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 Th24:
  for P being Instruction-Sequence of SCM+FSA
   st Bubble-Sort-Algorithm c= P
  for f being FinSeq-Location, k being Nat st
  k < 53 holds Bubble-Sort-Algorithm.k= P.k
proof
  let P be Instruction-Sequence of SCM+FSA such that
A1: Bubble-Sort-Algorithm c= P;
  let f be FinSeq-Location, k be Nat;
  assume
A2: k < 53;
  card (bubble-sort f0) = 53 by Th23;
  then k in dom Bubble-Sort-Algorithm by A2,AFINSQ_1:66;
 hence Bubble-Sort-Algorithm.k= P.k by A1,GRFUNC_1:2;
end;
