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