let s be SCM-State; :: thesis: for u, v being natural Number holds (SCM-Chg (s,u)) . v = s . v
let u, v be natural Number ; :: thesis: (SCM-Chg (s,u)) . v = s . v
not v in dom (NAT .--> u) by TARSKI:def 1;
hence (SCM-Chg (s,u)) . v = s . v by FUNCT_4:11; :: thesis: verum