reserve k for Nat,
  da,db for Int-Location,
  fa for FinSeq-Location;

theorem
   for q being non halt-free finite
      (the InstructionsF of SCM+FSA)-valued NAT-defined Function
  for p being q-autonomic non empty FinPartState of SCM+FSA,
      s1, s2
  being State of SCM+FSA st  p c= s1 &  p c= s2
  for P1,P2 being Instruction-Sequence of SCM+FSA
   st q c= P1 & q c= P2
  for i being Nat, da
being Int-Location, f being FinSeq-Location st
 CurInstr(P1,Comput(P1,s1,i)) =
da :=len f & da in dom p holds len( Comput(P1,s1,i).f)
 = len(Comput(P2,s2,i).f)
proof
  let q being non halt-free finite
      (the InstructionsF of SCM+FSA)-valued NAT-defined Function;
  let p be q-autonomic non empty FinPartState of SCM+FSA,
      s1, s2 be State
  of SCM+FSA such that
A1:  p c= s1 &  p c= s2;
  let P1,P2 be Instruction-Sequence of SCM+FSA
  such that
A2: q c= P1 & q c= P2;
  let i be Nat, da be Int-Location, f be FinSeq-Location;
  set Cs1i1 = Comput(P1,s1,i+1);
  set Cs2i1 = Comput(P2,s2,i+1);
A3: Cs1i1|dom  p = Cs2i1|dom  p by A1,A2,EXTPRO_1:def 10;
  set Cs2i = Comput(P2,s2,i);
  set Cs1i = Comput(P1,s1,i);
  set I = CurInstr(P1,Comput(P1,s1,i));
A4: Cs1i1 = Following(P1,Cs1i) by EXTPRO_1:3
    .= Exec (CurInstr(P1, Cs1i), Cs1i);
A5: da in dom  p implies
 (Cs1i1|dom  p).da = Cs1i1.da & (Cs2i1|dom  p).da =
  Cs2i1.da by FUNCT_1:49;
A6: Cs2i1 = Following(P2,Cs2i) by EXTPRO_1:3
    .= Exec (CurInstr(P2, Cs2i), Cs2i);
  assume that
A7: I = da :=len f and
A8: da in dom p & len( Comput(P1,s1,i).f) <> len( Comput(
P2,s2,i).f);
  Exec(I, Cs1i).da = len(Cs1i.f) & Exec(I, Cs2i).da = len(Cs2i.f) by A7,
SCMFSA_2:74;
  hence contradiction by A1,A4,A6,A5,A3,A8,A2,AMISTD_5:7;
end;
