reserve G for Abelian add-associative right_complementable right_zeroed
  non empty addLoopStr;
reserve GS for non empty addLoopStr;
reserve F for Field;
reserve F for Field,
  n for Nat,
  D for non empty set,
  d for Element of D,
  B for BinOp of D,
  C for UnOp of D;
reserve x,y for set;
reserve D for non empty set,
  H,G for BinOp of D,
  d for Element of D,
  t1,t2 for Element of n-tuples_on D;
reserve x,y,z for set,
  A for AbGroup;
reserve a for Domain-Sequence,
  i for Element of dom a,
  p for FinSequence;

theorem Th11:
  p is BinOps of a iff len p = len a & for i holds p.i is BinOp of a.i
proof
  dom p = dom a iff len p = len a by FINSEQ_3:29;
  hence thesis by Def6;
end;
