reserve s for State of SCM+FSA,
  I for MacroInstruction of SCM+FSA,
  a for read-write Int-Location;
reserve i,j,k,n for Nat;
reserve P,P1,P2,Q for Instruction-Sequence of SCM+FSA;

theorem Th11:
  for I be good InitHalting really-closed MacroInstruction of SCM+FSA,
      a be read-write
Int-Location st (for s be State of SCM+FSA,P holds IExec(I,P,s).a < s.a or
IExec(I,P,s).a <= 0) holds while>0(a,I) is InitHalting
proof
  let I be good InitHalting really-closed MacroInstruction of SCM+FSA,
      a be read-write Int-Location;
  assume
A1: for s be State of SCM+FSA,P holds IExec(I,P,s).a < s.a or IExec(I,P,s).a
  <= 0;
  now
    let t be State of SCM+FSA,Q;
    assume
A2: t.a > 0;
    per cases by A1;
    suppose
      IExec(I,Q,t).a < t.a;
      hence IExec(I,Q,t).a < t.a;
    end;
    suppose
      IExec(I,Q,t).a <= 0;
      hence IExec(I,Q,t).a < t.a by A2;
    end;
  end;
  hence thesis by SCM_HALT:76;
end;
