reserve I for Element of Segm 8,
  S for non empty 1-sorted,
  t for Element of S,
  x for set,
  k for Element of NAT;
 reserve R for Ring, T for InsType of SCM-Instr R;
reserve R for Ring,
  r for Element of R,
  a, b, c, d1, d2 for Data-Location of R,
  i1 for Nat;
reserve s for State of SCM R;

theorem Th19:
  for I being Instruction of SCM R st I = [0,{},{}] holds I is
  halting
proof
  let I be Instruction of SCM R such that
A1: I = [0,{},{}];
A2: I`3_3 = {} by A1;
  then
A3: ( not(ex mk, ml being Element of Data-Locations SCM st
 I = [ 1,{}, <*mk, ml*>]))&
  not( ex mk, ml being Element of Data-Locations SCM st I =
   [ 2, {}, <*mk, ml*>]);
A4: not(ex mk being Element of Data-Locations SCM, r being Element of R
 st I = [ 5,{}, <*mk,r*>]) by A2;
 I`2_3 = {} by A1;
  then
A5: ( not(ex mk being Element of NAT st I = [ 6, <*mk*>,{}]))&
not(ex mk being
Element of NAT, ml being Element of Data-Locations SCM st
 I = [ 7,<*mk*>,<*ml*>]);
  reconsider L = I as Element of SCM-Instr R by A1,SCMRINGI:6;
  let s be State of SCM R;
A6: the_Values_of SCM R = (SCM-VAL R)*SCM-OK by Lm1;
  reconsider t = s as SCM-State of R by A6,CARD_3:107;
A7: ( not(ex mk, ml being Element of Data-Locations SCM
st I = [ 3,{}, <*mk, ml*>]))&
  not( ex mk, ml being Element of Data-Locations SCM
  st I = [ 4,{}, <*mk, ml*>]) by A2;
  thus Exec(I,s) = SCM-Exec-Res(L,t) by Th10
    .= s by A3,A7,A5,A4,AMI_3:27,SCMRING1:def 14;
end;
