- 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 21697819cc68237a5f7ec6ae05c85f8d7f607cd0..fa388dacabf7e3bf895b5e873f9a3d0989a6087b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/fqu.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/fqu.ma
@@ -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
@@ -34,9 +34,9 @@ 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)⦄.
@@ -47,9 +47,9 @@ qed.
 
 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
+#G #L #K #T #U #m #HLK #HTU
 lapply (drop_fwd_lw_lt … HLK ?) -HLK // #HKL
-lapply (lift_fwd_tw … HTU) -e #H
+lapply (lift_fwd_tw … HTU) -m #H
 normalize in ⊢ (?%%); /2 width=1 by lt_minus_to_plus/
 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 …. (