reserve A for preIfWhileAlgebra;

theorem Th16:
  for f being INT-Exec for v being INT-Variable of NAT for t being
  INT-Expression of NAT holds v,t form_assignment_wrt f
proof
  let f be INT-Exec;
  set S = ECIW-signature, G = INT-ElemIns;
  set X = NAT;
  set A = FreeUnivAlgNSG(S,G);
  let v be INT-Variable of NAT;
  let t be INT-Expression of NAT;
  reconsider v9 = v as Element of Funcs(Funcs(X,INT),X) by FUNCT_2:8;
  reconsider t9 = t as Element of Funcs(Funcs(X,INT),INT) by FUNCT_2:8;
A1: Terminals DTConUA(S,G) = G by FREEALG:3;
A2: [v9,t9] in G by ZFMISC_1:87;
A3: ElementaryInstructions A = FreeGenSetNSG(S,G) by AOFA_000:70;
  then root-tree [v9,t9] in ElementaryInstructions A by A1,A2;
  then reconsider I = root-tree [v9,t9] as Element of A;
  take I;
  thus I in ElementaryInstructions A by A3,A1,A2;
  thus thesis by Def25;
end;
