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;
