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 IC in dom (Initialize p)
let S be non empty with_non-empty_values IC-Ins-separated Mem-Struct over N; :: thesis: for p being PartState of S holds IC in dom (Initialize p)
let p be PartState of S; :: thesis: IC in dom (Initialize p)
A1: dom (Initialize p) = (dom p) \/ {(IC )} by Th42;
IC in {(IC )} by TARSKI:def 1;
hence IC in dom (Initialize p) by A1, XBOOLE_0:def 3; :: thesis: verum