- some renaming according to the written version of basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / substitution / fqu.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/fqu.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/fqu.ma
index 651ca43221e15080fc45c7e001791218213ba37f..fa388dacabf7e3bf895b5e873f9a3d0989a6087b 100644 (file)
--- 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.
-               â\87©[e+1] L â\89¡ K â\86\92 â\87§[0, e+1] T ≡ U → fqu G L U G K T
+| fqu_drop   : ∀G,L,K,T,U,m.
+               â¬\87[m+1] L â\89¡ K â\86\92 â¬\86[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 →
-                   â\87©[e] L â\89¡ K â\86\92 â\87§[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 →
+                   â¬\87[m] L â\89¡ K â\86\92 â¬\86[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-.
 
@@ -66,6 +66,20 @@ 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 …. (