let N be with_non-empty_elements set ; :: thesis: for S being non empty IC-Ins-separated Mem-Struct of N
for p, q being PartState of S holds IC in dom (p +* (Initialize q))
let S be non empty IC-Ins-separated Mem-Struct of N; :: thesis: for p, q being PartState of S holds IC in dom (p +* (Initialize q))
let p, q be PartState of S; :: thesis: IC in dom (p +* (Initialize q))
A: dom (p +* (Initialize q)) = (dom p) \/ (dom (Initialize q)) by FUNCT_4:def 1;
IC in dom (Initialize q) by Th225;
hence IC in dom (p +* (Initialize q)) by A, XBOOLE_0:def 3; :: thesis: verum