let s be State of SCMPDS ; :: thesis: for I being halt-free parahalting shiftable Program of SCMPDS
for a being Int_position
for k1 being Integer holds IC (IExec (if=0 a,k1,I),s) = (card I) + 1
let I be halt-free parahalting shiftable Program of SCMPDS ; :: thesis: for a being Int_position
for k1 being Integer holds IC (IExec (if=0 a,k1,I),s) = (card I) + 1
let a be Int_position ; :: thesis: for k1 being Integer holds IC (IExec (if=0 a,k1,I),s) = (card I) + 1
let k1 be Integer; :: thesis: IC (IExec (if=0 a,k1,I),s) = (card I) + 1
set IF = if=0 a,k1,I;
A1: ( I is_closed_on s & I is_halting_on s ) by Th34, Th35;

per cases ( s . (DataLoc (s . a),k1) = 0 or s . (DataLoc (s . a),k1) <> 0 ) ;

suppose s . (DataLoc (s . a),k1) = 0 ; :: thesis: IC (IExec (if=0 a,k1,I),s) = (card I) + 1

then IExec (if=0 a,k1,I),s = (IExec I,s) +* (Start-At ((card I) + 1),SCMPDS ) by A1, Th64;
hence IC (IExec (if=0 a,k1,I),s) = (card I) + 1 by FUNCT_4:121; :: thesis: verum

end;

suppose s . (DataLoc (s . a),k1) <> 0 ; :: thesis: IC (IExec (if=0 a,k1,I),s) = (card I) + 1

then IExec (if=0 a,k1,I),s = s +* (Start-At ((card I) + 1),SCMPDS ) by Th65;
hence IC (IExec (if=0 a,k1,I),s) = (card I) + 1 by FUNCT_4:121; :: thesis: verum

end;

end;