let N be with_zero set ; :: thesis: for S being non empty with_non-empty_values Mem-Struct over N
for s being State of S holds IC in dom s
let S be non empty with_non-empty_values Mem-Struct over N; :: thesis: for s being State of S holds IC in dom s
let s be State of S; :: thesis: IC in dom s
dom s = the carrier of S by PARTFUN1:def 2;
hence IC in dom s ; :: thesis: verum