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 IC in dom (Initialize p)
let S be non empty IC-Ins-separated Mem-Struct of 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)
A: dom (Initialize p) = (dom p) \/ {(IC )} by Th76;
IC in {(IC )} by TARSKI:def 1;
hence IC in dom (Initialize p) by A, XBOOLE_0:def 3; :: thesis: verum