commit of the "unfold" component ...

diff --git a/matita/matita/contribs/lambdadelta/basic_2/unfold/lsstas_alt.ma b/matita/matita/contribs/lambdadelta/basic_2/unfold/lsstas_alt.ma
index 6fab6dec640d242cc4733df1317062ac093c60a0..849579fa8491b90d6a9df5f410dc3956d74af0a7 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/unfold/lsstas_alt.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/unfold/lsstas_alt.ma
@@ -21,9 +21,9 @@ include "basic_2/unfold/lsstas_lift.ma".
 inductive lsstasa (h) (g): genv → relation4 lenv nat term term ≝
 | lsstasa_O   : ∀G,L,T. lsstasa h g G L 0 T T
 | lsstasa_sort: ∀G,L,l,k. lsstasa h g G L l (⋆k) (⋆((next h)^l k))
-| lsstasa_ldef: ∀G,L,K,V,W,U,i,l. ⇩[0, i] L ≡ K.ⓓV → lsstasa h g G K (l+1) V W →
+| lsstasa_ldef: ∀G,L,K,V,W,U,i,l. ⇩[i] L ≡ K.ⓓV → lsstasa h g G K (l+1) V W →
                 ⇧[0, i+1] W ≡ U → lsstasa h g G L (l+1) (#i) U
-| lsstasa_ldec: ∀G,L,K,W,V,U,i,l,l0. ⇩[0, i] L ≡ K.ⓛW → ⦃G, K⦄ ⊢ W ▪[h, g] l0 →
+| lsstasa_ldec: ∀G,L,K,W,V,U,i,l,l0. ⇩[i] L ≡ K.ⓛW → ⦃G, K⦄ ⊢ W ▪[h, g] l0 →
                 lsstasa h g G K l W V → ⇧[0, i+1] V ≡ U → lsstasa h g G L (l+1) (#i) U
 | lsstasa_bind: ∀a,I,G,L,V,T,U,l. lsstasa h g G (L.ⓑ{I}V) l T U →
                 lsstasa h g G L l (ⓑ{a,I}V.T) (ⓑ{a,I}V.U)
@@ -38,7 +38,7 @@ interpretation "nat-iterated stratified static type assignment (term) alternativ
 
 lemma ssta_lsstasa: ∀h,g,G,L,T,U. ⦃G, L⦄ ⊢ T •[h, g] U → ⦃G, L⦄ ⊢ T ••*[h, g, 1] U.
 #h #g #G #L #T #U #H elim H -G -L -T -U
-// /2 width=1/ /2 width=6/ /2 width=8/
+/2 width=8 by lsstasa_O, lsstasa_sort, lsstasa_ldef, lsstasa_ldec, lsstasa_bind, lsstasa_appl, lsstasa_cast/
 qed.
 
 lemma lsstasa_step_dx: ∀h,g,G,L,T1,T,l. ⦃G, L⦄ ⊢ T1 ••*[h, g, l] T →
@@ -48,29 +48,29 @@ lemma lsstasa_step_dx: ∀h,g,G,L,T1,T,l. ⦃G, L⦄ ⊢ T1 ••*[h, g, l] T 
 | #G #L #l #k #X #H >(ssta_inv_sort1 … H) -X >commutative_plus //
 | #G #L #K #V #W #U #i #l #HLK #_ #HWU #IHVW #U2 #HU2
   lapply (ldrop_fwd_drop2 … HLK) #H
-  elim (ssta_inv_lift1 … HU2 … H … HWU) -H -U /3 width=6/
+  elim (ssta_inv_lift1 … HU2 … H … HWU) -H -U /3 width=6 by lsstasa_ldef/
 | #G #L #K #W #V #U #i #l #l0 #HLK #HWl0 #_ #HVU #IHWV #U2 #HU2
   lapply (ldrop_fwd_drop2 … HLK) #H
-  elim (ssta_inv_lift1 … HU2 … H … HVU) -H -U /3 width=8/
+  elim (ssta_inv_lift1 … HU2 … H … HVU) -H -U /3 width=8 by lsstasa_ldec/
 | #a #I #G #L #V #T1 #U1 #l #_ #IHTU1 #X #H
-  elim (ssta_inv_bind1 … H) -H #U #HU1 #H destruct /3 width=1/
+  elim (ssta_inv_bind1 … H) -H #U #HU1 #H destruct /3 width=1 by lsstasa_bind/
 | #G #L #V #T1 #U1 #l #_ #IHTU1 #X #H
-  elim (ssta_inv_appl1 … H) -H #U #HU1 #H destruct /3 width=1/
-| /3 width=1/
+  elim (ssta_inv_appl1 … H) -H #U #HU1 #H destruct /3 width=1 by lsstasa_appl/
+| /3 width=1 by lsstasa_cast/
 ]
 qed.
 
