theorem
  for A being non-empty MSAlgebra over S
  for s being SortSymbol of S
  for t1,t2,t3 being Element of TermAlg S,s
  holds A |= t1 '=' t2 & A |= t2 '=' t3 implies A |= t1 '=' t3
  proof
    let A be non-empty MSAlgebra over S;
    let s be SortSymbol of S;
    let t1,t2,t3 be Element of TermAlg S,s;
    assume
A1: A |= t1 '=' t2 & A |= t2 '=' t3;
    let h be ManySortedFunction of TermAlg S, A such that
A2: h is_homomorphism TermAlg S, A;
    h.s.t1 = h.s.t2 & h.s.t2 = h.s.t3 by A1,A2;
    hence thesis;
  end;
