let P be Instruction-Sequence of SCMPDS; :: thesis: 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-down (a,i,n,I)),P,(Initialize s))) = (card I) + 3

let s be State of SCMPDS; :: thesis: 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-down (a,i,n,I)),P,(Initialize s))) = (card I) + 3

let I be Program of ; :: thesis: for a being Int_position

for i being Integer

for n being Nat st s . (DataLoc ((s . a),i)) <= 0 holds

IC (IExec ((for-down (a,i,n,I)),P,(Initialize s))) = (card I) + 3

let a be Int_position; :: thesis: for i being Integer

for n being Nat st s . (DataLoc ((s . a),i)) <= 0 holds

IC (IExec ((for-down (a,i,n,I)),P,(Initialize s))) = (card I) + 3

let i be Integer; :: thesis: for n being Nat st s . (DataLoc ((s . a),i)) <= 0 holds

IC (IExec ((for-down (a,i,n,I)),P,(Initialize s))) = (card I) + 3

let n be Nat; :: thesis: ( s . (DataLoc ((s . a),i)) <= 0 implies IC (IExec ((for-down (a,i,n,I)),P,(Initialize s))) = (card I) + 3 )

assume s . (DataLoc ((s . a),i)) <= 0 ; :: thesis: IC (IExec ((for-down (a,i,n,I)),P,(Initialize s))) = (card I) + 3

then IExec ((for-down (a,i,n,I)),P,(Initialize s)) = s +* (Start-At (((card I) + 3),SCMPDS)) by Th43;

hence IC (IExec ((for-down (a,i,n,I)),P,(Initialize s))) = (card I) + 3 by FUNCT_4:113; :: thesis: verum

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-down (a,i,n,I)),P,(Initialize s))) = (card I) + 3

let s be State of SCMPDS; :: thesis: 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-down (a,i,n,I)),P,(Initialize s))) = (card I) + 3

let I be Program of ; :: thesis: for a being Int_position

for i being Integer

for n being Nat st s . (DataLoc ((s . a),i)) <= 0 holds

IC (IExec ((for-down (a,i,n,I)),P,(Initialize s))) = (card I) + 3

let a be Int_position; :: thesis: for i being Integer

for n being Nat st s . (DataLoc ((s . a),i)) <= 0 holds

IC (IExec ((for-down (a,i,n,I)),P,(Initialize s))) = (card I) + 3

let i be Integer; :: thesis: for n being Nat st s . (DataLoc ((s . a),i)) <= 0 holds

IC (IExec ((for-down (a,i,n,I)),P,(Initialize s))) = (card I) + 3

let n be Nat; :: thesis: ( s . (DataLoc ((s . a),i)) <= 0 implies IC (IExec ((for-down (a,i,n,I)),P,(Initialize s))) = (card I) + 3 )

assume s . (DataLoc ((s . a),i)) <= 0 ; :: thesis: IC (IExec ((for-down (a,i,n,I)),P,(Initialize s))) = (card I) + 3

then IExec ((for-down (a,i,n,I)),P,(Initialize s)) = s +* (Start-At (((card I) + 3),SCMPDS)) by Th43;

hence IC (IExec ((for-down (a,i,n,I)),P,(Initialize s))) = (card I) + 3 by FUNCT_4:113; :: thesis: verum