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 FinPartState 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 FinPartState of S
for d being data-only FinPartState of S holds IC (p +* d) = IC p
let p be FinPartState 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
A2: not IC S in dom d by Th22;
thus IC (p +* d) = (p +* d) . (IC S)
.= p . (IC S) by A2, FUNCT_4:12
.= IC p ; :: thesis: verum