X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fdama%2Fdama%2Fmodels%2Fq_support.ma;h=b948e61b5d8dc1e936e499e82de27bbb1a26b44e;hb=23dbce6cd7d599c10eb7801e91bc8b5164164418;hp=2073c8a77afad47f5b6d6c64b56464a1db1ff0a0;hpb=88b32d4e8fe371d59e41cd272064c9d486ae7ec5;p=helm.git

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 2073c8a77..b948e61b5 100644
--- 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.