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 Th16:
  for I,J being Program of SCM+FSA, k being Nat,
  i being Instruction of SCM+FSA st k< card J & i = J. k holds
  (I ";" J).(card I +k) =IncAddr( i, card I )
proof
  let I,J be Program of SCM+FSA, k be Nat,
  i be Instruction of SCM+FSA such that
A1: k< card J and
A2: i = J. k;
  set m=card I +k;
A3: m < card I + card J by A1,XREAL_1:6;
  (m -' card I) = k by NAT_D:34;
  hence thesis by A2,A3,NAT_1:11,SCMFSA8C:2;
end;
