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[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 ffc2d196545d87a8ac3047fc759cedf545877c64..4e7ded1c0bd27cb81bef713b7286b1424a94f4b9 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
@@ -34,22 +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, drop_drop, lift_lref_ge_minus/
+/4 width=3 by fqu_drop, drop_drop, lift_lref_ge_minus, yle_inj/
 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
+#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-.
 
@@ -72,7 +72,7 @@ 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 #e #HLK #_ #_ #H #_ -G -T -U >(drop_fwd_length … HLK) in H; -L
+#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-.
 
@@ -86,5 +86,5 @@ 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-.