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

for t being Element of SCM-Data-Loc

for u being Element of G holds (SCM-Chg (s,t,u)) . t = u

let s be SCM-State of G; :: thesis: for t being Element of SCM-Data-Loc

for u being Element of G holds (SCM-Chg (s,t,u)) . t = u

let t be Element of SCM-Data-Loc ; :: thesis: for u being Element of G holds (SCM-Chg (s,t,u)) . t = u

let u be Element of G; :: thesis: (SCM-Chg (s,t,u)) . t = u

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

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

.= u by FUNCOP_1:72 ;

:: thesis: verum

for t being Element of SCM-Data-Loc

for u being Element of G holds (SCM-Chg (s,t,u)) . t = u

let s be SCM-State of G; :: thesis: for t being Element of SCM-Data-Loc

for u being Element of G holds (SCM-Chg (s,t,u)) . t = u

let t be Element of SCM-Data-Loc ; :: thesis: for u being Element of G holds (SCM-Chg (s,t,u)) . t = u

let u be Element of G; :: thesis: (SCM-Chg (s,t,u)) . t = u

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

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

.= u by FUNCOP_1:72 ;

:: thesis: verum