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[helm.git] / helm / software / matita / contribs / dama / dama / models / q_support.ma

diff --git a/helm/software/matita/contribs/dama/dama/models/q_support.ma b/helm/software/matita/contribs/dama/dama/models/q_support.ma
index 2073c8a77afad47f5b6d6c64b56464a1db1ff0a0..b948e61b5d8dc1e936e499e82de27bbb1a26b44e 100644 (file)
--- a/helm/software/matita/contribs/dama/dama/models/q_support.ma
+++ b/helm/software/matita/contribs/dama/dama/models/q_support.ma
@@ -52,6 +52,10 @@ axiom q_le_minus: ∀a,b,c:ℚ. a ≤ c - b → a + b ≤ c.
 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.
@@ -109,3 +113,17 @@ rewrite > q_plus_minus;
 do 2 rewrite > q_plus_OQ; assumption;
 qed.
 
+lemma q_le_inj_plus_r:
+  ∀x,y,z:Q.x ≤ y → x + z ≤ y + z.
+intros;cases (q_le_cases ?? H);
+[1: rewrite > H1; apply q_eq_to_le; reflexivity;
+|2: apply q_lt_to_le; apply q_lt_inj_plus_r; assumption;]
+qed.
+
+lemma q_le_canc_plus_r:
+  ∀x,y,z:Q.x + z ≤ y + z → x ≤ y.
+intros; lapply (q_le_inj_plus_r ?? (Qopp z) H) as H1;
+do 2 rewrite < q_plus_assoc in H1;
+rewrite < q_elim_minus in H1; rewrite > q_plus_minus in H1;
+do 2 rewrite > q_plus_OQ in H1; assumption;
+qed.