theorem Th27:
  for r being SortSymbol of S, y being Element of X.r holds
  x-term is context of y iff r = s & x = y
  proof
    let r be SortSymbol of S, y be Element of X.r;
A0: ([x,s] in {[y,r]} iff [x,s] = [y,r]) & (x-term).{} = [x,s] &
    Coim(x-term, [y,r]) c= dom(x-term) = {{}} & {} in {{}}
    by TARSKI:def 1,TREES_1:29,TREES_4:3,RELAT_1:132;
    (ex a st Coim(x-term, [y,r]) = {a}) implies Coim(x-term, [y,r]) = {{}}
    by A0,ZFMISC_1:33;
    then card Coim(x-term, [y,r]) = 1 implies Coim(x-term, [y,r]) = {{}}
    by CARD_2:42;
    hence thesis by A0,CONTEXT,XTUPLE_0:1,FUNCT_1:def 7;
  end;
