let s be SCM-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_1:19;
then NAT in dom (NAT .--> u) by TARSKI:def 1;
hence (SCM-Chg s,u) . NAT = (NAT .--> u) . NAT by FUNCT_4:14
.= u by FUNCOP_1:87 ;
:: thesis: verum