let N be with_non-empty_elements set ; :: thesis: for i being Element of the Instructions of (STC N) holds JUMP i is empty
let i be Element of the Instructions of (STC N); :: thesis: JUMP i is empty
per cases
( InsCode i = 1 or InsCode i = 0 )
by Th22;
suppose A1:
InsCode i = 1
;
:: thesis: JUMP i is empty set X =
{ (NIC i,l) where l is Instruction-Location of STC N : verum } ;
assume
not
JUMP i is
empty
;
:: thesis: contradictionthen consider x being
set such that A2:
x in meet { (NIC i,l) where l is Instruction-Location of STC N : verum }
by XBOOLE_0:def 1;
reconsider l1 =
0 ,
l2 = 1 as
Instruction-Location of
STC N by AMI_1:def 4;
(
NIC i,
l1 in { (NIC i,l) where l is Instruction-Location of STC N : verum } &
NIC i,
l2 in { (NIC i,l) where l is Instruction-Location of STC N : verum } )
;
then
(
{(0 + 1)} in { (NIC i,l) where l is Instruction-Location of STC N : verum } &
{(1 + 1)} in { (NIC i,l) where l is Instruction-Location of STC N : verum } )
by A1, Lm5;
then
(
x in {1} &
x in {2} )
by A2, SETFAM_1:def 1;
then
(
x = 1 &
x = 2 )
by TARSKI:def 1;
hence
contradiction
;
:: thesis: verum end; end;