let N be with_non-empty_elements set ; :: thesis: for S being non empty IC-Ins-separated Mem-Struct of N
for p being PartState of S holds dom (Initialize p) = (dom p) \/ {(IC )}
let S be non empty IC-Ins-separated Mem-Struct of 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 )} by FUNCOP_1:13 ; :: thesis: verum