axiom q_le_cases : ∀x,y:ℚ.x ≤ y → q_le_elimination x y.
+axiom q_le_to_le_to_eq : ∀x,y. x ≤ y → y ≤ x → x = y.
+
axiom q_le_plus_l: ∀a,b,c:ℚ. a ≤ c - b → a + b ≤ c.
axiom q_le_plus_r: ∀a,b,c:ℚ. a - b ≤ c → a ≤ c + b.
axiom q_lt_plus_l: ∀a,b,c:ℚ. a < c - b → a + b < c.