reserve
  S for (4,1) integer bool-correct non empty non void BoolSignature,
  X for non-empty ManySortedSet of the carrier of S,
  T for vf-free integer all_vars_including inheriting_operations free_in_itself
  (X,S)-terms VarMSAlgebra over S,
  C for (4,1) integer bool-correct non-empty image of T,
  G for basic GeneratorSystem over S,X,T,
  A for IfWhileAlgebra of the generators of G,
  I for integer SortSymbol of S,
  x,y,z,m for pure (Element of (the generators of G).I),
  b for pure (Element of (the generators of G).the bool-sort of S),
  t,t1,t2 for Element of T,I,
  P for Algorithm of A,
  s,s1,s2 for Element of C-States(the generators of G);
reserve
  f for ExecutionFunction of A, C-States(the generators of G),
  (\falseC)-States(the generators of G, b);
reserve u for ManySortedFunction of FreeGen T, the Sorts of C;

theorem Th41:
  (t1-t2) value_at(C,s) = (t1 value_at(C,s))-(t2 value_at(C,s))
  proof
    thus (t1-t2) value_at(C,s) = (t1 value_at(C,s))+((-t2) value_at(C,s))
    by Th39
    .= (t1 value_at(C,s))-(t2 value_at(C,s)) by Th38;
  end;
