reserve A,X,X1,X2,Y,Y1,Y2 for set, a,b,c,d,x,y,z for object;
reserve P,P1,P2,Q,R,S for Relation;

theorem Th169:
  dom R misses dom S implies R misses S
proof
   assume
A1: dom R misses dom S;
   assume R meets S;
   then consider x being object such that
A2:x in R and
A3:x in S by XBOOLE_0:3;
   consider y,z such that
A4:x = [y,z] by A2,Def1;
   y in dom R & y in dom S by A2,A3,A4,XTUPLE_0:def 12;
   hence contradiction by A1,XBOOLE_0:3;
end;
