let s be State of SCMPDS; :: thesis: for I being 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 = s . b
let I be 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 = 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 = s . b
let k1 be Integer; :: thesis: ( s . (DataLoc ((s . a),k1)) >= 0 implies (IExec ((if<0 (a,k1,I)),s)) . b = s . b )
assume s . (DataLoc ((s . a),k1)) >= 0 ; :: thesis: (IExec ((if<0 (a,k1,I)),s)) . b = s . b
then A1: IExec ((if<0 (a,k1,I)),s) = s +* (Start-At (((card I) + 1),SCMPDS)) by Th125;
not b in dom (Start-At (((card I) + 1),SCMPDS)) by SCMPDS_4:59;
hence (IExec ((if<0 (a,k1,I)),s)) . b = s . b by A1, FUNCT_4:12; :: thesis: verum