partial commit: just the components before "static" ...

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/fsupp.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/fsupp.ma
index fb75c7338fcb9afd7b6117160b46233bffc7ae84..e51e5cd5ab05a56add39cf617546f59384ffee53 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/fsupp.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/fsupp.ma
@@ -12,85 +12,83 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "basic_2/notation/relations/suptermplus_6.ma".
 include "basic_2/relocation/fsup.ma".
 
 (* PLUS-ITERATED SUPCLOSURE *************************************************)
 
-definition fsupp: bi_relation lenv term ≝ bi_TC … fsup.
+definition fsupp: tri_relation genv lenv term ≝ tri_TC … fsup.
 
 interpretation "plus-iterated structural successor (closure)"
-   'SupTermPlus L1 T1 L2 T2 = (fsupp L1 T1 L2 T2).
+   'SupTermPlus G1 L1 T1 G2 L2 T2 = (fsupp G1 L1 T1 G2 L2 T2).
 
 (* Basic properties *********************************************************)
 
-lemma fsup_fsupp: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ → ⦃L1, T1⦄ ⊃+ ⦃L2, T2⦄.
+lemma fsup_fsupp: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄.
 /2 width=1/ qed.
 
-lemma fsupp_strap1: ∀L1,L,L2,T1,T,T2. ⦃L1, T1⦄ ⊃+ ⦃L, T⦄ → ⦃L, T⦄ ⊃ ⦃L2, T2⦄ →
-                    ⦃L1, T1⦄ ⊃+ ⦃L2, T2⦄.
-/2 width=4/ qed.
+lemma fsupp_strap1: ∀G1,G,G2,L1,L,L2,T1,T,T2.
+                    ⦃G1, L1, T1⦄ ⊃+ ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊃ ⦃G2, L2, T2⦄ →
+                    ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄.
+/2 width=5/ qed.
 
-lemma fsupp_strap2: ∀L1,L,L2,T1,T,T2. ⦃L1, T1⦄ ⊃ ⦃L, T⦄ → ⦃L, T⦄ ⊃+ ⦃L2, T2⦄ →
-                    ⦃L1, T1⦄ ⊃+ ⦃L2, T2⦄.
-/2 width=4/ qed.
+lemma fsupp_strap2: ∀G1,G,G2,L1,L,L2,T1,T,T2.
+                    ⦃G1, L1, T1⦄ ⊃ ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊃+ ⦃G2, L2, T2⦄ →
+                    ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄.
+/2 width=5/ qed.
 
-lemma fsupp_lref: ∀I,K,V,i,L. ⇩[0, i] L ≡ K.ⓑ{I}V → ⦃L, #i⦄ ⊃+ ⦃K, V⦄.
+lemma fsupp_lref: ∀I,G,L,K,V,i. ⇩[0, i] L ≡ K.ⓑ{I}V → ⦃G, L, #i⦄ ⊃+ ⦃G, K, V⦄.
 /3 width=2/ qed.
 
-lemma fsupp_pair_sn: ∀I,L,V,T. ⦃L, ②{I}V.T⦄ ⊃+ ⦃L, V⦄.
+lemma fsupp_pair_sn: ∀I,G,L,V,T. ⦃G, L, ②{I}V.T⦄ ⊃+ ⦃G, L, V⦄.
 /2 width=1/ qed.
 
-lemma fsupp_bind_dx: ∀a,K,I,V,T. ⦃K, ⓑ{a,I}V.T⦄ ⊃+ ⦃K.ⓑ{I}V, T⦄.
+lemma fsupp_bind_dx: ∀a,I,G,L,V,T. ⦃G, L, ⓑ{a,I}V.T⦄ ⊃+ ⦃G, L.ⓑ{I}V, T⦄.
 /2 width=1/ qed.
 
-lemma fsupp_flat_dx: ∀I,L,V,T. ⦃L, ⓕ{I}V.T⦄ ⊃+ ⦃L, T⦄.
+lemma fsupp_flat_dx: ∀I,G,L,V,T. ⦃G, L, ⓕ{I}V.T⦄ ⊃+ ⦃G, L, T⦄.
 /2 width=1/ qed.
 
