reserve J,J1,K for Element of Segm 13,
  b,b1,b2,c,c1,c2 for Element of SCM+FSA-Data-Loc,
  f,f1,f2 for Element of SCM+FSA-Data*-Loc;
reserve k for Nat,
  J,K,L for Element of Segm 13,
  O,P,R for Element of Segm 9;
reserve da for Int-Location,
  fa for FinSeq-Location,
  x,y for set;
reserve la,lb for Nat,
  La for Nat,
  i for Instruction of SCM+FSA,
  I for Instruction of SCM,
  l for Nat,
  LA,LB for Nat,
  dA,dB,dC,dD for Element of SCM+FSA-Data-Loc,
  DA,DB,DC for Element of SCM-Data-Loc,
  fA,fB,fC for Element of SCM+FSA-Data*-Loc,
  f,g for FinSeq-Location,
  A,B for Data-Location,
  a,b,c,db for Int-Location;
reserve S for State of SCM,
  s,s1 for State of SCM+FSA;

theorem Th67:
  Exec(c:=len g, s).IC SCM+FSA = IC s + 1 & Exec(c:=len g, s).c
  = len(s.g) & (for b st b <> c holds Exec(c:=len g, s).b = s.b) & for f holds
  Exec(c:=len g, s).f = s.f
proof
  reconsider S = s as SCM+FSA-State by CARD_3:107;
  reconsider p = g as Element of SCM+FSA-Data*-Loc by Def3;
  reconsider I = c:=len g as Element of SCM+FSA-Instr;
  set S1 = SCM+FSA-Chg(S,I int_addr3,len(S.(I coll_addr2)));
  reconsider J = 11 as Element of Segm 13 by NAT_1:44;
  reconsider ml = c as Element of SCM-Data-Loc by AMI_2:def 16;
A1: InsCode I = 11;
A2: Exec(c:=len g, s) = SCM+FSA-Exec-Res(I,S) by SCMFSA_1:def 17
    .= (SCM+FSA-Chg(S1, IC S + 1)) by A1,SCMFSA_1:def 16;
  hence Exec(c:=len g, s).IC SCM+FSA = IC s + 1 by Th1,SCMFSA_1:19;
A3: I = [J,{},<*ml,p*>] & I`3_3 = <*ml,p*>;
  then
A4: I int_addr3 = ml by SCMFSA_I:def 7;
A5: I coll_addr2 = p by A3,SCMFSA_I:def 8;
  thus Exec(c:=len g, s).c = S1.ml by A2,SCMFSA_1:20
    .= len(s.g) by A4,A5,SCMFSA_1:24;
  hereby
    let b;
    reconsider mn = b as Element of SCM-Data-Loc by AMI_2:def 16;
    assume
A6: b <> c;
    thus Exec(c:=len g, s).b = S1.mn by A2,SCMFSA_1:20
      .= s.b by A4,A6,SCMFSA_1:25;
  end;
  let f;
  reconsider q = f as Element of SCM+FSA-Data*-Loc by Def3;
  thus Exec(c:=len g, s).f = S1.q by A2,SCMFSA_1:21
    .= s.f by SCMFSA_1:26;
end;
