {2*n}, 2*n \ n :] \/ [: 2*n \ n, {2*n} :] by Def9;
 hence iR c= iMR by Th3;
end;
