theorem Th64:
  (s.a > 0 implies Exec(a >0_goto l, s).IC SCM+FSA = l) & (s.a <=
  0 implies Exec(a>0_goto l, s).IC SCM+FSA = IC s + 1) & (for c holds Exec(a
  >0_goto l, s).c = s.c) & for f holds Exec(a>0_goto l, s).f = s.f
proof
  consider A such that
A1: a = A and
A2: a >0_goto l = A >0_goto l by Def13;
  reconsider S = s|SCM-Memory as State of SCM by Th42;
A3: Exec(a >0_goto l, s)=s +* Exec(A >0_goto l, S) by A2,Th44;
  hereby
    assume s.a > 0;
    then
A4: S.A > 0 by A1,Th48;
    thus Exec(a >0_goto l, s).IC SCM+FSA = Exec(A >0_goto l, S).IC SCM by A3
,Th46
      .= l by A4,AMI_3:9;
  end;
  hereby
    assume s.a <= 0;
    then
A5: S.A <= 0 by A1,Th48;
    thus Exec(a >0_goto l, s).IC SCM+FSA = Exec(A >0_goto l, S).IC SCM by A3
,Th46
      .= IC S + 1 by A5,AMI_3:9
      .= IC s + 1 by Th55;
  end;
  hereby
    let c;
    reconsider C = c as Data-Location by Th5;
    thus Exec(a >0_goto l, s).c = Exec(A >0_goto l, S).C by A3,Th47
      .= S.C by AMI_3:9
      .= s.c by Th48;
  end;
  let f;
A6: not f in dom Exec(A >0_goto l, S) by Th37;
  thus Exec(a >0_goto l, s).f
    = s.f by A3,A6,FUNCT_4:11;
end;
