let s be SCM-State; :: thesis: for u, v being Nat holds (SCM-Chg (s,u)) . v = s . v
let u, v be Nat; :: thesis: (SCM-Chg (s,u)) . v = s . v
{NAT} = dom (NAT .--> u) by FUNCOP_1:19;
then not v in dom (NAT .--> u) by TARSKI:def 1;
hence (SCM-Chg (s,u)) . v = s . v by FUNCT_4:12; :: thesis: verum