bug fix in supclosure allows alternative definition of fpbs !

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / relocation / fsup.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/fsup.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/fsup.ma
index 80ec9b0b52ad9084a6e91a47a94529041b937269..9719b4992a16a9ea58b070bb6093f5be01a981a6 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/fsup.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/fsup.ma
@@ -20,15 +20,12 @@ include "basic_2/relocation/ldrop.ma".
 
 (* activate genv *)
 inductive fsup: tri_relation genv lenv term ≝
-| fsup_lref_O  : ∀I,G,L,V. fsup G (L.ⓑ{I}V) (#0) G L V
-| fsup_pair_sn : ∀I,G,L,V,T. fsup G L (②{I}V.T) G L V
-| fsup_bind_dx : ∀a,I,G,L,V,T. fsup G L (ⓑ{a,I}V.T) G (L.ⓑ{I}V) T
-| fsup_flat_dx : ∀I,G,L,V,T. fsup G L (ⓕ{I}V.T) G L T
-| fsup_ldrop_lt: ∀G,L,K,T,U,d,e.
-                 ⇩[d, e] L ≡ K → ⇧[d, e] T ≡ U → 0 < e → fsup G L U G K T
-| fsup_ldrop   : ∀G1,G2,L1,K1,K2,T1,T2,U1,d,e.
-                 ⇩[d, e] L1 ≡ K1 → ⇧[d, e] T1 ≡ U1 →
-                 fsup G1 K1 T1 G2 K2 T2 → fsup G1 L1 U1 G2 K2 T2
+| fsup_lref_O : ∀I,G,L,V. fsup G (L.ⓑ{I}V) (#0) G L V
+| fsup_pair_sn: ∀I,G,L,V,T. fsup G L (②{I}V.T) G L V
+| fsup_bind_dx: ∀a,I,G,L,V,T. fsup G L (ⓑ{a,I}V.T) G (L.ⓑ{I}V) T
+| fsup_flat_dx: ∀I,G,L,V,T. fsup G L (ⓕ{I}V.T) G L T
+| fsup_drop   : ∀G,L,K,T,U,e.
+                ⇩[0, e+1] L ≡ K → ⇧[0, e+1] T ≡ U → fsup G L U G K T
 .
 
 interpretation
@@ -37,32 +34,23 @@ interpretation
 
 (* Basic properties *********************************************************)
 
-lemma fsup_lref_S_lt: ∀I,G1,G2,L,K,V,T,i. 0 < i → ⦃G1, L, #(i-1)⦄ ⊃ ⦃G2, K, T⦄ → ⦃G1, L.ⓑ{I}V, #i⦄ ⊃ ⦃G2, K, T⦄.
-#I #G1 #G2 #L #K #V #T #i #Hi #H /3 width=7 by fsup_ldrop, ldrop_ldrop, lift_lref_ge_minus/ (**) (* auto too slow without trace *)
+lemma fsup_drop_lt: ∀G,L,K,T,U,e. 0 < e →
+                    ⇩[0, e] L ≡ K → ⇧[0, e] T ≡ U → fsup G L U G K T.
+#G #L #K #T #U #e #He >(plus_minus_m_m e 1) /2 width=3 by fsup_drop/
 qed.
 
-lemma fsup_lref: ∀I,G,K,V,i,L. ⇩[0, i] L ≡ K.ⓑ{I}V → ⦃G, L, #i⦄ ⊃ ⦃G, K, V⦄.
-#I #G #K #V #i @(nat_elim1 i) -i #i #IH #L #H
-elim (ldrop_inv_O1_pair2 … H) -H *
-[ #H1 #H2 destruct //
-| #I1 #K1 #V1 #HK1 #H #Hi destruct
-  lapply (IH … HK1) /2 width=1/
-]
+lemma fsup_lref_S_lt: ∀I,G,L,V,i. 0 < i → ⦃G, L.ⓑ{I}V, #i⦄ ⊃ ⦃G, L, #(i-1)⦄.
+/3 width=3 by fsup_drop, ldrop_ldrop, lift_lref_ge_minus/
 qed.
 
 (* Basic forward lemmas *****************************************************)
 
 lemma fsup_fwd_fw: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ → ♯{G2, L2, T2} < ♯{G1, L1, T1}.
 #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 //
-[ #G #L #K #T #U #d #e #HLK #HTU #HKL
-  lapply (ldrop_fwd_lw_lt … HLK HKL) -HKL -HLK #HKL
-  lapply (lift_fwd_tw … HTU) -d -e #H
-  normalize in ⊢ (?%%); /2 width=1/
-| #G1 #G2 #L1 #K1 #K2 #T1 #T2 #U1 #d #e #HLK1 #HTU1 #_ #IHT12
-  lapply (ldrop_fwd_lw … HLK1) -HLK1 #HLK1
-  lapply (lift_fwd_tw … HTU1) -HTU1 #HTU1
-  @(lt_to_le_to_lt … IHT12) -IHT12 /2 width=1/
-]
+#G #L #K #T #U #e #HLK #HTU
+lapply (ldrop_fwd_lw_lt … HLK ?) -HLK // #HKL
+lapply (lift_fwd_tw … HTU) -e #H
+normalize in ⊢ (?%%); /2 width=1 by lt_minus_to_plus/
 qed-.
 
 fact fsup_fwd_length_lref1_aux: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ →
@@ -71,10 +59,6 @@ fact fsup_fwd_length_lref1_aux: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2
 [1: normalize //
 |3: #a
 |5: /2 width=4 by ldrop_fwd_length_lt4/
-|6: #G1 #G2 #L1 #K1 #K2 #T1 #T2 #U1 #d #e #HLK1 #HTU1 #_ #IHT12 #i #H destruct
-    lapply (ldrop_fwd_length_le4 … HLK1) -HLK1 #HLK1
-    elim (lift_inv_lref2 … HTU1) -HTU1 * #Hdei #H destruct
-    @(lt_to_le_to_lt … HLK1) /2 width=2/
 ] #I #G #L #V #T #j #H destruct
 qed-.