From 23c056d7fb7269f952a02aad1cac8e400d2653b0 Mon Sep 17 00:00:00 2001
From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Wed, 7 Nov 2012 16:46:54 +0000
Subject: [PATCH] - commit of the component: static - notation updates missing
 in former commit

---
 .../contribs/lambda_delta/basic_2/notation.ma | 24 +++----
 .../lambda_delta/basic_2/static/ssta.ma       | 64 ++++++++++++++-----
 .../lambda_delta/basic_2/static/ssta_aaa.ma   |  2 +-
 .../lambda_delta/basic_2/static/ssta_lift.ma  | 18 +++---
 .../basic_2/static/ssta_ltpss_dx.ma           |  7 +-
 .../lambda_delta/basic_2/static/ssta_ssta.ma  |  5 +-
 6 files changed, 69 insertions(+), 51 deletions(-)

diff --git a/matita/matita/contribs/lambda_delta/basic_2/notation.ma b/matita/matita/contribs/lambda_delta/basic_2/notation.ma
index f53dcf867..affb8af13 100644
--- a/matita/matita/contribs/lambda_delta/basic_2/notation.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/notation.ma
@@ -162,9 +162,9 @@ notation "hvbox( ⇩ [ d , break e ] break term 46 L1 ≡ break term 46 L2 )"
    non associative with precedence 45
    for @{ 'RDrop $d $e $L1 $L2 }.
 
-notation "hvbox( ⦃ L1, break T1 ⦄ > break ⦃ L2 , break T2 ⦄ )"
+notation "hvbox( ⦃ L1, break T1 ⦄ ⧁ break ⦃ L2 , break T2 ⦄ )"
    non associative with precedence 45
-   for @{ 'SupTerm $L1 $T1 $L2 $T2 }.
+   for @{ 'RestSupTerm $L1 $T1 $L2 $T2 }.
 
 notation "hvbox( L ⊢ break ⌘ ⦃ T ⦄ ≡ break term 46 k )"
    non associative with precedence 45
@@ -192,9 +192,13 @@ notation "hvbox( ⇩ * [ e ] break term 46 L1 ≡ break term 46 L2 )"
    non associative with precedence 45
    for @{ 'RDropStar $e $L1 $L2 }.
 
-notation "hvbox( ⦃ L1, break T1 ⦄ > * break ⦃ L2 , break T2 ⦄ )"
+notation "hvbox( ⦃ L1, break T1 ⦄ ⧁ + break ⦃ L2 , break T2 ⦄ )"
    non associative with precedence 45
-   for @{ 'SupTermStar $L1 $T1 $L2 $T2 }.
+   for @{ 'RestSupTermPlus $L1 $T1 $L2 $T2 }.
+
+notation "hvbox( ⦃ L1, break T1 ⦄ ⧁ * break ⦃ L2 , break T2 ⦄ )"
+   non associative with precedence 45
+   for @{ 'RestSupTermStar $L1 $T1 $L2 $T2 }.
 
 notation "hvbox( T1 break ▶ * [ d , break e ] break term 46 T2 )"
    non associative with precedence 45
@@ -340,10 +344,6 @@ notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T1 • ➡ break [ g ] br
    non associative with precedence 45
    for @{ 'XPRed $h $g $L $T1 $T2 }.
 
-notation "hvbox( h ⊢ break ⦃ L1, break T1 ⦄ • ⥸ break [ g ] break ⦃ L2 , break T2 ⦄ )"
-   non associative with precedence 45
-   for @{ 'YPRed $h $g $L1 $T1 $L2 $T2 }.
-
 (* Computation **************************************************************)
 
 notation "hvbox( T1 ➡ * break term 46 T2 )"
@@ -406,14 +406,6 @@ notation "hvbox( ⦃ h , break L ⦄ ⊢ • ⬊ * break [ g ] break term 46 T2
    non associative with precedence 45
    for @{ 'XSN $h $g $L $T }.
 
-notation "hvbox( h ⊢ break ⦃ L1, break T1 ⦄ • ⥸  * break [ g ] break ⦃ L2 , break T2 ⦄ )"
-   non associative with precedence 45
-   for @{ 'YPRedStar $h $g $L1 $T1 $L2 $T2 }.
-
-notation "hvbox( h ⊢ break ⦃ L1, break T1 ⦄ • ⭃ * break [ g ] break ⦃ L2 , break T2 ⦄ )"
-   non associative with precedence 45
-   for @{ 'YPRedStepStar $h $g $L1 $T1 $L2 $T2 }.
-
 (* Conversion ***************************************************************)
 
 notation "hvbox( L ⊢ break term 46 T1 ⬌ break term 46 T2 )"
diff --git a/matita/matita/contribs/lambda_delta/basic_2/static/ssta.ma b/matita/matita/contribs/lambda_delta/basic_2/static/ssta.ma
index ec990f13b..3cd0134bb 100644
--- a/matita/matita/contribs/lambda_delta/basic_2/static/ssta.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/static/ssta.ma
@@ -13,6 +13,7 @@
 (**************************************************************************)
 
 include "basic_2/substitution/ldrop.ma".
+include "basic_2/unfold/frsups.ma".
 include "basic_2/static/sd.ma".
 
