reserve i for Nat,
  j for Element of NAT,
  X,Y,x,y,z for set;
reserve C for initialized ConstructorSignature,
  s for SortSymbol of C,
  o for OperSymbol of C,
  c for constructor OperSymbol of C;
reserve a,b for expression of C, an_Adj C;
reserve t, t1,t2 for expression of C, a_Type C;
reserve p for FinSequence of QuasiTerms C;
reserve e for expression of C;
reserve a,a9 for expression of C, an_Adj C;
reserve q for pure expression of C, a_Type C,
  A for finite Subset of QuasiAdjs C;
reserve T for quasi-type of C;
reserve f for valuation of C;
reserve x for variable;

theorem Th144:
  for A being Subset of QuasiAdjs C for a being quasi-adjective of C st A = {a}
  holds A at f = {a at f}
proof
  let A be Subset of QuasiAdjs C;
  let a be quasi-adjective of C such that
A1: A = {a};
  thus A at f c= {a at f}
  proof
    let x be object;
    assume x in A at f;
    then ex b being quasi-adjective of C st x = b at f & b in A;
    then x = a at f by A1,TARSKI:def 1;
    hence thesis by TARSKI:def 1;
  end;
  let x be object;
  assume x in {a at f};
  then
A2: x = a at f by TARSKI:def 1;
  a in A by A1,TARSKI:def 1;
  hence thesis by A2;
end;
