let R be good Ring; :: thesis: for i being Instruction of (SCM R) st ( for l being Instruction-Location of SCM R holds NIC i,l = {(Next l)} ) holds
JUMP i is empty
let i be Instruction of (SCM R); :: thesis: ( ( for l being Instruction-Location of SCM R holds NIC i,l = {(Next l)} ) implies JUMP i is empty )
assume A1: for l being Instruction-Location of SCM R holds NIC i,l = {(Next l)} ; :: thesis: JUMP i is empty
set p = 1;
set q = 2;
reconsider p = 1, q = 2 as Instruction-Location of SCM R by AMI_1:def 4;
set X = { (NIC i,f) where f is Instruction-Location of SCM R : verum } ;
assume not JUMP i is empty ; :: thesis: contradiction
then consider x being set such that
A3: x in meet { (NIC i,f) where f is Instruction-Location of SCM R : verum } by XBOOLE_0:def 1;
( NIC i,p = {(Next p)} & NIC i,q = {(Next q)} ) by A1;
then ( {(Next p)} in { (NIC i,f) where f is Instruction-Location of SCM R : verum } & {(Next q)} in { (NIC i,f) where f is Instruction-Location of SCM R : verum } ) ;
then ( x in {(Next p)} & x in {(Next q)} ) by A3, SETFAM_1:def 1;
then ( x = Next p & x = Next q ) by TARSKI:def 1;
hence contradiction ; :: thesis: verum