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

theorem
  Web(C) = Web(D) implies C = D
proof
  assume
A1: Web(C) = Web(D);
  thus C c= D
  proof
    let x be object;
    reconsider xx=x as set by TARSKI:1;
    assume x in C;
    then for z,y st z in xx & y in xx holds [z,y] in Web(D) by A1,Th7;
    hence thesis by Th7;
  end;
  let x be object;
    reconsider xx=x as set by TARSKI:1;
  assume x in D;
  then for z,y st z in xx & y in xx holds [z,y] in Web(C) by A1,Th7;
  hence thesis by Th7;
end;
