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 Th17:
  for I,J be Program of SCM+FSA,
      i be ins-loc-free Instruction of SCM+FSA st i <> halt SCM+FSA
  holds (I ";" i ";" J).card I = i
proof
  let I,J be Program of SCM+FSA,
  i be ins-loc-free Instruction of SCM+FSA;
  assume that
A1: i <> halt SCM+FSA;
  set x1= card I;
A2: card (I ";" i) = card I +2 by SCMFSA6A:34;
  card I + 0 < card I + 2 by XREAL_1:6;
  then
A3: x1 in dom (I ";" i) by A2,AFINSQ_1:66;
A4: (Macro i).( 0) = i by COMPOS_1:58;
A5: card (Macro i) = 2 by COMPOS_1:56;
A6: (I ";" i).x1 = (I ";" Macro i). (card I+0) by SCMFSA6A:def 6
    .=IncAddr( i, card I ) by A4,A5,Th16
    .=i by COMPOS_0:4;
  thus (I ";" i ";" J).x1 = (Directed (I ";" i)).x1 by A3,SCMFSA8A:14
    .=i by A1,A3,A6,SCMFSA8A:16;
end;
