reserve p for preProgram of SCM+FSA,
  ic for Instruction of SCM+FSA,
  i,j,k for Nat,
  fa,f for FinSeq-Location,
  a,b,da,db for Int-Location,
  la,lb for Nat;
reserve p1,p2,q for Instruction-Sequence of SCM+FSA;
reserve n for Nat;

theorem Th27:
  for i being Nat, s being State of SCM+FSA,
  P being Instruction-Sequence of SCM+FSA
   st Bubble-Sort-Algorithm c= P
  for w being FinSequence of INT
  st (Initialized ((fsloc 0) .--> w)) c= s
  holds IC Comput(P,s,i) in dom Bubble-Sort-Algorithm
proof
  set Ba=Bubble-Sort-Algorithm,
     Ib=((intloc 0) .--> 1) +* Start-At(0,SCM+FSA);
  let i be Nat, s be State of SCM+FSA,
  P be Instruction-Sequence of SCM+FSA such that
A1:  Bubble-Sort-Algorithm c= P;
  let w be FinSequence of INT;
  set x = (fsloc 0) .--> w;
  assume
A2: (Initialized x) c= s;
  set BSA = Bubble-Sort-Algorithm;
   Initialize ((intloc 0) .--> 1) c= Initialized x by FUNCT_4:25;
   then Initialize ((intloc 0) .--> 1) c= s by A2,XBOOLE_1:1;
   then IC s = 0 by MEMSTR_0:47;
   then IC s in dom Bubble-Sort-Algorithm by AFINSQ_1:65;
  hence thesis by A1,AMISTD_1:21;
end;
