let G be non empty good 1-sorted ; :: thesis: for s being SCM-State of G
for u, v being Nat holds (SCM-Chg (s,u)) . v = s . v
let s be SCM-State of G; :: 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