let s be SCMPDS-State; :: thesis: for u being Nat holds (SCM-Chg (s,u)) . NAT = u
let u be Nat; :: thesis: (SCM-Chg (s,u)) . NAT = u
{NAT} = dom (NAT .--> u) by FUNCOP_1:13;
then NAT in dom (NAT .--> u) by TARSKI:def 1;
hence (SCM-Chg (s,u)) . NAT = (NAT .--> u) . NAT by FUNCT_4:13
.= u by FUNCOP_1:72 ;
:: thesis: verum