 (* STRATIFIED STATIC TYPE ASSIGNMENT ON TERMS *******************************)
@@ -27,8 +28,7 @@ inductive ssta (h:sh) (g:sd h): nat → lenv → relation term ≝
              ssta h g l L (ⓑ{a,I}V.T) (ⓑ{a,I}V.U)
 | ssta_appl: ∀L,V,T,U,l. ssta h g l L T U →
              ssta h g l L (ⓐV.T) (ⓐV.U)
-| ssta_cast: ∀L,V,W,T,U,l. ssta h g (l - 1) L V W → ssta h g l L T U →
-                           ssta h g l L (ⓝV. T) (ⓝW. U)
+| ssta_cast: ∀L,W,T,U,l. ssta h g l L T U → ssta h g l L (ⓝW. T) U
 .
 
 interpretation "stratified static type assignment (term)"
@@ -44,7 +44,7 @@ fact ssta_inv_sort1_aux: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g, l] U → ∀k0.
 | #L #K #W #V #U #i #l #_ #_ #_ #k0 #H destruct
 | #a #I #L #V #T #U #l #_ #k0 #H destruct
 | #L #V #T #U #l #_ #k0 #H destruct
-| #L #V #W #T #U #l #_ #_ #k0 #H destruct
+| #L #W #T #U #l #_ #k0 #H destruct
 qed.
 
 (* Basic_1: was just: sty0_gen_sort *)
@@ -65,7 +65,7 @@ fact ssta_inv_lref1_aux: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g, l] U → ∀j.
 | #L #K #W #V #U #i #l #HLK #HWV #HWU #j #H destruct /3 width=8/
 | #a #I #L #V #T #U #l #_ #j #H destruct
 | #L #V #T #U #l #_ #j #H destruct
-| #L #V #W #T #U #l #_ #_ #j #H destruct
+| #L #W #T #U #l #_ #j #H destruct
 ]
 qed.
 
@@ -88,7 +88,7 @@ fact ssta_inv_bind1_aux: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g, l] U →
 | #L #K #W #V #U #i #l #_ #_ #_ #a #I #X #Y #H destruct
 | #b #J #L #V #T #U #l #HTU #a #I #X #Y #H destruct /2 width=3/
 | #L #V #T #U #l #_ #a #I #X #Y #H destruct
-| #L #V #W #T #U #l #_ #_ #a #I #X #Y #H destruct
+| #L #W #T #U #l #_ #a #I #X #Y #H destruct
 ]
 qed.
 
@@ -105,7 +105,7 @@ fact ssta_inv_appl1_aux: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g, l] U → ∀X,Y
 | #L #K #W #V #U #i #l #_ #_ #_ #X #Y #H destruct
 | #a #I #L #V #T #U #l #_ #X #Y #H destruct
 | #L #V #T #U #l #HTU #X #Y #H destruct /2 width=3/
-| #L #V #W #T #U #l #_ #_ #X #Y #H destruct
+| #L #W #T #U #l #_ #X #Y #H destruct
 ]
 qed.
 
@@ -114,31 +114,53 @@ lemma ssta_inv_appl1: ∀h,g,L,Y,X,U,l. ⦃h, L⦄ ⊢ ⓐY.X •[g, l] U →
                       ∃∃Z. ⦃h, L⦄ ⊢ X •[g, l] Z & U = ⓐY.Z.
 /2 width=3/ qed-.
 
