reserve A for preIfWhileAlgebra;
reserve A for Euclidean preIfWhileAlgebra;
reserve X for non empty countable set;
reserve T for Subset of Funcs(X, INT);
reserve f for Euclidean ExecutionFunction of A, Funcs(X, INT), T;

theorem Th23:
  for v being INT-Variable of A,f for t being INT-Expression of A,
  f holds v:=t in ElementaryInstructions A
proof
  let v be INT-Variable of A,f;
  let t be INT-Expression of A,f;
  set Y = {I where I is Element of A: I in ElementaryInstructions A & for s
  being Element of Funcs(X, INT) holds f.(s,I) = s+*(v.s,t.s)};
  v,t form_assignment_wrt f by Def22;
  then consider I0 being Element of A such that
A1: I0 in ElementaryInstructions A and
A2: for s being Element of Funcs(X, INT) holds f.(s,I0) = s+*(v.s,t.s);
  I0 in Y by A1,A2;
  then v:=t in Y;
  then ex I being Element of A st v:=t = I & I in ElementaryInstructions A &
  for s being Element of Funcs(X, INT) holds f.(s,I) = s+*(v.s,t.s);
  hence thesis;
end;
