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) + 2),SCMPDS ) by Th75;
not b in dom (Start-At ((card I) + 2),SCMPDS ) by SCMPDS_4:59;
hence (IExec (if<>0 a,k1,I),s) . b = s . b by A1, FUNCT_4:12; :: thesis: verum