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

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

let s be SCM-State of G; :: 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

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

let s be SCM-State of G; :: 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