Infix "≡" := (eqm wB) (at level 70, no associativity) : uint63_scope.

(* Specifications: *)
Lemma add_assoc x y z: (x + (y + z) = (x + y) + z)%uint63.
Lemma add_comm x y: (x + y = y + x)%uint63.
Lemma add_le_r m n: if (n <=? m + n)%uint63 then (φ m + φ n < wB)%Z else (wB <= φ m + φ n)%Z.
Lemma add_cancel_l x y z : (x + y = x + z)%uint63 -> y = z.
Lemma add_cancel_r x y z : (y + x = z + x)%uint63 -> y = z.