let s be SCM+FSA-State; :: thesis: for u being Nat

for p being Element of SCM+FSA-Data*-Loc holds (SCM+FSA-Chg (s,u)) . p = s . p

let u be Nat; :: thesis: for p being Element of SCM+FSA-Data*-Loc holds (SCM+FSA-Chg (s,u)) . p = s . p

let mk be Element of SCM+FSA-Data*-Loc ; :: thesis: (SCM+FSA-Chg (s,u)) . mk = s . mk

A2: SCM+FSA-OK . NAT = 0 by Lm4;

SCM+FSA-OK . mk = 2 by Lm6;

then NAT <> mk by A2;

then not mk in dom (NAT .--> u) by TARSKI:def 1;

hence (SCM+FSA-Chg (s,u)) . mk = s . mk by FUNCT_4:11; :: thesis: verum

for p being Element of SCM+FSA-Data*-Loc holds (SCM+FSA-Chg (s,u)) . p = s . p

let u be Nat; :: thesis: for p being Element of SCM+FSA-Data*-Loc holds (SCM+FSA-Chg (s,u)) . p = s . p

let mk be Element of SCM+FSA-Data*-Loc ; :: thesis: (SCM+FSA-Chg (s,u)) . mk = s . mk

A2: SCM+FSA-OK . NAT = 0 by Lm4;

SCM+FSA-OK . mk = 2 by Lm6;

then NAT <> mk by A2;

then not mk in dom (NAT .--> u) by TARSKI:def 1;

hence (SCM+FSA-Chg (s,u)) . mk = s . mk by FUNCT_4:11; :: thesis: verum