consider w being State of (SCM S);
consider e being Element of S such that
A1: e <> 0. S by STRUCT_0:def 19;
reconsider e = e as Element of S ;
set t = w +* ((dl. S,0 ),(dl. S,1) --> (0. S),e);
A2: dom ((dl. S,0 ),(dl. S,1) --> (0. S),e) = {(dl. S,0 ),(dl. S,1)} by FUNCT_4:65;
then dl. S,0 in dom ((dl. S,0 ),(dl. S,1) --> (0. S),e) by TARSKI:def 2;
then A3: (w +* ((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_4:14
.= 0. S by AMI_3:52, FUNCT_4:66 ;
IC (SCM S) = IC SCM by AMI_3:4, SCMRING2:9;
then A4: dl. S,0 <> IC (SCM S) by AMI_3:57;
A5: InsCode (AddTo p,q) = 2 by MCART_1:def 1
.= InsCode (AddTo (dl. S,0 ),(dl. S,1)) by MCART_1:def 1 ;
dl. S,1 in dom ((dl. S,0 ),(dl. S,1) --> (0. S),e) by A2, TARSKI:def 2;
then A6: (w +* ((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_4:14
.= e by FUNCT_4:66 ;
(Exec (AddTo (dl. S,0 ),(dl. S,1)),(w +* ((dl. S,0 ),(dl. S,1) --> (0. S),e))) . (dl. S,0 ) = ((w +* ((dl. S,0 ),(dl. S,1) --> (0. S),e)) . (dl. S,0 )) + ((w +* ((dl. S,0 ),(dl. S,1) --> (0. S),e)) . (dl. S,1)) by SCMRING2:14
.= e by A3, A6, RLVECT_1:10 ;
hence for b₁ being InsType of (SCM S) st b₁ = InsCode (AddTo p,q) holds
not b₁ is jump-only by A1, A5, A4, A3, AMISTD_1:def 3; :: thesis: verum