reserve l, m, n for Nat;
reserve a,b for Int-Location,
  f for FinSeq-Location,
  s,s1,s2 for State of SCM+FSA;
reserve L for finite Subset of Int-Locations;
reserve L for finite Subset of FinSeq-Locations;
reserve L for finite Subset of Int-Locations;

theorem
  for x being set,i,m,n being Nat
   st x in dom (((intloc i) .--> m) +* Start-At(n,SCM+FSA))
    holds x=intloc i or x=IC SCM+FSA
proof
  let x be set,i,m,n be Nat;
  set iS = ((intloc i) .--> m) +* Start-At(n,SCM+FSA);
  dom ((intloc i) .--> m) ={intloc i } & dom(Start-At(n,SCM+FSA)) = {IC
  SCM+FSA};
  then
A1: dom iS ={intloc i} \/ {IC SCM+FSA} by FUNCT_4:def 1;
  assume x in dom iS;
  then x in{intloc i} or x in {IC SCM+FSA} by A1,XBOOLE_0:def 3;
  hence thesis by TARSKI:def 1;
end;
