let s be State of SCM+FSA; :: thesis: for iloc being Nat
for a being FinSeq-Location holds s . a = (s +* (Start-At (iloc,SCM+FSA))) . a
let iloc be Nat; :: thesis: for a being FinSeq-Location holds s . a = (s +* (Start-At (iloc,SCM+FSA))) . a
let a be FinSeq-Location ; :: thesis: s . a = (s +* (Start-At (iloc,SCM+FSA))) . a
a in the carrier of SCM+FSA ;
then a in dom s by PARTFUN1:def 2;
then A1: ( dom (Start-At (iloc,SCM+FSA)) = {(IC )} & a in (dom s) \/ (dom (Start-At (iloc,SCM+FSA))) ) by XBOOLE_0:def 3;
a <> IC by SCMFSA_2:57;
then not a in {(IC )} by TARSKI:def 1;
hence s . a = (s +* (Start-At (iloc,SCM+FSA))) . a by A1, FUNCT_4:def 1; :: thesis: verum