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, q being PartState of S holds IC in dom (p +* (Initialize q))
let S be non empty with_non-empty_values IC-Ins-separated Mem-Struct over 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))
A1: dom (p +* (Initialize q)) = (dom p) \/ (dom (Initialize q)) by FUNCT_4:def 1;
IC in dom (Initialize q) by Th48;
hence IC in dom (p +* (Initialize q)) by A1, XBOOLE_0:def 3; :: thesis: verum