- ynat: some additions

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/cpy.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/cpy.ma
index 80688b96309012bbb0e888c7c2041ad70f688ca1..05b77349e21a65356138862f6dc7620a1f4d20fa 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/cpy.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/cpy.ma
@@ -103,6 +103,37 @@ lapply (cpy_weak … HT12 0 (d + e) ? ?) -HT12
 /2 width=2 by cpy_weak_top/
 qed-.
 
+lemma cpy_up: ∀G,L,U1,U2,dt,et. ⦃G, L⦄ ⊢ U1 ▶×[dt, et] U2 →
+              ∀T1,d,e. ⇧[d, e] T1 ≡ U1 →
+              d ≤ dt → d + e ≤ dt + et →
+              ∃∃T2. ⦃G, L⦄ ⊢ U1 ▶×[d+e, dt+et-(d+e)] U2 & ⇧[d, e] T2 ≡ U2.
+#G #L #U1 #U2 #dt #et #H elim H -G -L -U1 -U2 -dt -et
+[ * #i #G #L #dt #et #T1 #d #e #H #_
+  [ lapply (lift_inv_sort2 … H) -H #H destruct /2 width=3 by ex2_intro/
+  | elim (lift_inv_lref2 … H) -H * #Hid #H destruct /3 width=3 by lift_lref_ge_minus, lift_lref_lt, ex2_intro/
+  | lapply (lift_inv_gref2 … H) -H #H destruct /2 width=3 by ex2_intro/
+  ]
+| #I #G #L #K #V #W #i #dt #et #Hdti #Hidet #HLK #HVW #T1 #d #e #H #Hddt #Hdedet
+  elim (lift_inv_lref2 … H) -H * #Hid #H destruct [ -V -Hidet -Hdedet | -Hdti -Hddt ]
+  [ elim (ylt_yle_false … Hddt) -Hddt /3 width=3 by yle_ylt_trans, ylt_inj/
+  | elim (le_inv_plus_l … Hid) #Hdie #Hei
+    elim (lift_split … HVW d (i-e+1) ? ? ?) [2,3,4: /2 width=1 by le_S_S, le_S/ ] -Hdie
+    #T2 #_ >plus_minus // <minus_minus /2 width=1 by le_S/ <minus_n_n <plus_n_O #H -Hei
+    @(ex2_intro … H) -H @(cpy_subst … HLK HVW) /2 width=1 by yle_inj/ >ymax_pre_sn_comm // (**) (* explicit constructor *)
+  ]
+| #a #I #G #L #W1 #W2 #U1 #U2 #dt #et #_ #_ #IHW12 #IHU12 #X #d #e #H #Hddt #Hdedet
+  elim (lift_inv_bind2 … H) -H #V1 #T1 #HVW1 #HTU1 #H destruct
+  elim (IHW12 … HVW1) -V1 -IHW12 //
+  elim (IHU12 … HTU1) -T1 -IHU12 /2 width=1 by yle_succ/
+  <yplus_inj >yplus_SO2 >yplus_succ1 >yplus_succ1
+  /3 width=2 by cpy_bind, lift_bind, ex2_intro/
+| #I #G #L #W1 #W2 #U1 #U2 #dt #et #_ #_ #IHW12 #IHU12 #X #d #e #H #Hddt #Hdedet
+  elim (lift_inv_flat2 … H) -H #V1 #T1 #HVW1 #HTU1 #H destruct
+  elim (IHW12 … HVW1) -V1 -IHW12 // elim (IHU12 … HTU1) -T1 -IHU12
+  /3 width=2 by cpy_flat, lift_flat, ex2_intro/
+]
+qed-.
+
 lemma cpy_split_up: ∀G,L,T1,T2,d,e. ⦃G, L⦄ ⊢ T1 ▶×[d, e] T2 → ∀i. i ≤ d + e →
                     ∃∃T. ⦃G, L⦄ ⊢ T1 ▶×[d, i-d] T & ⦃G, L⦄ ⊢ T ▶×[i, d+e-i] T2.
 #G #L #T1 #T2 #d #e #H elim H -G -L -T1 -T2 -d -e
@@ -248,6 +279,12 @@ qed-.
 lemma cpy_inv_refl_O2: ∀G,L,T1,T2,d. ⦃G, L⦄ ⊢ T1 ▶×[d, 0] T2 → T1 = T2.
 /2 width=6 by cpy_inv_refl_O2_aux/ qed-.
 
+lemma cpy_inv_lift1_eq: ∀G,T1,U1,d,e. ⇧[d, e] T1 ≡ U1 →
+                        ∀L,U2. ⦃G, L⦄ ⊢ U1 ▶×[d, e] U2 → U1 = U2.
+#G #T1 #U1 #d #e #HTU1 #L #U2 #HU12 elim (cpy_up … HU12 … HTU1) -HU12 -HTU1
+/2 width=4 by cpy_inv_refl_O2/
+qed-.
+
 (* Basic forward lemmas *****************************************************)
 
 lemma cpy_fwd_tw: ∀G,L,T1,T2,d,e. ⦃G, L⦄ ⊢ T1 ▶×[d, e] T2 → ♯{T1} ≤ ♯{T2}.