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;
reserve
  A0 for (X,S)-terms non-empty MSAlgebra over S,
  A1 for all_vars_including (X,S)-terms MSAlgebra over S,
  A2 for all_vars_including inheriting_operations (X,S)-terms MSAlgebra over S,
  A for all_vars_including inheriting_operations free_in_itself
  (X,S)-terms MSAlgebra over S;

theorem Th54:
  for A being MSAlgebra over S
  holds A |= Equations(S,A)
  proof
    let A be MSAlgebra over S;
    let s be SortSymbol of S;
    let r be Element of (Equations S).s;
    assume r in Equations(S,A).s; then
    r in {e where e is Element of (Equations S).s: A |= e} by Def14; then
    consider e being Element of (Equations S).s such that
A1: r = e & A |= e;
    thus thesis by A1;
  end;
