let s be State of SCMPDS ; :: thesis: for I being halt-free shiftable Program of SCMPDS
for J being shiftable Program of SCMPDS
for a, b being Int_position
for k1 being Integer st s . (DataLoc (s . a),k1) > 0 & I is_closed_on s & I is_halting_on s holds
(IExec (if>0 a,k1,I,J),s) . b = (IExec I,s) . b
let I be halt-free shiftable Program of SCMPDS ; :: thesis: for J being shiftable Program of SCMPDS
for a, b being Int_position
for k1 being Integer st s . (DataLoc (s . a),k1) > 0 & I is_closed_on s & I is_halting_on s holds
(IExec (if>0 a,k1,I,J),s) . b = (IExec I,s) . b
let J be shiftable Program of SCMPDS ; :: thesis: for a, b being Int_position
for k1 being Integer st s . (DataLoc (s . a),k1) > 0 & I is_closed_on s & I is_halting_on s holds
(IExec (if>0 a,k1,I,J),s) . b = (IExec I,s) . b
let a, b be Int_position ; :: thesis: for k1 being Integer st s . (DataLoc (s . a),k1) > 0 & I is_closed_on s & I is_halting_on s holds
(IExec (if>0 a,k1,I,J),s) . b = (IExec I,s) . b
let k1 be Integer; :: thesis: ( s . (DataLoc (s . a),k1) > 0 & I is_closed_on s & I is_halting_on s implies (IExec (if>0 a,k1,I,J),s) . b = (IExec I,s) . b )
assume that
A1: s . (DataLoc (s . a),k1) > 0 and
A2: I is_closed_on s and
A3: I is_halting_on s ; :: thesis: (IExec (if>0 a,k1,I,J),s) . b = (IExec I,s) . b
A4: not b in dom (Start-At (((card I) + (card J)) + 2),SCMPDS ) by SCMPDS_4:59;
IExec (if>0 a,k1,I,J),s = (IExec I,s) +* (Start-At (((card I) + (card J)) + 2),SCMPDS ) by A1, A2, A3, SCMPDS_6:84;
hence (IExec (if>0 a,k1,I,J),s) . b = (IExec I,s) . b by A4, FUNCT_4:12; :: thesis: verum