let a be Int_position ; :: thesis: for i being Integer
for I being Program of SCMPDS holds
( 0 in dom (while<>0 a,i,I) & 1 in dom (while<>0 a,i,I) )
let i be Integer; :: thesis: for I being Program of SCMPDS holds
( 0 in dom (while<>0 a,i,I) & 1 in dom (while<>0 a,i,I) )
let I be Program of SCMPDS ; :: thesis: ( 0 in dom (while<>0 a,i,I) & 1 in dom (while<>0 a,i,I) )
3 <= (card I) + 3 by NAT_1:11;
then ( 0 < (card I) + 3 & 1 < (card I) + 3 ) by XXREAL_0:2;
hence ( 0 in dom (while<>0 a,i,I) & 1 in dom (while<>0 a,i,I) ) by Th13; :: thesis: verum