axiom q_le_minus_r: ∀a,b,c:ℚ. a - b ≤ c → a ≤ c + b.
axiom q_lt_plus: ∀a,b,c:ℚ. a - b < c → a < c + b.
axiom q_lt_minus: ∀a,b,c:ℚ. a + b < c → a < c - b.
+axiom q_le_plus: ∀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_r: ∀a,b,c:ℚ. a + b < c → a < c - b.
+axiom q_lt_minus_r: ∀a,b,c:ℚ. a - b < c → a < c + b.
axiom q_lt_opp_opp: ∀a,b.b < a → Qopp a < Qopp b.
axiom q_lt_to_le: ∀a,b:ℚ.a < b → a ≤ b.
axiom q_le_to_diff_ge_OQ : ∀a,b.a ≤ b → OQ ≤ b-a.