let a be Int-Location ; :: thesis: for I being Program of
for k being Element of NAT st k < 6 holds
k in dom (while=0 (a,I))
let I be Program of ; :: 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 Th4;
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_1:66; :: thesis: verum