let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty stored-program IC-Ins-separated definite realistic standard-ins homogeneous regular J/A-independent COM-Struct of N
for p being FinPartState of S holds NPP (Initialize p) = Initialize (NPP p)
let S be non empty stored-program IC-Ins-separated definite realistic standard-ins homogeneous regular J/A-independent COM-Struct of N; :: thesis: for p being FinPartState of S holds NPP (Initialize p) = Initialize (NPP p)
let p be FinPartState of S; :: thesis: NPP (Initialize p) = Initialize (NPP p)
A: dom (Start-At (0,S)) misses dom (ProgramPart p) by Th130;
ProgramPart (Initialize p) = ProgramPart p by Th206;
hence NPP (Initialize p) = (Initialize p) \ (ProgramPart p)
.= (p \ (ProgramPart p)) +* (Start-At (0,S)) by A, FUNCT_4:129
.= Initialize (NPP p) ;
:: thesis: verum