set T = Trivial-AMI N;
set f = (NAT --> {[0 ,{} ,{} ]}) +* (NAT .--> NAT );
A1: product the Object-Kind of (Trivial-AMI N) = product ((NAT --> {[0 ,{} ,{} ]}) +* (NAT .--> NAT )) by Def2;
set I = the haltF of (Trivial-AMI N);
A2: the haltF of (Trivial-AMI N) = [0 ,{} ,{} ] by Def2;
let s be State of (Trivial-AMI N); :: according to AMI_1:def 8,AMI_1:def 9 :: thesis: Exec the haltF of (Trivial-AMI N),s = s
reconsider ss = s as Element of product the Object-Kind of (Trivial-AMI N) by PBOOLE:155;
(the haltF of (Trivial-AMI N) .--> (id (product ((NAT --> {[0 ,{} ,{} ]}) +* (NAT .--> NAT ))))) . the haltF of (Trivial-AMI N) = id (product ((NAT --> {[0 ,{} ,{} ]}) +* (NAT .--> NAT ))) by FUNCOP_1:87;
hence Exec the haltF of (Trivial-AMI N),s = (id (product ((NAT --> {[0 ,{} ,{} ]}) +* (NAT .--> NAT )))) . ss by A2, Def2
.= s by A1, FUNCT_1:35 ;
:: thesis: verum