reserve p for preProgram of SCM+FSA,
  ic for Instruction of SCM+FSA,
  i,j,k for Nat,
  fa,f for FinSeq-Location,
  a,b,da,db for Int-Location,
  la,lb for Nat;
reserve p1,p2,q for Instruction-Sequence of SCM+FSA;
reserve n for Nat;

theorem Th19:
  for p being Program of SCM+FSA,s being State of SCM+FSA holds
  UsedI*Loc p \/ UsedILoc p c= dom s
proof
  let p be Program of SCM+FSA,s be State of SCM+FSA;
  Int-Locations c= dom(s) by SCMFSA_2:45;
  then
A1: UsedILoc p c= dom(s) by XBOOLE_1:1;
  FinSeq-Locations c= dom (s) by SCMFSA_2:46;
  then UsedI*Loc p c= dom(s) by XBOOLE_1:1;
  hence thesis by A1,XBOOLE_1:8;
end;
