let P be Instruction-Sequence of SCMPDS; for s being 0 -started State of SCMPDS
for I being Program of SCMPDS
for a being Int_position
for i being Integer st s . (DataLoc ((s . a),i)) <= 0 holds
IC (IExec ((while>0 (a,i,I)),P,s)) = (card I) + 2
let s be 0 -started State of SCMPDS; for I being Program of SCMPDS
for a being Int_position
for i being Integer st s . (DataLoc ((s . a),i)) <= 0 holds
IC (IExec ((while>0 (a,i,I)),P,s)) = (card I) + 2
let I be Program of SCMPDS; for a being Int_position
for i being Integer st s . (DataLoc ((s . a),i)) <= 0 holds
IC (IExec ((while>0 (a,i,I)),P,s)) = (card I) + 2
let a be Int_position; for i being Integer st s . (DataLoc ((s . a),i)) <= 0 holds
IC (IExec ((while>0 (a,i,I)),P,s)) = (card I) + 2
let i be Integer; ( s . (DataLoc ((s . a),i)) <= 0 implies IC (IExec ((while>0 (a,i,I)),P,s)) = (card I) + 2 )
assume
s . (DataLoc ((s . a),i)) <= 0
; IC (IExec ((while>0 (a,i,I)),P,s)) = (card I) + 2
then
IExec ((while>0 (a,i,I)),P,s) = s +* (Start-At (((card I) + 2),SCMPDS))
by Th19;
hence
IC (IExec ((while>0 (a,i,I)),P,s)) = (card I) + 2
by FUNCT_4:113; verum