basic properties of cpr ...

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / lib / arith.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_2/lib/arith.ma b/matita/matita/contribs/lambdadelta/ground_2/lib/arith.ma
index f86f7a3bd75b1ca4532acfa39c2829a704335c9f..83322f4d8de57107b0eeb097bb7cd96d3cd83d86 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/lib/arith.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/lib/arith.ma
@@ -35,6 +35,9 @@ normalize // qed.
 lemma pred_S: ∀m. pred (S m) = m.
 // qed.
 
+lemma plus_S1: ∀x,y. ⫯(x+y) = (⫯x) + y.
+// qed.
+
 lemma max_O1: ∀n. n = (0 ∨ n).
 // qed.
 
@@ -48,6 +51,9 @@ qed.
 
 (* Equations ****************************************************************)
 
+lemma plus_SO: ∀n. n + 1 = ⫯n.
+// qed.
+
 lemma minus_plus_m_m_commutative: ∀n,m:nat. n = m + n - m.
 // qed-.
 
@@ -152,6 +158,13 @@ qed.
 
 (* Inversion & forward lemmas ***********************************************)
 
+lemma max_inv_O3: ∀x,y. (x ∨ y) = 0 → 0 = x ∧ 0 = y.
+/4 width=2 by le_maxr, le_maxl, le_n_O_to_eq, conj/
+qed-.
+
+lemma plus_inv_O3: ∀x,y. x + y = 0 → x = 0 ∧ y = 0.
+/2 width=1 by plus_le_0/ qed-.
+
 lemma discr_plus_xy_y: ∀x,y. x + y = y → x = 0.
 // qed-.