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 Th8;
hence IC (IExec ((while<0 (a,i,I)),P,s)) = (card I) + 2 by FUNCT_4:113; :: thesis: verum