-fact ssta_inv_cast1_aux: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g, l] U → ∀X,Y. T = ⓝY.X →
-                         ∃∃Z1,Z2. ⦃h, L⦄ ⊢ Y •[g, l-1] Z1 & ⦃h, L⦄ ⊢ X •[g, l] Z2 &
-                                  U = ⓝZ1.Z2.
+fact ssta_inv_cast1_aux: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g, l] U →
+                         ∀X,Y. T = ⓝY.X → ⦃h, L⦄ ⊢ X •[g, l] U.
 #h #g #L #T #U #l * -L -T -U -l
 [ #L #k #l #_ #X #Y #H destruct
 | #L #K #V #W #U #l #i #_ #_ #_ #X #Y #H destruct
 | #L #K #W #V #U #l #i #_ #_ #_ #X #Y #H destruct
 | #a #I #L #V #T #U #l #_ #X #Y #H destruct
 | #L #V #T #U #l #_ #X #Y #H destruct
-| #L #V #W #T #U #l #HVW #HTU #X #Y #H destruct /2 width=5/
+| #L #W #T #U #l #HTU #X #Y #H destruct //
 ]
 qed.
 
 (* Basic_1: was just: sty0_gen_cast *)
 lemma ssta_inv_cast1: ∀h,g,L,X,Y,U,l. ⦃h, L⦄ ⊢ ⓝY.X •[g, l] U →
-                      ∃∃Z1,Z2. ⦃h, L⦄ ⊢ Y •[g, l-1] Z1 & ⦃h, L⦄ ⊢ X •[g, l] Z2 &
-                               U = ⓝZ1.Z2.
+                      ⦃h, L⦄ ⊢ X •[g, l] U.
 /2 width=4/ qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
+lemma ssta_inv_frsupp: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g, l] U → ⦃L, U⦄ ⧁+ ⦃L, T⦄ → ⊥.
+#h #g #L #T #U #l #H elim H -L -T -U -l
+[ #L #k #l #_ #H
+  elim (frsupp_inv_atom1_frsups … H)
+| #L #K #V #W #U #i #l #_ #_ #HWU #_ #H
+  elim (lift_frsupp_trans … (⋆) … H … HWU) -U #X #H
+  elim (lift_inv_lref2_be … H ? ?) -H //
+| #L #K #W #V #U #i #l #_ #_ #HWU #_ #H
+  elim (lift_frsupp_trans … (⋆) … H … HWU) -U #X #H
+  elim (lift_inv_lref2_be … H ? ?) -H //
+| #a #I #L #V #T #U #l #_ #IHTU #H
+  elim (frsupp_inv_bind1_frsups … H) -H #H [2: /4 width=4/ ] -IHTU
+  lapply (frsups_fwd_fw … H) -H normalize
+  <associative_plus <associative_plus #H
+  elim (le_plus_xySz_x_false … H)
+| #L #V #T #U #l #_ #IHTU #H
+  elim (frsupp_inv_flat1_frsups … H) -H #H [2: /4 width=4/ ] -IHTU
+  lapply (frsups_fwd_fw … H) -H normalize
+  <associative_plus <associative_plus #H
+  elim (le_plus_xySz_x_false … H)
+| /3 width=4/
+]
+qed-.
+
 fact ssta_inv_refl_aux: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g, l] U → T = U → ⊥.
 #h #g #L #T #U #l #H elim H -L -T -U -l
 [ #L #k #l #_ #H
-  lapply (next_lt h k) destruct -H -e0 (**) (* these premises are not erased *)
+  lapply (next_lt h k) destruct -H -e0 (**) (* destruct: these premises are not erased *)
   <e1 -e1 #H elim (lt_refl_false … H)
 | #L #K #V #W #U #i #l #_ #_ #HWU #_ #H destruct
   elim (lift_inv_lref2_be … HWU ? ?) -HWU //
@@ -146,9 +168,17 @@ fact ssta_inv_refl_aux: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g, l] U → T = U 
   elim (lift_inv_lref2_be … HWU ? ?) -HWU //
 | #a #I #L #V #T #U #l #_ #IHTU #H destruct /2 width=1/
 | #L #V #T #U #l #_ #IHTU #H destruct /2 width=1/
-| #L #V #W #T #U #l #_ #_ #_ #IHTU #H destruct /2 width=1/
+| #L #W #T #U #l #HTU #_ #H destruct
+  elim (ssta_inv_frsupp … HTU ?) -HTU /2 width=1/
 ]
-qed.
+qed-.
+
+lemma ssta_inv_refl: ∀h,g,T,L,l. ⦃h, L⦄ ⊢ T •[g, l] T → ⊥.
+/2 width=8 by ssta_inv_refl_aux/ qed-.
 
