let G be non empty good 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} = dom (t .--> u) by FUNCOP_1:19;
then t in dom (t .--> u) by TARSKI:def 1;
hence (SCM-Chg s,t,u) . t = (t .--> u) . t by FUNCT_4:14
.= u by FUNCOP_1:87 ;
:: thesis: verum