- the trace is explicit in all auto tactics with depth > 1

[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 ce2918fddf05341f4f391defd23d79df3700a1d0..ac00f87b3e1f8df47c54d7407b559b476b90eeea 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/multiple/mr2_minus.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/multiple/mr2_minus.ma
@@ -19,58 +19,58 @@ include "basic_2/multiple/mr2.ma".
 
 inductive minuss: nat → relation (list2 nat nat) ≝
 | minuss_nil: ∀i. minuss i (◊) (◊)
-| minuss_lt : ∀des1,des2,l,m,i. i < l → minuss i des1 des2 →
-              minuss i ({l, m} @ des1) ({l - i, m} @ des2)
-| minuss_ge : ∀des1,des2,l,m,i. l ≤ i → minuss (m + i) des1 des2 →
-              minuss i ({l, m} @ des1) des2
+| minuss_lt : ∀cs1,cs2,l,m,i. 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 i ({l, m} @ cs1) cs2
 .
 
 interpretation "minus (multiple relocation with pairs)"
-   'RMinus des1 i des2 = (minuss i des1 des2).
+   'RMinus cs1 i cs2 = (minuss i cs1 cs2).
 
 (* Basic inversion lemmas ***************************************************)
 
-fact minuss_inv_nil1_aux: ∀des1,des2,i. des1 ▭ i ≡ des2 → des1 = ◊ → des2 = ◊.
-#des1 #des2 #i * -des1 -des2 -i
+fact minuss_inv_nil1_aux: ∀cs1,cs2,i. cs1 ▭ i ≡ cs2 → cs1 = ◊ → cs2 = ◊.
+#cs1 #cs2 #i * -cs1 -cs2 -i
 [ //
-| #des1 #des2 #l #m #i #_ #_ #H destruct
-| #des1 #des2 #l #m #i #_ #_ #H destruct
+| #cs1 #cs2 #l #m #i #_ #_ #H destruct
+| #cs1 #cs2 #l #m #i #_ #_ #H destruct
 ]
 qed-.
 
-lemma minuss_inv_nil1: ∀des2,i. ◊ ▭ i ≡ des2 → des2 = ◊.
+lemma minuss_inv_nil1: ∀cs2,i. ◊ ▭ i ≡ cs2 → cs2 = ◊.
 /2 width=4 by minuss_inv_nil1_aux/ qed-.
 
-fact minuss_inv_cons1_aux: ∀des1,des2,i. des1 ▭ i ≡ des2 →
-                           ∀l,m,des. des1 = {l, m} @ des →
-                           l ≤ i ∧ des ▭ m + i ≡ des2 ∨
-                           ∃∃des0. i < l & des ▭ i ≡ des0 &
-                                   des2 = {l - i, m} @ des0.
-#des1 #des2 #i * -des1 -des2 -i
-[ #i #l #m #des #H destruct
-| #des1 #des #l1 #m1 #i1 #Hil1 #Hcs #l2 #m2 #des2 #H destruct /3 width=3 by ex3_intro, or_intror/
-| #des1 #des #l1 #m1 #i1 #Hli1 #Hcs #l2 #m2 #des2 #H destruct /3 width=1 by or_introl, conj/
+fact minuss_inv_cons1_aux: ∀cs1,cs2,i. cs1 ▭ i ≡ cs2 →
+                           ∀l,m,cs. cs1 = {l, m} @ cs →
+                           l ≤ i ∧ cs ▭ m + i ≡ cs2 ∨
+                           ∃∃cs0. i < l & cs ▭ i ≡ cs0 &
+                                   cs2 = {l - i, m} @ cs0.
+#cs1 #cs2 #i * -cs1 -cs2 -i
+[ #i #l #m #cs #H destruct
+| #cs1 #cs #l1 #m1 #i1 #Hil1 #Hcs #l2 #m2 #cs2 #H destruct /3 width=3 by ex3_intro, or_intror/
+| #cs1 #cs #l1 #m1 #i1 #Hli1 #Hcs #l2 #m2 #cs2 #H destruct /3 width=1 by or_introl, conj/
 ]
 qed-.
 
-lemma minuss_inv_cons1: ∀des1,des2,l,m,i. {l, m} @ des1 ▭ i ≡ des2 →
-                        l ≤ i ∧ des1 ▭ m + i ≡ des2 ∨
-                        ∃∃des. i < l & des1 ▭ i ≡ des &
-                               des2 = {l - i, m} @ des.
+lemma minuss_inv_cons1: ∀cs1,cs2,l,m,i. {l, m} @ cs1 ▭ i ≡ cs2 →
+                        l ≤ i ∧ cs1 ▭ m + i ≡ cs2 ∨
+                        ∃∃cs. i < l & cs1 ▭ i ≡ cs &
+                               cs2 = {l - i, m} @ cs.
 /2 width=3 by minuss_inv_cons1_aux/ qed-.
 
-lemma minuss_inv_cons1_ge: ∀des1,des2,l,m,i. {l, m} @ des1 ▭ i ≡ des2 →
-                           l ≤ i → des1 ▭ m + i ≡ des2.
-#des1 #des2 #l #m #i #H
-elim (minuss_inv_cons1 … H) -H * // #des #Hil #_ #_ #Hli
+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)
 qed-.
 
-lemma minuss_inv_cons1_lt: ∀des1,des2,l,m,i. {l, m} @ des1 ▭ i ≡ des2 →
+lemma minuss_inv_cons1_lt: ∀cs1,cs2,l,m,i. {l, m} @ cs1 ▭ i ≡ cs2 →
                            i < l →
-                           ∃∃des. des1 ▭ i ≡ des & des2 = {l - i, m} @ des.
-#des1 #des2 #l #m #i #H elim (minuss_inv_cons1 … H) -H * /2 width=3 by ex2_intro/
+                           ∃∃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)
 qed-.