X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambda_delta%2Fbasic_2%2Fgrammar%2Ftshf.ma;h=a8873c18b286459cb87ef7b04c7b5a5e028cc8ba;hb=439b6ec33d749ba4e6ae0938e973a85bc23e306e;hp=364a530e1d5e5a1c706f6a225e70a25721f64504;hpb=eb918fc784eacd2094e3986ba321ef47690d9983;p=helm.git

diff --git a/matita/matita/contribs/lambda_delta/basic_2/grammar/tshf.ma b/matita/matita/contribs/lambda_delta/basic_2/grammar/tshf.ma
index 364a530e1..a8873c18b 100644
--- a/matita/matita/contribs/lambda_delta/basic_2/grammar/tshf.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/grammar/tshf.ma
@@ -12,14 +12,15 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "Basic_2/grammar/term_simple.ma".
+include "basic_2/grammar/term_simple.ma".
 
 (* SAME HEAD TERM FORMS *****************************************************)
 
 inductive tshf: relation term ≝
    | tshf_atom: ∀I. tshf (⓪{I}) (⓪{I})
-   | tshf_abst: ∀V1,V2,T1,T2. tshf (ⓛV1. T1) (ⓛV2. T2)
-   | tshf_appl: ∀V1,V2,T1,T2. tshf T1 T2 → 𝐒[T1] → 𝐒[T2] →
+   | tshf_abbr: ∀V1,V2,T1,T2. tshf (-ⓓV1. T1) (-ⓓV2. T2)
+   | tshf_abst: ∀a,V1,V2,T1,T2. tshf (ⓛ{a}V1. T1) (ⓛ{a}V2. T2)
+   | tshf_appl: ∀V1,V2,T1,T2. tshf T1 T2 → 𝐒⦃T1⦄ → 𝐒⦃T2⦄ →
                 tshf (ⓐV1. T1) (ⓐV2. T2)
 .
 
@@ -38,41 +39,48 @@ qed.
 lemma tshf_refl1: ∀T1,T2. T1 ≈ T2 → T1 ≈ T1.
 /3 width=2/ qed.
 
-lemma simple_tshf_repl_dx: ∀T1,T2. T1 ≈ T2 → 𝐒[T1] → 𝐒[T2].
+lemma simple_tshf_repl_dx: ∀T1,T2. T1 ≈ T2 → 𝐒⦃T1⦄ → 𝐒⦃T2⦄.
 #T1 #T2 #H elim H -T1 -T2 //
-#V1 #V2 #T1 #T2 #H
-elim (simple_inv_bind … H)
+[ #V1 #V2 #T1 #T2 #H
+  elim (simple_inv_bind … H)
+| #a #V1 #V2 #T1 #T2 #H
+  elim (simple_inv_bind … H)
+]
 qed. (**) (* remove from index *)
 
-lemma simple_tshf_repl_sn: ∀T1,T2. T1 ≈ T2 → 𝐒[T2] → 𝐒[T1].
+lemma simple_tshf_repl_sn: ∀T1,T2. T1 ≈ T2 → 𝐒⦃T2⦄ → 𝐒⦃T1⦄.
 /3 width=3/ qed-.
 
 (* Basic inversion lemmas ***************************************************)
 
-fact tshf_inv_bind1_aux: ∀T1,T2. T1 ≈ T2 → ∀I,W1,U1. T1 = ⓑ{I}W1.U1 →
-                         ∃∃W2,U2. I = Abst & T2 = ⓛW2. U2.
+fact tshf_inv_bind1_aux: ∀T1,T2. T1 ≈ T2 → ∀a,I,W1,U1. T1 = ⓑ{a,I}W1.U1 →
+                         ∃∃W2,U2. T2 = ⓑ{a,I}W2. U2 &
+                                  (Bind2 a I = Bind2 false Abbr ∨ I = Abst).
 #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
+[ #J #a #I #W1 #U1 #H destruct
+| #V1 #V2 #T1 #T2 #a #I #W1 #U1 #H destruct /3 width=3/
+| #b #V1 #V2 #T1 #T2 #a #I #W1 #U1 #H destruct /3 width=3/
+| #V1 #V2 #T1 #T2 #_ #_ #_ #a #I #W1 #U1 #H destruct
 ]
 qed.
 
-lemma tshf_inv_bind1: ∀I,W1,U1,T2. ⓑ{I}W1.U1 ≈ T2 →
-                      ∃∃W2,U2. I = Abst & T2 = ⓛW2. U2.
+lemma tshf_inv_bind1: ∀a,I,W1,U1,T2. ⓑ{a,I}W1.U1 ≈ T2 →
+                      ∃∃W2,U2. T2 = ⓑ{a,I}W2. U2 &
+                               (Bind2 a I = Bind2 false Abbr ∨ I = Abst).
 /2 width=5/ qed-.
 
 fact tshf_inv_flat1_aux: ∀T1,T2. T1 ≈ T2 → ∀I,W1,U1. T1 = ⓕ{I}W1.U1 →
-                         ∃∃W2,U2. U1 ≈ U2 & 𝐒[U1] & 𝐒[U2] &
+                         ∃∃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
+| #a #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.
 
 lemma tshf_inv_flat1: ∀I,W1,U1,T2. ⓕ{I}W1.U1 ≈ T2 →
-                      ∃∃W2,U2. U1 ≈ U2 & 𝐒[U1] & 𝐒[U2] &
+                      ∃∃W2,U2. U1 ≈ U2 & 𝐒⦃U1⦄ & 𝐒⦃U2⦄ &
                                I = Appl & T2 = ⓐW2. U2.
 /2 width=4/ qed-.