let P be Instruction-Sequence of SCMPDS; for s being State of SCMPDS
for I being Program of
for a being Int_position
for i being Integer
for n being Nat st s . (DataLoc ((s . a),i)) >= 0 holds
IC (IExec ((for-up (a,i,n,I)),P,(Initialize s))) = (card I) + 3
let s be State of SCMPDS; for I being Program of
for a being Int_position
for i being Integer
for n being Nat st s . (DataLoc ((s . a),i)) >= 0 holds
IC (IExec ((for-up (a,i,n,I)),P,(Initialize s))) = (card I) + 3
let I be Program of ; for a being Int_position
for i being Integer
for n being Nat st s . (DataLoc ((s . a),i)) >= 0 holds
IC (IExec ((for-up (a,i,n,I)),P,(Initialize s))) = (card I) + 3
let a be Int_position; for i being Integer
for n being Nat st s . (DataLoc ((s . a),i)) >= 0 holds
IC (IExec ((for-up (a,i,n,I)),P,(Initialize s))) = (card I) + 3
let i be Integer; for n being Nat st s . (DataLoc ((s . a),i)) >= 0 holds
IC (IExec ((for-up (a,i,n,I)),P,(Initialize s))) = (card I) + 3
let n be Nat; ( s . (DataLoc ((s . a),i)) >= 0 implies IC (IExec ((for-up (a,i,n,I)),P,(Initialize s))) = (card I) + 3 )
assume
s . (DataLoc ((s . a),i)) >= 0
; IC (IExec ((for-up (a,i,n,I)),P,(Initialize s))) = (card I) + 3
then
IExec ((for-up (a,i,n,I)),P,(Initialize s)) = s +* (Start-At (((card I) + 3),SCMPDS))
by Th34;
hence
IC (IExec ((for-up (a,i,n,I)),P,(Initialize s))) = (card I) + 3
by FUNCT_4:113; verum