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 Th70:
  for i being Instruction of SCM, I being Instruction of SCM+FSA
  st i = I & i is halting holds I is halting
proof
  let i be Instruction of SCM, I be Instruction of SCM+FSA such that
A1: i = I;
  assume
A2: i is halting;
  let S be State of SCM+FSA;
  reconsider s = (S|SCM-Memory) as State of SCM by Th42;
  thus Exec(I,S) = S +* Exec(i,s) by A1,Th44
    .= S +* s by A2
    .= S by Th45;
end;
