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 DataPart (p +* f) = DataPart p
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 DataPart (p +* f) = DataPart p
let p be PartState of S; :: thesis: for f being NAT -defined the Instructions of S -valued Function holds DataPart (p +* f) = DataPart p
let f be NAT -defined the Instructions of S -valued Function; :: thesis: DataPart (p +* f) = DataPart p
B: NAT misses Data-Locations S by Th51;
dom f c= NAT by RELAT_1:def 18;
then A: dom f misses Data-Locations S by B, XBOOLE_1:63;
thus DataPart (p +* f) = (DataPart p) +* (f | (Data-Locations S)) by FUNCT_4:75
.= (DataPart p) +* {} by A, RELAT_1:95
.= DataPart p by FUNCT_4:22 ; :: thesis: verum