let G be non empty 1-sorted ; :: thesis: for s being SCM-State of G

for u being natural Number holds (SCM-Chg (s,u)) . NAT = u

let s be SCM-State of G; :: thesis: for u being natural Number holds (SCM-Chg (s,u)) . NAT = u

let u be natural Number ; :: thesis: (SCM-Chg (s,u)) . NAT = u

NAT in dom (NAT .--> u) by TARSKI:def 1;

hence (SCM-Chg (s,u)) . NAT = (NAT .--> u) . NAT by FUNCT_4:13

.= u by FUNCOP_1:72 ;

:: thesis: verum

for u being natural Number holds (SCM-Chg (s,u)) . NAT = u

let s be SCM-State of G; :: thesis: for u being natural Number holds (SCM-Chg (s,u)) . NAT = u

let u be natural Number ; :: thesis: (SCM-Chg (s,u)) . NAT = u

NAT in dom (NAT .--> u) by TARSKI:def 1;

hence (SCM-Chg (s,u)) . NAT = (NAT .--> u) . NAT by FUNCT_4:13

.= u by FUNCOP_1:72 ;

:: thesis: verum