let N be with_zero set ; :: thesis: for S being non empty with_non-empty_values IC-Ins-separated Mem-Struct over N
for p being PartState of S holds dom (Initialize p) = (dom p) \/ {(IC )}
let S be non empty with_non-empty_values IC-Ins-separated Mem-Struct over N; :: thesis: for p being PartState of S holds dom (Initialize p) = (dom p) \/ {(IC )}
let p be PartState of S; :: thesis: dom (Initialize p) = (dom p) \/ {(IC )}
thus dom (Initialize p) = (dom p) \/ (dom (Start-At (0,S))) by FUNCT_4:def 1
.= (dom p) \/ {(IC )} ; :: thesis: verum