let a be Int_position ; :: thesis: for i being Integer
for m being Element of NAT
for I being Program of SCMPDS holds
( m < (card I) + 3 iff inspos m in dom (while<>0 a,i,I) )
let i be Integer; :: thesis: for m being Element of NAT
for I being Program of SCMPDS holds
( m < (card I) + 3 iff inspos m in dom (while<>0 a,i,I) )
let m be Element of NAT ; :: thesis: for I being Program of SCMPDS holds
( m < (card I) + 3 iff inspos m in dom (while<>0 a,i,I) )
let I be Program of SCMPDS ; :: thesis: ( m < (card I) + 3 iff inspos m in dom (while<>0 a,i,I) )
card (while<>0 a,i,I) = (card I) + 3 by Th12;
hence ( m < (card I) + 3 iff inspos m in dom (while<>0 a,i,I) ) by SCMPDS_4:1; :: thesis: verum