reconsider p = 0 , q = 1 as Element of NAT ;
let i be Instruction of ; ( ( for l being Instruction-Location of SCM+FSA holds NIC i,l = {(Next l)} ) implies JUMP i is empty )
assume A1:
for l being Instruction-Location of SCM+FSA holds NIC i,l = {(Next l)}
; JUMP i is empty
set X = { (NIC i,f) where f is Instruction-Location of SCM+FSA : verum } ;
reconsider p = p, q = q as Instruction-Location of SCM+FSA by AMI_1:def 4;
assume
not JUMP i is empty
; contradiction
then consider x being set such that
A2:
x in meet { (NIC i,f) where f is Instruction-Location of SCM+FSA : verum }
by XBOOLE_0:def 1;
NIC i,p = {(Next p)}
by A1;
then
{(Next p)} in { (NIC i,f) where f is Instruction-Location of SCM+FSA : verum }
;
then
x in {(Next p)}
by A2, SETFAM_1:def 1;
then A3:
x = Next p
by TARSKI:def 1;
NIC i,q = {(Next q)}
by A1;
then
{(Next q)} in { (NIC i,f) where f is Instruction-Location of SCM+FSA : verum }
;
then
x in {(Next q)}
by A2, SETFAM_1:def 1;
hence
contradiction
by A3, TARSKI:def 1; verum