let N be with_non-empty_elements set ; :: thesis: for S being non empty COM-Struct of N
for s being State of S holds IC S in dom s
let S be non empty 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
dom s = the carrier of S by PARTFUN1:def 4;
hence IC S in dom s ; :: thesis: verum