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 EXTPRO_1:def 3,EXTPRO_1:def 4 :: 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