-lemma ssta_inv_refl: ∀h,g,L,T,l. ⦃h, L⦄ ⊢ T •[g, l] T → ⊥.
-/2 width=8/ qed-.
+lemma ssta_inv_frsups: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g, l] U → ⦃L, U⦄ ⧁* ⦃L, T⦄ → ⊥.
+#h #g #L #T #U #L #HTU #H elim (frsups_inv_all … H) -H
+[ * #_ #H destruct /2 width=6 by ssta_inv_refl/
+| /2 width=8 by ssta_inv_frsupp/
+]
+qed-.
diff --git a/matita/matita/contribs/lambda_delta/basic_2/static/ssta_aaa.ma b/matita/matita/contribs/lambda_delta/basic_2/static/ssta_aaa.ma
index 729f08333..d14083a45 100644
--- a/matita/matita/contribs/lambda_delta/basic_2/static/ssta_aaa.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/static/ssta_aaa.ma
@@ -35,7 +35,7 @@ lemma ssta_aaa: ∀h,g,L,T,A. L ⊢ T ⁝ A → ∀U,l. ⦃h, L⦄ ⊢ T •[g,
 | #L #V #T #B #A #HV #_ #_ #IHT #X #l #H
   elim (ssta_inv_appl1 … H) -H #U #HTU #H destruct /3 width=3/
 | #L #V #T #A #_ #_ #IHV #IHT #X #l #H
-  elim (ssta_inv_cast1 … H) -H #W #U #HVW #HTU #H destruct /3 width=2/
+  lapply (ssta_inv_cast1 … H) -H /2 width=2/
 ]
 qed.
 
diff --git a/matita/matita/contribs/lambda_delta/basic_2/static/ssta_lift.ma b/matita/matita/contribs/lambda_delta/basic_2/static/ssta_lift.ma
index 6dbd9c7c9..e4f78acd6 100644
--- a/matita/matita/contribs/lambda_delta/basic_2/static/ssta_lift.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/static/ssta_lift.ma
@@ -54,9 +54,8 @@ lemma ssta_lift: ∀h,g,L1,T1,U1,l. ⦃h, L1⦄ ⊢ T1 •[g, l] U1 →
   elim (lift_inv_flat1 … H1) -H1 #V2 #T2 #HV12 #HT12 #H destruct
   elim (lift_inv_flat1 … H2) -H2 #X #U2 #H1 #HU12 #H2 destruct
   lapply (lift_mono … H1 … HV12) -H1 #H destruct /4 width=5/
-| #L1 #V1 #W1 #T1 #U1 #l #_ #_ #IHVW1 #IHTU1 #L2 #d #e #HL21 #X1 #H1 #X2 #H2
-  elim (lift_inv_flat1 … H1) -H1 #V2 #W2 #HV12 #HW12 #H destruct
-  elim (lift_inv_flat1 … H2) -H2 #T2 #U2 #HT12 #HU12 #H destruct /3 width=5/
+| #L1 #W1 #T1 #U1 #l #_ #IHTU1 #L2 #d #e #HL21 #X #H #U2 #HU12
+  elim (lift_inv_flat1 … H) -H #W2 #T2 #HW12 #HT12 #H destruct /3 width=5/
 ]
 qed.
 
@@ -76,7 +75,7 @@ lemma ssta_inv_lift1: ∀h,g,L2,T2,U2,l. ⦃h, L2⦄ ⊢ T2 •[g, l] U2 →
     elim (le_inv_plus_l … Hid) -Hid #Hdie #ei
     elim (lift_split … HW2 d (i-e+1) ? ? ?) -HW2 // [3: /2 width=1/ ]
     [ #W0 #HW20 <le_plus_minus_comm // >minus_minus_m_m /2 width=1/ /3 width=6/
-    | <le_plus_minus_comm // /2 width=1/
+    | <le_plus_minus_comm //
     ]
   ]
 | #L2 #K2 #W2 #V2 #W #i #l #HLK2 #HWV2 #HW2 #IHWV2 #L1 #d #e #HL21 #X #H
@@ -88,7 +87,7 @@ lemma ssta_inv_lift1: ∀h,g,L2,T2,U2,l. ⦃h, L2⦄ ⊢ T2 •[g, l] U2 →
     elim (le_inv_plus_l … Hid) -Hid #Hdie #ei
     elim (lift_split … HW2 d (i-e+1) ? ? ?) -HW2 // [3: /2 width=1/ ]
     [ #W0 #HW20 <le_plus_minus_comm // >minus_minus_m_m /2 width=1/ /3 width=6/
-    | <le_plus_minus_comm // /2 width=1/
+    | <le_plus_minus_comm //
     ]
   ]
 | #a #I #L2 #V2 #T2 #U2 #l #_ #IHTU2 #L1 #d #e #HL21 #X #H
@@ -97,10 +96,9 @@ lemma ssta_inv_lift1: ∀h,g,L2,T2,U2,l. ⦃h, L2⦄ ⊢ T2 •[g, l] U2 →
 | #L2 #V2 #T2 #U2 #l #_ #IHTU2 #L1 #d #e #HL21 #X #H
   elim (lift_inv_flat2 … H) -H #V1 #T1 #HV12 #HT12 #H destruct
   elim (IHTU2 … HL21 … HT12) -L2 -HT12 /3 width=5/
-| #L2 #V2 #W2 #T2 #U2 #l #_ #_ #IHVW2 #IHTU2 #L1 #d #e #HL21 #X #H
-  elim (lift_inv_flat2 … H) -H #V1 #T1 #HV12 #HT12 #H destruct
-  elim (IHVW2 … HL21 … HV12) -IHVW2
-  elim (IHTU2 … HL21 … HT12) -L2 -HT12 /3 width=5/
+| #L2 #W2 #T2 #U2 #l #_ #IHTU2 #L1 #d #e #HL21 #X #H
+  elim (lift_inv_flat2 … H) -H #W1 #T1 #HW12 #HT12 #H destruct
+  elim (IHTU2 … HL21 … HT12) -L2 -HT12 /3 width=3/
 ]
 qed.
 
