let a be Int_position ; :: thesis: for s being State of SCMPDS
for I being Program of SCMPDS holds (s +* (Initialized I)) . a = s . a
let s be State of SCMPDS ; :: thesis: for I being Program of SCMPDS holds (s +* (Initialized I)) . a = s . a
let I be Program of SCMPDS ; :: thesis: (s +* (Initialized I)) . a = s . a
not a in dom (Initialized I) by SCMPDS_4:31;
hence (s +* (Initialized I)) . a = s . a by FUNCT_4:12; :: thesis: verum