initial properies of the "same top term constructor" predicate

[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / unfold / gr2_gr2.ma

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/unfold/gr2_gr2.ma b/matita/matita/contribs/lambda_delta/Basic_2/unfold/gr2_gr2.ma
index dd2d34d079d6ac6eb410d6bbe505c9ecbc0752e0..438605e85cf190dd93f2fffa29e8930fef46125e 100644 (file)
--- a/matita/matita/contribs/lambda_delta/Basic_2/unfold/gr2_gr2.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/unfold/gr2_gr2.ma
@@ -18,4 +18,12 @@ include "Basic_2/unfold/gr2.ma".
 
 (* Main properties **********************************************************)
 
-axiom at_mono: ∀des,i,i1. @[i] des ≡ i1 → ∀i2. @[i] des ≡ i2 → i1 = i2. 
+theorem at_mono: ∀des,i,i1. @[i] des ≡ i1 → ∀i2. @[i] des ≡ i2 → i1 = i2.
+#des #i #i1 #H elim H -des -i -i1
+[ #i #x #H <(at_inv_nil … H) -x //
+| #des #d #e #i #i1 #Hid #_ #IHi1 #x #H
+  lapply (at_inv_cons_lt … H Hid) -H -Hid /2 width=1/
+| #des #d #e #i #i1 #Hdi #_ #IHi1 #x #H
+  lapply (at_inv_cons_ge … H Hdi) -H -Hdi /2 width=1/
+]
+qed-.