reserve C1, C2 for Coherence_Space;

theorem
  for x,y being set holds not [[x,1],[y,2]] in Web (C1 "\/" C2) & not [[
  y,2],[x,1]] in Web (C1 "\/" C2)
proof
  let x,y be set;
A1: {x} U+ {y} = [:{x},{1}:] \/ [:{y},{2}:] by Th73
    .= {[x,1]} \/ [:{y},{2}:] by ZFMISC_1:29
    .= {[x,1]} \/ {[y,2]} by ZFMISC_1:29
    .= {[x,1],[y,2]} by ENUMSET1:1;
A2: not {x} U+ {y} in C1 "\/" C2 by Th86;
  hence not [[x,1],[y,2]] in Web (C1 "\/" C2) by A1,COH_SP:5;
  thus thesis by A2,A1,COH_SP:5;
end;
