let a be Int-Location ; :: thesis: for I being Program of SCM+FSA
for k being Element of NAT st k < 6 holds
k in dom (while>0 a,I)
let I be Program of SCM+FSA ; :: thesis: for k being Element of NAT st k < 6 holds
k in dom (while>0 a,I)
let k be Element of NAT ; :: thesis: ( k < 6 implies k in dom (while>0 a,I) )
A1: 6 <= (card I) + 6 by NAT_1:11;
A2: card (while>0 a,I) = (card I) + 6 by Th5;
assume k < 6 ; :: thesis: k in dom (while>0 a,I)
then k < (card I) + 6 by A1, XXREAL_0:2;
hence k in dom (while>0 a,I) by A2, AFINSQ_1:70; :: thesis: verum