
theorem Th8:
  for nt being NonTerminal of SCM-AE, t1, t2 being bin-term, n
being Element of NAT, rtl, rtr being Symbol of SCM-AE st rtl = root-label t1 &
rtr = root-label t2 & nt ==> <*rtl, rtr*> holds SCM-Compile(nt-tree(t1,t2), n)
  = SCM-Compile(t1, n)^SCM-Compile(t2, n+1)^Selfwork(nt, n)
proof
  let nt be NonTerminal of SCM-AE, t1, t2 be bin-term, n be Element of NAT,
  rtl, rtr be Symbol of SCM-AE;
  assume
A1: rtl = root-label t1 & rtr = root-label t2 & nt ==> <*rtl, rtr*>;
  consider g, f1, f2 being sequence of  (the InstructionsF of SCM)^omega
 such that
A2: g = SCM-Compile.(nt-tree (t1, t2)) and
A3: f1 = SCM-Compile.t1 and
A4: f2 = SCM-Compile.t2 and
A5: for n being Nat holds g.n
    = (f1.In(n,NAT))^(f2.In(n+1,NAT))^Selfwork(nt, n)
          by A1,Def11;
   g.n = (f1.In(n,NAT))^(f2.In(n+1,NAT))^Selfwork(nt, n) by A5;
  hence SCM-Compile(nt-tree(t1,t2), n)
   = SCM-Compile(t1, n)^SCM-Compile(t2, n+1)^Selfwork(nt, n) by A3,A4,A2;
end;
