reserve C1, C2 for Coherence_Space;

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