reserve C1, C2 for Coherence_Space;

theorem
  for x,y being set holds [[x,2],[y,2]] in Web (C1 "/\" C2) iff [x,y] in Web C2
proof
  let x,y be set;
A1: [[x,2],[y,2]] in Web (C1 "/\" C2) iff {[x,2],[y,2]} in C1 "/\" C2 by
COH_SP:5;
A2: [x,y] in Web C2 iff {x,y} in C2 by COH_SP:5;
A3: [:{x,y},{2}:] = {[x,2],[y,2]} by ZFMISC_1:30;
  {} U+ {x,y} = [:{x,y},{2}:] & {} in C1 by Th74,COH_SP:1;
  hence thesis by A1,A2,A3,Th84;
end;
