let N be with_non-empty_elements set ; :: thesis: for S being non empty stored-program IC-Ins-separated COM-Struct of N
for s being State of S holds IC s in dom s
let S be non empty stored-program IC-Ins-separated COM-Struct of N; :: thesis: for s being State of S holds IC s in dom s
let s be State of S; :: thesis: IC s in dom s
X: IC s in NAT ;
NAT c= the carrier of S by Def3;
then IC s in the carrier of S by X;
hence IC s in dom s by PARTFUN1:def 4; :: thesis: verum