let P be Instruction-Sequence of SCMPDS; :: thesis: 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; :: thesis: 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; :: thesis: 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; :: thesis: 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; :: thesis: ( 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 ; :: thesis: 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; :: thesis: verum

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; :: thesis: 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; :: thesis: 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; :: thesis: 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; :: thesis: ( 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 ; :: thesis: 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; :: thesis: verum