X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fsubstitution%2Ffqu.ma;h=47bd0eabe6f09d811e4b97f3e2b534d49119ea16;hb=e258362c37ec6d9132ec57bd5e4987d148c10799;hp=651ca43221e15080fc45c7e001791218213ba37f;hpb=598a5c56535a8339f6533227ab580aff64e2d41c;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/fqu.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/fqu.ma
index 651ca4322..47bd0eabe 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/fqu.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/fqu.ma
@@ -14,7 +14,7 @@
 
 include "basic_2/notation/relations/supterm_6.ma".
 include "basic_2/grammar/cl_weight.ma".
-include "basic_2/substitution/ldrop.ma".
+include "basic_2/substitution/drop.ma".
 
 (* SUPCLOSURE ***************************************************************)
 
@@ -24,8 +24,8 @@ inductive fqu: tri_relation genv lenv term ≝
 | fqu_pair_sn: ∀I,G,L,V,T. fqu G L (②{I}V.T) G L V
 | fqu_bind_dx: ∀a,I,G,L,V,T. fqu G L (ⓑ{a,I}V.T) G (L.ⓑ{I}V) T
 | fqu_flat_dx: ∀I,G,L,V,T. fqu G L (ⓕ{I}V.T) G L T
-| fqu_drop   : ∀G,L,K,T,U,e.
-               ⇩[e+1] L ≡ K → ⇧[0, e+1] T ≡ U → fqu G L U G K T
+| fqu_drop   : ∀G,L,K,T,U,m.
+               ⬇[m+1] L ≡ K → ⬆[0, m+1] T ≡ U → fqu G L U G K T
 .
 
 interpretation
@@ -34,22 +34,22 @@ interpretation
 
 (* Basic properties *********************************************************)
 
-lemma fqu_drop_lt: ∀G,L,K,T,U,e. 0 < e →
-                   ⇩[e] L ≡ K → ⇧[0, e] T ≡ U → ⦃G, L, U⦄ ⊐ ⦃G, K, T⦄.
-#G #L #K #T #U #e #He >(plus_minus_m_m e 1) /2 width=3 by fqu_drop/
+lemma fqu_drop_lt: ∀G,L,K,T,U,m. 0 < m →
+                   ⬇[m] L ≡ K → ⬆[0, m] T ≡ U → ⦃G, L, U⦄ ⊐ ⦃G, K, T⦄.
+#G #L #K #T #U #m #Hm >(plus_minus_m_m m 1) /2 width=3 by fqu_drop/
 qed.
 
 lemma fqu_lref_S_lt: ∀I,G,L,V,i. 0 < i → ⦃G, L.ⓑ{I}V, #i⦄ ⊐ ⦃G, L, #(i-1)⦄.
-/3 width=3 by fqu_drop, ldrop_drop, lift_lref_ge_minus/
+/3 width=3 by fqu_drop, drop_drop, lift_lref_ge_minus/
 qed.
 
 (* Basic forward lemmas *****************************************************)
 
 lemma fqu_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 #e #HLK #HTU
-lapply (ldrop_fwd_lw_lt … HLK ?) -HLK // #HKL
-lapply (lift_fwd_tw … HTU) -e #H
+#G #L #K #T #U #m #HLK #HTU
+lapply (drop_fwd_lw_lt … HLK ?) -HLK // #HKL
+lapply (lift_fwd_tw … HTU) -m #H
 normalize in ⊢ (?%%); /2 width=1 by lt_minus_to_plus/
 qed-.
 
@@ -58,7 +58,7 @@ fact fqu_fwd_length_lref1_aux: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2,
 #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
 [1: normalize //
 |3: #a
-|5: /2 width=4 by ldrop_fwd_length_lt4/
+|5: /2 width=4 by drop_fwd_length_lt4/
 ] #I #G #L #V #T #j #H destruct
 qed-.
 
@@ -66,11 +66,25 @@ lemma fqu_fwd_length_lref1: ∀G1,G2,L1,L2,T2,i. ⦃G1, L1, #i⦄ ⊐ ⦃G2, L2,
 /2 width=7 by fqu_fwd_length_lref1_aux/
 qed-.
 
+(* Basic inversion lemmas ***************************************************)
+
+fact fqu_inv_eq_aux: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
+                     G1 = G2 → |L1| = |L2| → T1 = T2 → ⊥.
+#G1 #G2 #L1 #L2 #T1 #T2 * -G1 -G2 -L1 -L2 -T1 -T2 normalize
+/2 width=4 by discr_tpair_xy_y, discr_tpair_xy_x, plus_xSy_x_false/
+#G #L #K #T #U #m #HLK #_ #_ #H #_ -G -T -U >(drop_fwd_length … HLK) in H; -L
+/2 width=4 by plus_xySz_x_false/
+qed-.
+
+lemma fqu_inv_eq: ∀G,L1,L2,T. ⦃G, L1, T⦄ ⊐ ⦃G, L2, T⦄ → |L1| = |L2| → ⊥.
+#G #L1 #L2 #T #H #H0 @(fqu_inv_eq_aux … H … H0) // (**) (* full auto fails *)
+qed-. 
+
 (* Advanced eliminators *****************************************************)
 
 lemma fqu_wf_ind: ∀R:relation3 …. (
                      ∀G1,L1,T1. (∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → R G2 L2 T2) →
 		                R G1 L1 T1
 		  ) → ∀G1,L1,T1. R G1 L1 T1.
-#R #HR @(f3_ind … fw) #n #IHn #G1 #L1 #T1 #H destruct /4 width=1 by fqu_fwd_fw/
+#R #HR @(f3_ind … fw) #x #IHx #G1 #L1 #T1 #H destruct /4 width=1 by fqu_fwd_fw/
 qed-.