- revision of ground_2 and basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / multiple / mr2_minus.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/multiple/mr2_minus.ma b/matita/matita/contribs/lambdadelta/basic_2/multiple/mr2_minus.ma
index ac00f87b3e1f8df47c54d7407b559b476b90eeea..3c5f8da5cf55ec2e9cb453db6dc75a37c0c533e1 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/multiple/mr2_minus.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/multiple/mr2_minus.ma
@@ -12,16 +12,17 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "ground_2/ynat/ynat_minus.ma".
 include "basic_2/notation/relations/rminus_3.ma".
 include "basic_2/multiple/mr2.ma".
 
 (* MULTIPLE RELOCATION WITH PAIRS *******************************************)
 
-inductive minuss: nat → relation (list2 nat nat) ≝
+inductive minuss: nat → relation (list2 ynat nat) ≝
 | minuss_nil: ∀i. minuss i (◊) (◊)
-| minuss_lt : ∀cs1,cs2,l,m,i. i < l → minuss i cs1 cs2 →
+| minuss_lt : ∀cs1,cs2,l,m,i. yinj i < l → minuss i cs1 cs2 →
               minuss i ({l, m} @ cs1) ({l - i, m} @ cs2)
-| minuss_ge : ∀cs1,cs2,l,m,i. l ≤ i → minuss (m + i) cs1 cs2 →
+| minuss_ge : ∀cs1,cs2,l,m,i. l ≤ yinj i → minuss (m + i) cs1 cs2 →
               minuss i ({l, m} @ cs1) cs2
 .
 
@@ -63,14 +64,12 @@ lemma minuss_inv_cons1_ge: ∀cs1,cs2,l,m,i. {l, m} @ cs1 ▭ i ≡ cs2 →
                            l ≤ i → cs1 ▭ m + i ≡ cs2.
 #cs1 #cs2 #l #m #i #H
 elim (minuss_inv_cons1 … H) -H * // #cs #Hil #_ #_ #Hli
-lapply (lt_to_le_to_lt … Hil Hli) -Hil -Hli #Hi
-elim (lt_refl_false … Hi)
+elim (ylt_yle_false … Hil Hli)
 qed-.
 
 lemma minuss_inv_cons1_lt: ∀cs1,cs2,l,m,i. {l, m} @ cs1 ▭ i ≡ cs2 →
                            i < l →
                            ∃∃cs. cs1 ▭ i ≡ cs & cs2 = {l - i, m} @ cs.
 #cs1 #cs2 #l #m #i #H elim (minuss_inv_cons1 … H) -H * /2 width=3 by ex2_intro/
-#Hli #_ #Hil lapply (lt_to_le_to_lt … Hil Hli) -Hil -Hli
-#Hi elim (lt_refl_false … Hi)
+#Hli #_ #Hil elim (ylt_yle_false … Hil Hli)
 qed-.