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 Th18:
  for I,J be Program of SCM+FSA, i be Instruction of SCM+FSA
  holds (I ";" i ";" J).(card I+1) = goto(card I+2)
proof
  let I,J be Program of SCM+FSA, i be Instruction of SCM+FSA;
  set x1= card I;
A1: card (I ";" i) = card I +2 by SCMFSA6A:34;
A2: card (Macro i) = 2 by COMPOS_1:56;
  set x2= card I+1;
  card I + 1 < card I + 2 by XREAL_1:6;
  then
A3: x2 in dom (I ";" i) by A1,AFINSQ_1:66;
  (Macro i).1 = halt SCM+FSA by COMPOS_1:59;
  then (I ";" Macro i).x2 =IncAddr( halt SCM+FSA, card I ) by A2,Th16;
  then
A4: (I ";" i).x2 =IncAddr( halt SCM+FSA, card I ) by SCMFSA6A:def 6
    .=halt SCM+FSA by COMPOS_0:4;
  thus (I ";" i ";" J).x2 = (Directed (I ";" i)).x2 by A3,SCMFSA8A:14
    .= goto  (card I+2) by A1,A3,A4,SCMFSA8A:16;
end;
