let s be State of SCMPDS ; :: thesis: for I being parahalting shiftable No-StopCode Program of SCMPDS
for a being Int_position
for k1 being Integer holds IC (IExec (if>0 a,k1,I),s) = inspos ((card I) + 1)
let I be parahalting shiftable No-StopCode Program of SCMPDS ; :: thesis: for a being Int_position
for k1 being Integer holds IC (IExec (if>0 a,k1,I),s) = inspos ((card I) + 1)
let a be Int_position ; :: thesis: for k1 being Integer holds IC (IExec (if>0 a,k1,I),s) = inspos ((card I) + 1)
let k1 be Integer; :: thesis: IC (IExec (if>0 a,k1,I),s) = inspos ((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) = inspos ((card I) + 1)

then IExec (if>0 a,k1,I),s = (IExec I,s) +* (Start-At (inspos ((card I) + 1))) by A1, Th94;
hence IC (IExec (if>0 a,k1,I),s) = inspos ((card I) + 1) by AMI_1:111; :: thesis: verum

end;

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

then IExec (if>0 a,k1,I),s = s +* (Start-At (inspos ((card I) + 1))) by Th95;
hence IC (IExec (if>0 a,k1,I),s) = inspos ((card I) + 1) by AMI_1:111; :: thesis: verum

end;

end;