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 s being State of S
for I being Program of S holds (Initialize s) +* I = s +* (Initialize I)
let S be non empty stored-program IC-Ins-separated definite realistic COM-Struct of N; :: thesis: for s being State of S
for I being Program of S holds (Initialize s) +* I = s +* (Initialize I)
set SA0 = Start-At (0,S);
let s be State of S; :: thesis: for I being Program of S holds (Initialize s) +* I = s +* (Initialize I)
let I be Program of S; :: thesis: (Initialize s) +* I = s +* (Initialize I)
A2: not IC S in dom I by Th3;
B1: dom (Start-At (0,S)) = {(IC S)} by FUNCOP_1:19;
thus (Initialize s) +* I = s +* ((Start-At (0,S)) +* I) by FUNCT_4:15
.= s +* (Initialize I) by B1, A2, FUNCT_4:36, ZFMISC_1:56 ; :: thesis: verum