let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty stored-program IC-Ins-separated definite realistic COM-Struct of N
for I being Program of S holds I c= Initialize I
let S be non empty stored-program IC-Ins-separated definite realistic COM-Struct of N; :: thesis: for I being Program of S holds I c= Initialize I
let I be Program of S; :: thesis: I c= Initialize I
A2: not IC S in dom I by Th3;
dom (Start-At (0,S)) = {(IC S)} by FUNCOP_1:19;
then dom I misses dom (Start-At (0,S)) by A2, ZFMISC_1:56;
hence I c= Initialize I by FUNCT_4:33; :: thesis: verum