set w = the State of (SCM S);
consider e being Element of S such that
A1: e <> 0. S by STRUCT_0:def 18;
reconsider e = e as Element of S ;
A2: now :: thesis: not - e = 0. S
assume - e = 0. S ; :: thesis: contradiction
then e = - (0. S) by RLVECT_1:17;
hence contradiction by A1, RLVECT_1:12; :: thesis: verum
end;
set t = the State of (SCM S) +* (((dl. (S,0)),(dl. (S,1))) --> ((0. S),e));
A3: InsCode (SubFrom (p,q)) = 3
.= InsCode (SubFrom ((dl. (S,0)),(dl. (S,1)))) ;
A4: dom (((dl. (S,0)),(dl. (S,1))) --> ((0. S),e)) = {(dl. (S,0)),(dl. (S,1))} by FUNCT_4:62;
then dl. (S,0) in dom (((dl. (S,0)),(dl. (S,1))) --> ((0. S),e)) by TARSKI:def 2;
then A5: ( the State of (SCM S) +* (((dl. (S,0)),(dl. (S,1))) --> ((0. S),e))) . (dl. (S,0)) = (((dl. (S,0)),(dl. (S,1))) --> ((0. S),e)) . (dl. (S,0)) by FUNCT_4:13
.= 0. S by AMI_3:10, FUNCT_4:63 ;
dl. (S,1) in dom (((dl. (S,0)),(dl. (S,1))) --> ((0. S),e)) by A4, TARSKI:def 2;
then A6: ( the State of (SCM S) +* (((dl. (S,0)),(dl. (S,1))) --> ((0. S),e))) . (dl. (S,1)) = (((dl. (S,0)),(dl. (S,1))) --> ((0. S),e)) . (dl. (S,1)) by FUNCT_4:13
.= e by FUNCT_4:63 ;
dl. (S,0) in Data-Locations by SCMRING2:1;
then A7: dl. (S,0) in Data-Locations by SCMRING2:22;
(Exec ((SubFrom ((dl. (S,0)),(dl. (S,1)))),( the State of (SCM S) +* (((dl. (S,0)),(dl. (S,1))) --> ((0. S),e))))) . (dl. (S,0)) = (( the State of (SCM S) +* (((dl. (S,0)),(dl. (S,1))) --> ((0. S),e))) . (dl. (S,0))) - (( the State of (SCM S) +* (((dl. (S,0)),(dl. (S,1))) --> ((0. S),e))) . (dl. (S,1))) by SCMRING2:13
.= - e by A5, A6, RLVECT_1:14 ;
hence for b1 being InsType of the InstructionsF of (SCM S) st b1 = InsCode (SubFrom (p,q)) holds
not b1 is jump-only by A3, A5, A2, A7; :: thesis: verum