- site update

[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / grammar / thom.ma

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/grammar/thom.ma b/matita/matita/contribs/lambda_delta/Basic_2/grammar/thom.ma
index 23aa62e03b83a77c5c05629363a538ab685ff995..5b90bd1d37bcbdb1a803253d520222a0046944e6 100644 (file)
--- a/matita/matita/contribs/lambda_delta/Basic_2/grammar/thom.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/grammar/thom.ma
@@ -12,15 +12,15 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "Basic-2/grammar/term_simple.ma".
+include "Basic_2/grammar/term_simple.ma".
 
 (* HOMOMORPHIC TERMS ********************************************************)
 
 inductive thom: relation term ≝
-   | thom_atom: ∀I. thom (𝕒{I}) (𝕒{I})
-   | thom_abst: ∀V1,V2,T1,T2. thom (𝕔{Abst} V1. T1) (𝕔{Abst} V2. T2)
-   | thom_appl: â\88\80V1,V2,T1,T2. thom T1 T2 â\86\92 ð\9d\95\8a[T1] â\86\92 ð\9d\95\8a[T2] →
-                thom (𝕔{Appl} V1. T1) (𝕔{Appl} V2. T2)
+   | thom_atom: ∀I. thom (⓪{I}) (⓪{I})
+   | thom_abst: ∀V1,V2,T1,T2. thom (ⓛV1. T1) (ⓛV2. T2)
+   | thom_appl: â\88\80V1,V2,T1,T2. thom T1 T2 â\86\92 ð\9d\90\92[T1] â\86\92 ð\9d\90\92[T2] →
+                thom (ⓐV1. T1) (ⓐV2. T2)
 .
 
 interpretation "homomorphic (term)" 'napart T1 T2 = (thom T1 T2).
@@ -28,29 +28,51 @@ interpretation "homomorphic (term)" 'napart T1 T2 = (thom T1 T2).
 (* Basic properties *********************************************************)
 
 lemma thom_sym: ∀T1,T2. T1 ≈ T2 → T2 ≈ T1.
-#T1 #T2 #H elim H -H T1 T2 /2/
+#T1 #T2 #H elim H -T1 -T2 /2 width=1/
 qed.
 
 lemma thom_refl2: ∀T1,T2. T1 ≈ T2 → T2 ≈ T2.
-#T1 #T2 #H elim H -H T1 T2 /2/
+#T1 #T2 #H elim H -T1 -T2 // /2 width=1/
 qed.
 
 lemma thom_refl1: ∀T1,T2. T1 ≈ T2 → T1 ≈ T1.
-/3/ qed.
+/3 width=2/ qed.
 
-lemma simple_thom_repl_dx: â\88\80T1,T2. T1 â\89\88 T2 â\86\92 ð\9d\95\8a[T1] â\86\92 ð\9d\95\8a[T2].
-#T1 #T2 #H elim H -H T1 T2 //
+lemma simple_thom_repl_dx: â\88\80T1,T2. T1 â\89\88 T2 â\86\92 ð\9d\90\92[T1] â\86\92 ð\9d\90\92[T2].
+#T1 #T2 #H elim H -T1 -T2 //
 #V1 #V2 #T1 #T2 #H
 elim (simple_inv_bind … H)
-qed.
+qed. (**) (* remove from index *)
 
-lemma simple_thom_repl_sn: â\88\80T1,T2. T1 â\89\88 T2 â\86\92 ð\9d\95\8a[T2] â\86\92 ð\9d\95\8a[T1].
-/3/ qed.
+lemma simple_thom_repl_sn: â\88\80T1,T2. T1 â\89\88 T2 â\86\92 ð\9d\90\92[T2] â\86\92 ð\9d\90\92[T1].
+/3 width=3/ qed-.
 
 (* Basic inversion lemmas ***************************************************)
 
+fact thom_inv_bind1_aux: ∀T1,T2. T1 ≈ T2 → ∀I,W1,U1. T1 = ⓑ{I}W1.U1 →
+                         ∃∃W2,U2. I = Abst & T2 = ⓛW2. U2.
+#T1 #T2 * -T1 -T2
+[ #J #I #W1 #U1 #H destruct
+| #V1 #V2 #T1 #T2 #I #W1 #U1 #H destruct /2 width=3/
+| #V1 #V2 #T1 #T2 #H_ #_ #_ #I #W1 #U1 #H destruct
+]
+qed.
+
+lemma thom_inv_bind1: ∀I,W1,U1,T2. ⓑ{I}W1.U1 ≈ T2 →
+                      ∃∃W2,U2. I = Abst & T2 = ⓛW2. U2.
+/2 width=5/ qed-.
+
+fact thom_inv_flat1_aux: ∀T1,T2. T1 ≈ T2 → ∀I,W1,U1. T1 = ⓕ{I}W1.U1 →
+                         ∃∃W2,U2. U1 ≈ U2 & 𝐒[U1] & 𝐒[U2] &
+                                  I = Appl & T2 = ⓐW2. U2.
+#T1 #T2 * -T1 -T2
+[ #J #I #W1 #U1 #H destruct
+| #V1 #V2 #T1 #T2 #I #W1 #U1 #H destruct
+| #V1 #V2 #T1 #T2 #HT12 #HT1 #HT2 #I #W1 #U1 #H destruct /2 width=5/
+]
+qed.
 
-(* Basic-1: removed theorems 7:
-            iso_gen_sort iso_gen_lref iso_gen_head iso_refl iso_trans
-            iso_flats_lref_bind_false iso_flats_flat_bind_false
-*)
+lemma thom_inv_flat1: ∀I,W1,U1,T2. ⓕ{I}W1.U1 ≈ T2 →
+                      ∃∃W2,U2. U1 ≈ U2 & 𝐒[U1] & 𝐒[U2] &
+                               I = Appl & T2 = ⓐW2. U2.
+/2 width=4/ qed-.