reserve x,y,z,a,b,c,X,A for set;
reserve C,D for Coherence_Space;
reserve T for Tolerance of union C;
reserve E for Tolerance of X;

theorem
  CohSp(Web(C)) = C
proof
  thus CohSp(Web(C)) c= C
  proof
    let x be object;
    reconsider xx=x as set by TARSKI:1;
    assume x in CohSp(Web(C));
    then for y,z st y in xx & z in xx holds [y,z] in Web(C) by Def3;
    hence thesis by Th7;
  end;
  let x be object;
    reconsider xx=x as set by TARSKI:1;
  assume x in C;
  then for y,z st y in xx & z in xx holds [y,z] in Web(C) by Th7;
  hence thesis by Def3;
end;
