reserve A for preIfWhileAlgebra,
  C,I,J for Element of A;
reserve S for non empty set,
  T for Subset of S,
  s for Element of S;
reserve f for ExecutionFunction of A,S,T;

theorem
  for A being free ECIW-strict preIfWhileAlgebra
  for f1,f2 being ExecutionFunction of A, S, T
  st f1|[:S, ElementaryInstructions A:] = f2|[:S, ElementaryInstructions A:]
  for s being Element of S
  for I being Element of A st [s,I] in TerminatingPrograms(A,S,T,f1)
  holds f1.(s, I) = f2.(s, I) by Lm3;