 (* Main properties **********************************************************)
 
 theorem lsstas_lsstasa: ∀h,g,G,L,T,U,l. ⦃G, L⦄ ⊢ T •*[h, g, l] U → ⦃G, L⦄ ⊢ T ••*[h, g, l] U.
-#h #g #G #L #T #U #l #H @(lsstas_ind_dx … H) -U -l // /2 width=3/
+#h #g #G #L #T #U #l #H @(lsstas_ind_dx … H) -U -l /2 width=3 by lsstasa_step_dx, lsstasa_O/
 qed.
 
 (* Main inversion lemmas ****************************************************)
 
 theorem lsstasa_inv_lsstas: ∀h,g,G,L,T,U,l. ⦃G, L⦄ ⊢ T ••*[h, g, l] U → ⦃G, L⦄ ⊢ T •*[h, g, l] U.
 #h #g #G #L #T #U #l #H elim H -G -L -T -U -l
-// /2 width=1/ /2 width=6/ /3 width=8 by lsstas_ldec, lsstas_inv_SO/
+/2 width=8 by lsstas_inv_SO, lsstas_ldec, lsstas_ldef, lsstas_cast, lsstas_appl, lsstas_bind/
 qed-.
 
 (* Advanced eliminators *****************************************************)
@@ -79,11 +79,11 @@ lemma lsstas_ind_alt: ∀h,g. ∀R:genv→relation4 lenv nat term term.
                       (∀G,L,T. R G L O T T) →
                       (∀G,L,l,k. R G L l (⋆k) (⋆((next h)^l k))) → (
                          ∀G,L,K,V,W,U,i,l.
-                         ⇩[O, i] L ≡ K.ⓓV → ⦃G, K⦄ ⊢ V •*[h, g, l+1] W → ⇧[O, i+1] W ≡ U →
+                         ⇩[i] L ≡ K.ⓓV → ⦃G, K⦄ ⊢ V •*[h, g, l+1] W → ⇧[O, i+1] W ≡ U →
                          R G K (l+1) V W → R G L (l+1) (#i) U
                       ) → (
                          ∀G,L,K,W,V,U,i,l,l0.
-                         ⇩[O, i] L ≡ K.ⓛW → ⦃G, K⦄ ⊢ W ▪[h, g] l0 →
+                         ⇩[i] L ≡ K.ⓛW → ⦃G, K⦄ ⊢ W ▪[h, g] l0 →
                          ⦃G, K⦄ ⊢ W •*[h, g, l]V → ⇧[O, i+1] V ≡ U →
                          R G K l W V → R G L (l+1) (#i) U
                       ) → (

diff --git a/matita/matita/contribs/lambdadelta/basic_2/unfold/lsstas_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/unfold/lsstas_lift.ma
index 76c9c27f3e14c4cc27db6be48064aba5859ef7bc..2a7cc800ed971cb62c9125990e35466fe123d90a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/unfold/lsstas_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/unfold/lsstas_lift.ma
@@ -20,27 +20,28 @@ include "basic_2/unfold/lsstas.ma".
 (* Properties on relocation *************************************************)
 
 lemma lsstas_lift: ∀h,g,G,l. l_liftable (llstar … (ssta h g G) l).
-/2 width=1/ qed.
+/3 width=10 by l_liftable_llstar, ssta_lift/ qed.
 
