let s be State of SCM; :: thesis: for iloc being Nat
for a being Data-Location holds s . a = (s +* (Start-At (iloc,SCM))) . a
let iloc be Nat; :: thesis: for a being Data-Location holds s . a = (s +* (Start-At (iloc,SCM))) . a
let a be Data-Location; :: thesis: s . a = (s +* (Start-At (iloc,SCM))) . a
a in the carrier of SCM ;
then a in dom s by PARTFUN1:def 2;
then A1: ( dom (Start-At (iloc,SCM)) = {(IC )} & a in (dom s) \/ (dom (Start-At (iloc,SCM))) ) by XBOOLE_0:def 3;
a <> IC by Th2;
then not a in {(IC )} by TARSKI:def 1;
hence s . a = (s +* (Start-At (iloc,SCM))) . a by A1, FUNCT_4:def 1; :: thesis: verum