let s be SCM+FSA-State; :: thesis: for u being Element of NAT holds (SCM+FSA-Chg s,u) . NAT = u
let u be Element of NAT ; :: thesis: (SCM+FSA-Chg s,u) . NAT = u
{NAT } = dom (NAT .--> u) by FUNCOP_1:19;
then NAT in dom (NAT .--> u) by TARSKI:def 1;
hence (SCM+FSA-Chg s,u) . NAT = (NAT .--> u) . NAT by FUNCT_4:14
.= u by FUNCOP_1:87 ;
:: thesis: verum