let s be State of SCMPDS; :: thesis: for I being halt-free parahalting shiftable Program of SCMPDS
for a, b being Int_position
for k1 being Integer st s . (DataLoc ((s . a),k1)) >= 0 holds
(IExec ((if>=0 (a,k1,I)),s)) . b = (IExec (I,s)) . b
let I be halt-free parahalting shiftable Program of SCMPDS; :: thesis: for a, b being Int_position
for k1 being Integer st s . (DataLoc ((s . a),k1)) >= 0 holds
(IExec ((if>=0 (a,k1,I)),s)) . b = (IExec (I,s)) . b
let a, b be Int_position ; :: thesis: for k1 being Integer st s . (DataLoc ((s . a),k1)) >= 0 holds
(IExec ((if>=0 (a,k1,I)),s)) . b = (IExec (I,s)) . b
let k1 be Integer; :: thesis: ( s . (DataLoc ((s . a),k1)) >= 0 implies (IExec ((if>=0 (a,k1,I)),s)) . b = (IExec (I,s)) . b )
assume A1: s . (DataLoc ((s . a),k1)) >= 0 ; :: thesis: (IExec ((if>=0 (a,k1,I)),s)) . b = (IExec (I,s)) . b
A2: not b in dom (Start-At (((card I) + 2),SCMPDS)) by SCMPDS_4:59;
( I is_closed_on s & I is_halting_on s ) by Th34, Th35;
then IExec ((if>=0 (a,k1,I)),s) = (IExec (I,s)) +* (Start-At (((card I) + 2),SCMPDS)) by A1, Th134;
hence (IExec ((if>=0 (a,k1,I)),s)) . b = (IExec (I,s)) . b by A2, FUNCT_4:12; :: thesis: verum