let a be Int_position ; :: thesis: for i being Integer
for n, m being Element of NAT
for I being Program of SCMPDS holds
( m < (card I) + 3 iff m in dom (for-up (a,i,n,I)) )
let i be Integer; :: thesis: for n, m being Element of NAT
for I being Program of SCMPDS holds
( m < (card I) + 3 iff m in dom (for-up (a,i,n,I)) )
let n, m be Element of NAT ; :: thesis: for I being Program of SCMPDS holds
( m < (card I) + 3 iff m in dom (for-up (a,i,n,I)) )
let I be Program of SCMPDS; :: thesis: ( m < (card I) + 3 iff m in dom (for-up (a,i,n,I)) )
card (for-up (a,i,n,I)) = (card I) + 3 by Th51;
hence ( m < (card I) + 3 iff m in dom (for-up (a,i,n,I)) ) by AFINSQ_1:66; :: thesis: verum