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 d being data-only FinPartState of S holds IC (p +* d) = IC 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 d being data-only FinPartState of S holds IC (p +* d) = IC p
let p be PartState of S; :: thesis: for d being data-only FinPartState of S holds IC (p +* d) = IC p
let d be data-only FinPartState of S; :: thesis: IC (p +* d) = IC p
A1: not IC in dom d by Th57;
thus IC (p +* d) = (p +* d) . (IC )
.= p . (IC ) by A1, FUNCT_4:12
.= IC p ; :: thesis: verum