eliminators of arited terms based on "big tree" proper computation

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / fsb_aaa.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/fsb_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/fsb_aaa.ma
index 49b11f97188e2643bb50af4b02b58a7556501c16..1074ef74d3dad0a0254d3dd7391afcc60b91d9d8 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/fsb_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/fsb_aaa.ma
@@ -12,6 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "basic_2/computation/fpbs_aaa.ma".
 include "basic_2/computation/csx_aaa.ma".
 include "basic_2/computation/fsb_csx.ma".
 
@@ -28,14 +29,43 @@ theorem aaa_fsba: ∀h,g,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ⦃G, L⦄ ⊢ ⦥
 /3 width=2 by fsb_fsba, aaa_fsb/ qed.
 
 (* Advanced eliminators on atomica arity assignment for terms ***************)
-(*
-fact aaa_ind_fpbu: ∀h,g. ∀R:relation3 genv lenv term.
-                   (∀G1,L1,T1,A. ⦃G1, L1⦄ ⊢ T1 ⁝ A →
-                                 (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
-                                 R G1 L1 T1
-                    ) →
-                    ∀G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → ∀A. ⦃G, L⦄ ⊢ T ⁝ A → R G L T.
+
+fact aaa_ind_fpbu_aux: ∀h,g. ∀R:relation3 genv lenv term.
+                       (∀G1,L1,T1,A. ⦃G1, L1⦄ ⊢ T1 ⁝ A →
+                                     (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
+                                     R G1 L1 T1
+                       ) →
+                       ∀G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → ∀A. ⦃G, L⦄ ⊢ T ⁝ A → R G L T.
 #h #g #R #IH #G #L #T #H @(csx_ind_fpbu … H) -G -L -T
 #G1 #L1 #T1 #H1 #IH1 #A1 #HTA1 @IH -IH //
-#G2 #L2 #T2 #H12 @IH1 //
-*)
+#G2 #L2 #T2 #H12 elim (aaa_fpbs_conf h g … G2 … L2 … T2 … HTA1) -A1
+/2 width=2 by fpbu_fwd_fpbs/
+qed-.
+
+lemma aaa_ind_fpbu: ∀h,g. ∀R:relation3 genv lenv term.
+                    (∀G1,L1,T1,A. ⦃G1, L1⦄ ⊢ T1 ⁝ A →
+                                  (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
+                                  R G1 L1 T1
+                    ) →
+                    ∀G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → R G L T.
+/4 width=4 by aaa_ind_fpbu_aux, aaa_csx/ qed-.
+
+fact aaa_ind_fpbg_aux: ∀h,g. ∀R:relation3 genv lenv term.
+                       (∀G1,L1,T1,A. ⦃G1, L1⦄ ⊢ T1 ⁝ A →
+                                     (∀G2,L2,T2. ⦃G1, L1, T1⦄ >⋕[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
+                                     R G1 L1 T1
+                       ) →
+                       ∀G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → ∀A. ⦃G, L⦄ ⊢ T ⁝ A → R G L T.
+#h #g #R #IH #G #L #T #H @(csx_ind_fpbg … H) -G -L -T
+#G1 #L1 #T1 #H1 #IH1 #A1 #HTA1 @IH -IH //
+#G2 #L2 #T2 #H12 elim (aaa_fpbs_conf h g … G2 … L2 … T2 … HTA1) -A1
+/2 width=2 by fpbg_fwd_fpbs/
+qed-.
+
+lemma aaa_ind_fpbg: ∀h,g. ∀R:relation3 genv lenv term.
+                    (∀G1,L1,T1,A. ⦃G1, L1⦄ ⊢ T1 ⁝ A →
+                                  (∀G2,L2,T2. ⦃G1, L1, T1⦄ >⋕[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
+                                  R G1 L1 T1
+                    ) →
+                    ∀G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → R G L T.
+/4 width=4 by aaa_ind_fpbg_aux, aaa_csx/ qed-.