- lambda_delta: programmed renaming to lambdadelta

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / unfold / gr2_minus.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/unfold/gr2_minus.ma b/matita/matita/contribs/lambda_delta/basic_2/unfold/gr2_minus.ma
deleted file mode 100644 (file)
index 6138548..0000000
--- a/matita/matita/contribs/lambda_delta/basic_2/unfold/gr2_minus.ma
+++ /dev/null
@@ -1,76 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-include "basic_2/unfold/gr2.ma".
-
-(* GENERIC RELOCATION WITH PAIRS ********************************************)
-
-inductive minuss: nat → relation (list2 nat nat) ≝
-| minuss_nil: ∀i. minuss i ⟠ ⟠ 
-| minuss_lt : ∀des1,des2,d,e,i. i < d → minuss i des1 des2 →
-              minuss i ({d, e} @ des1) ({d - i, e} @ des2)
-| minuss_ge : ∀des1,des2,d,e,i. d ≤ i → minuss (e + i) des1 des2 →
-              minuss i ({d, e} @ des1) des2
-.
-
-interpretation "minus (generic relocation with pairs)"
-   'RMinus des1 i des2 = (minuss i des1 des2).
-
-(* Basic inversion lemmas ***************************************************)
-
-fact minuss_inv_nil1_aux: ∀des1,des2,i. des1 ▭ i ≡ des2 → des1 = ⟠ → des2 = ⟠.
-#des1 #des2 #i * -des1 -des2 -i
-[ //
-| #des1 #des2 #d #e #i #_ #_ #H destruct
-| #des1 #des2 #d #e #i #_ #_ #H destruct
-]
-qed.
-
-lemma minuss_inv_nil1: ∀des2,i. ⟠ ▭ i ≡ des2 → des2 = ⟠.
-/2 width=4/ qed-.
-
-fact minuss_inv_cons1_aux: ∀des1,des2,i. des1 ▭ i ≡ des2 →
-                           ∀d,e,des. des1 = {d, e} @ des →
-                           d ≤ i ∧ des ▭ e + i ≡ des2 ∨
-                           ∃∃des0. i < d & des ▭ i ≡ des0 &
-                                   des2 = {d - i, e} @ des0.
-#des1 #des2 #i * -des1 -des2 -i
-[ #i #d #e #des #H destruct 
-| #des1 #des #d1 #e1 #i1 #Hid1 #Hdes #d2 #e2 #des2 #H destruct /3 width=3/
-| #des1 #des #d1 #e1 #i1 #Hdi1 #Hdes #d2 #e2 #des2 #H destruct /3 width=1/
-]
-qed.
-
-lemma minuss_inv_cons1: ∀des1,des2,d,e,i. {d, e} @ des1 ▭ i ≡ des2 →
-                        d ≤ i ∧ des1 ▭ e + i ≡ des2 ∨
-                        ∃∃des. i < d & des1 ▭ i ≡ des &
-                               des2 = {d - i, e} @ des.
-/2 width=3/ qed-.
-
-lemma minuss_inv_cons1_ge: ∀des1,des2,d,e,i. {d, e} @ des1 ▭ i ≡ des2 →
-                           d ≤ i → des1 ▭ e + i ≡ des2.
-#des1 #des2 #d #e #i #H
-elim (minuss_inv_cons1 … H) -H * // #des #Hid #_ #_ #Hdi
-lapply (lt_to_le_to_lt … Hid Hdi) -Hid -Hdi #Hi
-elim (lt_refl_false … Hi)
-qed-.
-
-lemma minuss_inv_cons1_lt: ∀des1,des2,d,e,i. {d, e} @ des1 ▭ i ≡ des2 →
-                           i < d → 
-                           ∃∃des. des1 ▭ i ≡ des & des2 = {d - i, e} @ des.
-#des1 #des2 #d #e #i #H
-elim (minuss_inv_cons1 … H) -H * /2 width=3/ #Hdi #_ #Hid
-lapply (lt_to_le_to_lt … Hid Hdi) -Hid -Hdi #Hi
-elim (lt_refl_false … Hi)
-qed-.