reserve S for non empty non void ManySortedSign;
reserve X for non-empty ManySortedSet of S;
reserve x,y,z for set, i,j for Nat;

theorem Th31:
  for A being trivial non-empty MSAlgebra over S
  for s being SortSymbol of S
  for e being Element of (Equations S).s
  holds A |= e
  proof
    let A be trivial non-empty MSAlgebra over S;
    let s be SortSymbol of S;
    let e be Element of (Equations S).s;
    let h be ManySortedFunction of TermAlg S, A;
    assume h is_homomorphism TermAlg S, A;
    h.s.(e`1) in (the Sorts of A).s &
    h.s.(e`2) in (the Sorts of A).s by FUNCT_2:5,EQUATION:30,29;
    hence h.s.(e`1) = h.s.(e`2) by ZFMISC_1:def 10;
  end;
