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