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, db  being Int-Location st
   CurInstr(P1,Comput(P1,s1,i)) = da := db & da in dom p
  holds Comput(P1,s1,i).db = Comput(P2,s2,i).db
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, db be Int-Location;
  set I = CurInstr(P1,Comput(P1,s1,i));
  set Cs1i = Comput(P1,s1,i);
  set Cs2i = Comput(P2,s2,i);
  set Cs1i1 = Comput(P1,s1,i+1);
  set Cs2i1 = Comput(P2,s2,i+1);
A3: Cs2i1 = Following(P2,Cs2i) by EXTPRO_1:3
    .= Exec (CurInstr(P2, Cs2i), Cs2i);
A4: da in dom  p implies
    (Cs1i1|dom  p).da = Cs1i1.da & (Cs2i1|dom  p).da =
  Cs2i1.da by FUNCT_1:49;
  assume that
A5: I = da := db and
A6: da in dom p & Comput(P1,s1,i).db <> Comput(P2,s2,i).db;
  Cs1i1 = Following(P1,Cs1i) by EXTPRO_1:3
    .= Exec (CurInstr(P1, Cs1i), Cs1i);
  then
A7: Cs1i1.da = Cs1i.db by A5,SCMFSA_2:63;
  I = CurInstr(P2,Comput(P2,s2,i)) by A1,A2,AMISTD_5:7;
  then Cs2i1.da = Cs2i.db by A3,A5,SCMFSA_2:63;
  hence contradiction by A4,A6,A7,A2,A1,EXTPRO_1:def 10;
end;