-lemma fsupp_flat_dx_pair_sn: ∀I1,I2,L,V1,V2,T. ⦃L, ⓕ{I1}V1.②{I2}V2.T⦄ ⊃+ ⦃L, V2⦄.
-/2 width=4/ qed.
-
-lemma fsupp_bind_dx_flat_dx: ∀a,I1,I2,L,V1,V2,T. ⦃L, ⓑ{a,I1}V1.ⓕ{I2}V2.T⦄ ⊃+ ⦃L.ⓑ{I1}V1, T⦄.
-/2 width=4/ qed.
-
-lemma fsupp_flat_dx_bind_dx: ∀a,I1,I2,L,V1,V2,T. ⦃L, ⓕ{I1}V1.ⓑ{a,I2}V2.T⦄ ⊃+ ⦃L.ⓑ{I2}V2, T⦄.
-/2 width=4/ qed.
-(*
-lemma fsupp_append_sn: ∀I,L,K,V,T. ⦃L.ⓑ{I}V@@K, T⦄ ⊃+ ⦃L, V⦄.
-#I #L #K #V *
-[ * #i
-normalize /3 width=1 by monotonic_lt_plus_l, monotonic_le_plus_r/ (**) (* auto too slow without trace *)
-qed.
-*)
+lemma fsupp_flat_dx_pair_sn: ∀I1,I2,G,L,V1,V2,T. ⦃G, L, ⓕ{I1}V1.②{I2}V2.T⦄ ⊃+ ⦃G, L, V2⦄.
+/2 width=5/ qed.
+
+lemma fsupp_bind_dx_flat_dx: ∀a,G,I1,I2,L,V1,V2,T. ⦃G, L, ⓑ{a,I1}V1.ⓕ{I2}V2.T⦄ ⊃+ ⦃G, L.ⓑ{I1}V1, T⦄.
+/2 width=5/ qed.
+
+lemma fsupp_flat_dx_bind_dx: ∀a,I1,I2,G,L,V1,V2,T. ⦃G, L, ⓕ{I1}V1.ⓑ{a,I2}V2.T⦄ ⊃+ ⦃G, L.ⓑ{I2}V2, T⦄.
+/2 width=5/ qed.
+
 (* Basic eliminators ********************************************************)
 
-lemma fsupp_ind: ∀L1,T1. ∀R:relation2 lenv term.
-                 (∀L2,T2. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ → R L2 T2) →
-                 (∀L,T,L2,T2. ⦃L1, T1⦄ ⊃+ ⦃L, T⦄ → ⦃L, T⦄ ⊃ ⦃L2, T2⦄ → R L T → R L2 T2) →
-                 ∀L2,T2. ⦃L1, T1⦄ ⊃+ ⦃L2, T2⦄ → R L2 T2.
-#L1 #T1 #R #IH1 #IH2 #L2 #T2 #H
-@(bi_TC_ind … IH1 IH2 ? ? H)
+lemma fsupp_ind: ∀G1,L1,T1. ∀R:relation3 ….
+                 (∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ → R G2 L2 T2) →
+                 (∀G,G2,L,L2,T,T2. ⦃G1, L1, T1⦄ ⊃+ ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊃ ⦃G2, L2, T2⦄ → R G L T → R G2 L2 T2) →
+                 ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄ → R G2 L2 T2.
+#G1 #L1 #T1 #R #IH1 #IH2 #G2 #L2 #T2 #H
+@(tri_TC_ind … IH1 IH2 G2 L2 T2 H)
 qed-.
 
-lemma fsupp_ind_dx: ∀L2,T2. ∀R:relation2 lenv term.
-                    (∀L1,T1. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ → R L1 T1) →
-                    (∀L1,L,T1,T. ⦃L1, T1⦄ ⊃ ⦃L, T⦄ → ⦃L, T⦄ ⊃+ ⦃L2, T2⦄ → R L T → R L1 T1) →
-                    ∀L1,T1. ⦃L1, T1⦄ ⊃+ ⦃L2, T2⦄ → R L1 T1.
-#L2 #T2 #R #IH1 #IH2 #L1 #T1 #H
-@(bi_TC_ind_dx … IH1 IH2 ? ? H)
+lemma fsupp_ind_dx: ∀G2,L2,T2. ∀R:relation3 ….
+                    (∀G1,L1,T1. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ → R G1 L1 T1) →
+                    (∀G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ⊃ ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊃+ ⦃G2, L2, T2⦄ → R G L T → R G1 L1 T1) →
+                    ∀G1,L1,T1. ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄ → R G1 L1 T1.
+#G2 #L2 #T2 #R #IH1 #IH2 #G1 #L1 #T1 #H
+@(tri_TC_ind_dx … IH1 IH2 G1 L1 T1 H)
 qed-.
 
 (* Basic forward lemmas *****************************************************)
 
-lemma fsupp_fwd_fw: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊃+ ⦃L2, T2⦄ → ♯{L2, T2} < ♯{L1, T1}.
-#L1 #L2 #T1 #T2 #H @(fsupp_ind … H) -L2 -T2
+lemma fsupp_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 @(fsupp_ind … H) -G2 -L2 -T2
 /3 width=3 by fsup_fwd_fw, transitive_lt/
 qed-.
 
 (* Advanced eliminators *****************************************************)
 
-lemma fsupp_wf_ind: ∀R:relation2 lenv term. (
-                       ∀L1,T1. (∀L2,T2. ⦃L1, T1⦄ ⊃+ ⦃L2, T2⦄ → R L2 T2) →
-                       ∀L2,T2. L1 = L2 → T1 = T2 → R L2 T2
-                    ) → ∀L1,T1. R L1 T1.
-#R #HR @(f2_ind … fw) #n #IHn #L1 #T1 #H destruct /4 width=5 by fsupp_fwd_fw/
+lemma fsupp_wf_ind: ∀R:relation3 …. (
+                       ∀G1,L1,T1. (∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄ → R G2 L2 T2) →
+                       ∀G2,L2,T2. G1 = G2 → L1 = L2 → T1 = T2 → R G2 L2 T2
+                    ) → ∀G1,L1,T1. R G1 L1 T1.
+#R #HR @(f3_ind … fw) #n #IHn #G1 #L1 #T1 #H destruct /4 width=7 by fsupp_fwd_fw/
 qed-.