proposition: Lemma norm_aux_PEadd pe1 pe2 : norm_aux (PEadd pe1 pe2) = match get_PEopp pe1, get_PEopp pe2 with | Some pe1', _ => (norm_aux pe2) -- (norm_aux pe1') | None, Some pe2' => (norm_aux pe1) -- (norm_aux pe2') | None, None => (norm_aux pe1) ++ (norm_aux pe2) end.
proof: Proof. simpl (norm_aux (PEadd _ _)). destruct pe1; [ | | | | | reflexivity | ]; destruct pe2; simpl get_PEopp; reflexivity. Qed.
imports: Setoid Morphisms Env BinPos BinNat BinInt Ring_theory