@@ -119,6 +117,6 @@ lemma ssta_fwd_correct: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g, l] U →
   elim (lift_total V 0 (i+1)) /3 width=10/
 | #a #I #L #V #T #U #l #_ * /3 width=2/
 | #L #V #T #U #l #_ * #T0 #HUT0 /3 width=2/
-| #L #V #W #T #U #l #_ #_ * #W0 #HW0  * /3 width=2/
+| #L #W #T #U #l #_ * /2 width=2/
 ]
 qed-.
diff --git a/matita/matita/contribs/lambda_delta/basic_2/static/ssta_ltpss_dx.ma b/matita/matita/contribs/lambda_delta/basic_2/static/ssta_ltpss_dx.ma
index 1839c67bd..ccc9ecc9d 100644
--- a/matita/matita/contribs/lambda_delta/basic_2/static/ssta_ltpss_dx.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/static/ssta_ltpss_dx.ma
@@ -96,10 +96,9 @@ lemma ssta_ltpss_dx_tpss_conf: ∀h,g,L1,T1,U1,l. ⦃h, L1⦄ ⊢ T1 •[g, l] U
 | #L1 #V1 #T1 #U1 #l #_ #IHTU1 #L2 #d #e #HL12 #X #H
   elim (tpss_inv_flat1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct
   elim (IHTU1 … HT12) -IHTU1 -HT12 // -HL12 /3 width=5/
-| #L1 #V1 #W1 #T1 #U1 #l #_ #_ #IHVW1 #IHTU1 #L2 #d #e #HL12 #X #H
-  elim (tpss_inv_flat1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct
-  elim (IHVW1 … HV12) -IHVW1 -HV12 //
-  elim (IHTU1 … HT12) -IHTU1 -HT12 // -HL12 /3 width=5/
+| #L1 #W1 #T1 #U1 #l #_ #IHTU1 #L2 #d #e #HL12 #X #H
+  elim (tpss_inv_flat1 … H) -H #W2 #T2 #HW12 #HT12 #H destruct
+  elim (IHTU1 … HT12) -IHTU1 -HT12 // -HL12 /3 width=3/
 ]
 qed.
 
diff --git a/matita/matita/contribs/lambda_delta/basic_2/static/ssta_ssta.ma b/matita/matita/contribs/lambda_delta/basic_2/static/ssta_ssta.ma
index a9c027cc6..b20e4366a 100644
--- a/matita/matita/contribs/lambda_delta/basic_2/static/ssta_ssta.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/static/ssta_ssta.ma
@@ -42,9 +42,8 @@ theorem ssta_mono: ∀h,g,L,T,U1,l1. ⦃h, L⦄ ⊢ T •[g, l1] U1 →
 | #L #V #T #U1 #l1 #_ #IHTU1 #X #l2 #H
   elim (ssta_inv_appl1 … H) -H #U2 #HTU2 #H destruct
   elim (IHTU1 … HTU2) -T /3 width=1/
-| #L #V #W1 #T #U1 #l1 #_ #_ #IHVW1 #IHTU1 #U2 #l2 #H
-  elim (ssta_inv_cast1 … H) -H #W2 #T2 #HVW2 #HTU2 #H destruct
-  elim (IHVW1 … HVW2) -V
+| #L #W1 #T #U1 #l1 #_ #IHTU1 #U2 #l2 #H
+  lapply (ssta_inv_cast1 … H) -H #HTU2
   elim (IHTU1 … HTU2) -T /2 width=1/
 ]
 qed-.
-- 
2.39.2