reserve i,j for Nat;
reserve i,j for Nat,
  x for variable,
  l for quasi-loci;
reserve C for initialized ConstructorSignature,
  c for constructor OperSymbol of C;
reserve a,a9 for quasi-adjective,
  t,t1,t2 for quasi-term,
  T for quasi-type,

  c for Element of Constructors;

theorem
 for t1,t2,t being expression of C st t is_a_unification_of t1,t2
  holds t matches_with t1 & t matches_with t2
  proof
   let t1,t2,t be expression of C;
   given f being valuation of C such that
A1: f unifies t1,t2 & t = t1 at f;
   thus ex f being valuation of C st t = t1 at f by A1;
   take f; thus t = t2 at f by A1;
  end;
