let N be with_non-empty_elements set ; :: thesis: for S being AMI-Struct of N
for s being State of S holds dom s = the carrier of S
let S be AMI-Struct of N; :: thesis: for s being State of S holds dom s = the carrier of S
let s be State of S; :: thesis: dom s = the carrier of S
thus dom s = dom the Object-Kind of S by CARD_3:18
.= the carrier of S by FUNCT_2:def 1 ; :: thesis: verum