 (* Inversion lemmas on relocation *******************************************)
 
 lemma lsstas_inv_lift1: ∀h,g,G,l. l_deliftable_sn (llstar … (ssta h g G) l).
-/3 width=5 by l_deliftable_sn_llstar, ssta_inv_lift1/ qed-.
+/3 width=6 by l_deliftable_sn_llstar, ssta_inv_lift1/ qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
 lemma lsstas_inv_lref1: ∀h,g,G,L,U,i,l. ⦃G, L⦄ ⊢ #i •*[h, g, l+1] U →
-                        (∃∃K,V,W. ⇩[0, i] L ≡ K.ⓓV & ⦃G, K⦄ ⊢ V •*[h, g, l+1] W &
+                        (∃∃K,V,W. ⇩[i] L ≡ K.ⓓV & ⦃G, K⦄ ⊢ V •*[h, g, l+1] W &
                                   ⇧[0, i + 1] W ≡ U
                         ) ∨
-                        (∃∃K,W,V,l0. ⇩[0, i] L ≡ K.ⓛW & ⦃G, K⦄ ⊢ W ▪[h, g] l0 &
+                        (∃∃K,W,V,l0. ⇩[i] L ≡ K.ⓛW & ⦃G, K⦄ ⊢ W ▪[h, g] l0 &
                                      ⦃G, K⦄ ⊢ W •*[h, g, l] V & ⇧[0, i + 1] V ≡ U
                         ).
 #h #g #G #L #U #i #l #H elim (lsstas_inv_step_sn … H) -H
 #X #H #HXU elim (ssta_inv_lref1 … H) -H
 * #K [ #V #W | #W #l0 ] #HLK [ #HVW | #HWl0 ] #HWX
 lapply (ldrop_fwd_drop2 … HLK) #H0LK
-elim (lsstas_inv_lift1 … HXU … H0LK … HWX) -H0LK -X /3 width=8/ /4 width=6/
+elim (lsstas_inv_lift1 … HXU … H0LK … HWX) -H0LK -X
+/4 width=8 by lsstas_step_sn, ex4_4_intro, ex3_3_intro, or_introl, or_intror/
 qed-.
 
 (* Advanced forward lemmas **************************************************)
@@ -48,35 +49,35 @@ qed-.
 lemma lsstas_fwd_correct: ∀h,g,G,L,T1,U1. ⦃G, L⦄ ⊢ T1 •[h, g] U1 →
                           ∀T2,l. ⦃G, L⦄ ⊢ T1 •*[h, g, l] T2 →
                           ∃U2. ⦃G, L⦄ ⊢ T2 •[h, g] U2.
-#h #g #G #L #T1 #U1 #HTU1 #T2 #l #H @(lsstas_ind_dx … H) -l -T2 [ /2 width=3/ ] -HTU1
+#h #g #G #L #T1 #U1 #HTU1 #T2 #l #H @(lsstas_ind_dx … H) -l -T2 [ /2 width=3 by ex_intro/ ] -HTU1
 #l #T #T2 #_ #HT2 #_ -T1 -U1 -l
-elim (ssta_fwd_correct … HT2) -T /2 width=2/
+elim (ssta_fwd_correct … HT2) -T /2 width=2 by ex_intro/
 qed-.
 
