reserve C1, C2 for Coherence_Space;

theorem
  for x,y being set st x in union C1 & y in union C2 holds [[x,1],[y,2]]
  in Web (C1 "/\" C2) & [[y,2],[x,1]] in Web (C1 "/\" C2)
proof
  let x,y be set;
  assume x in union C1 & y in union C2;
  then {x} in C1 & {y} in C2 by COH_SP:4;
  then {x} U+ {y} in C1 "/\" C2;
  then [:{x},{1}:] \/ [:{y},{2}:] in C1 "/\" C2 by Th73;
  then {[x,1]} \/ [:{y},{2}:] in C1 "/\" C2 by ZFMISC_1:29;
  then {[x,1]} \/ {[y,2]} in C1 "/\" C2 by ZFMISC_1:29;
  then
A1: {[x,1],[y,2]} in C1 "/\" C2 by ENUMSET1:1;
  hence [[x,1],[y,2]] in Web (C1 "/\" C2) by COH_SP:5;
  thus thesis by A1,COH_SP:5;
end;
