reserve i,j,e,u for object;
reserve I for set; 
reserve x,X,Y,Z,V for ManySortedSet of I;

theorem Th107:
  X meets Y & Y c= Z implies X meets Z
proof
  assume that
A1: X meets Y and
A2: Y c= Z;
  consider i being object such that
A3: i in I and
A4: X.i meets Y.i by A1;
  take i;
  Y.i c= Z.i by A2,A3;
  hence thesis by A3,A4,XBOOLE_1:63;
end;