 (* Advanced properties ******************************************************)
 
 lemma lsstas_total: ∀h,g,G,L,T,U. ⦃G, L⦄ ⊢ T •[h, g] U →
                     ∀l. ∃U0. ⦃G, L⦄ ⊢ T •*[h, g, l] U0.
-#h #g #G #L #T #U #HTU #l @(nat_ind_plus … l) -l [ /2 width=2/ ]
+#h #g #G #L #T #U #HTU #l @(nat_ind_plus … l) -l [ /2 width=2 by lstar_O, ex_intro/ ]
 #l * #U0 #HTU0
-elim (lsstas_fwd_correct … HTU … HTU0) -U /3 width=4/
+elim (lsstas_fwd_correct … HTU … HTU0) -U /3 width=4 by lsstas_step_dx, ex_intro/
 qed-.
 
-lemma lsstas_ldef: ∀h,g,G,L,K,V,i. ⇩[0, i] L ≡ K.ⓓV →
+lemma lsstas_ldef: ∀h,g,G,L,K,V,i. ⇩[i] L ≡ K.ⓓV →
                    ∀W,l. ⦃G, K⦄ ⊢ V •*[h, g, l+1] W →
                    ∀U. ⇧[0, i+1] W ≡ U → ⦃G, L⦄ ⊢ #i •*[h, g, l+1] U.
 #h #g #G #L #K #V #i #HLK #W #l #HVW #U #HWU
 lapply (ldrop_fwd_drop2 … HLK)
 elim (lsstas_inv_step_sn … HVW) -HVW #W0
-elim (lift_total W0 0 (i+1)) /3 width=11/
+elim (lift_total W0 0 (i+1)) /3 width=12 by lsstas_step_sn, ssta_ldef, lsstas_lift/
 qed.
 
-lemma lsstas_ldec: ∀h,g,G,L,K,W,i. ⇩[0, i] L ≡ K.ⓛW → ∀l0. ⦃G, K⦄ ⊢ W ▪[h, g] l0 →
+lemma lsstas_ldec: ∀h,g,G,L,K,W,i. ⇩[i] L ≡ K.ⓛW → ∀l0. ⦃G, K⦄ ⊢ W ▪[h, g] l0 →
                    ∀V,l. ⦃G, K⦄ ⊢ W •*[h, g, l] V →
                    ∀U. ⇧[0, i+1] V ≡ U → ⦃G, L⦄ ⊢ #i •*[h, g, l+1] U.
 #h #g #G #L #K #W #i #HLK #T #HWT #V #l #HWV #U #HVU
 lapply (ldrop_fwd_drop2 … HLK) #H
-elim (lift_total W 0 (i+1)) /3 width=11/
+elim (lift_total W 0 (i+1)) /3 width=12 by lsstas_step_sn, ssta_ldec, lsstas_lift/
 qed.
 
 (* Properties on degree assignment for terms ********************************)

diff --git a/matita/matita/contribs/lambdadelta/basic_2/unfold/unfold.ma b/matita/matita/contribs/lambdadelta/basic_2/unfold/unfold.ma
index 160c6da76a5ad2ca417778a600f22f8e7e9fbaf0..4599cf0380515db8a085a1fb1ade5fef83e10d69 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/unfold/unfold.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/unfold/unfold.ma
@@ -22,8 +22,8 @@ include "basic_2/relocation/ldrop.ma".
 (* activate genv *)
 inductive unfold: relation4 genv lenv term lenv ≝
 | unfold_sort: ∀G,L,k. unfold G L (⋆k) L
-| unfold_lref: ∀I,G,L1,L2,K1,K2,V,i. ⇩[0, i] L1 ≡ K1. ⓑ{I}V →
-               unfold G K1 V K2 → ⇩[|L2|, i] L2 ≡ K2 →
+| unfold_lref: ∀I,G,L1,L2,K1,K2,V,i. ⇩[i] L1 ≡ K1. ⓑ{I}V →
+               unfold G K1 V K2 → ⇩[Ⓣ, |L2|, i] L2 ≡ K2 →
                unfold G L1 (#i) (L1@@L2)
 | unfold_bind: ∀a,I,G,L1,L2,V,T.
                unfold G (L1.ⓑ{I}V) T L2 → unfold G L1 (ⓑ{a,I}V.T) L2