One needs the additional axioms, see #15. ```coq ; in_pos_def1 :> ∀ v, PropHolds (0 ≤ ⟨v,v⟩) ; in_pos_def2 :> ∀ v, 0 = ⟨v,v⟩ <-> v = mon_unit ; inprod_proper :> Proper ((=) ==> (=) ==> (=)) (⟨⟩) ```