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 p being PartState of S
for f being NAT -defined the Instructions of b₁ -valued Function holds Initialize (p +* f) = (Initialize p) +* f
let S be non empty stored-program IC-Ins-separated definite realistic COM-Struct of N; :: thesis: for p being PartState of S
for f being NAT -defined the Instructions of S -valued Function holds Initialize (p +* f) = (Initialize p) +* f
let p be PartState of S; :: thesis: for f being NAT -defined the Instructions of S -valued Function holds Initialize (p +* f) = (Initialize p) +* f
let f be NAT -defined the Instructions of S -valued Function; :: thesis: Initialize (p +* f) = (Initialize p) +* f
B: NAT misses dom (Start-At (0,S)) by Th26;
dom f c= NAT by RELAT_1:def 18;
then A: dom f misses dom (Start-At (0,S)) by B, XBOOLE_1:63;
thus Initialize (p +* f) = p +* (f +* (Start-At (0,S))) by FUNCT_4:15
.= p +* ((Start-At (0,S)) +* f) by A, FUNCT_4:36
.= (Initialize p) +* f by FUNCT_4:15 ; :: thesis: verum