component "reducibility" updated to new syntax!

[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 d796e10ba0ac3723c9268ee1fb4a24de641b16e3..aaade3b54324f39304ce3343af8cbddd5cd93e2d 100644 (file)
--- a/matita/matita/contribs/lambda_delta/Basic_2/grammar/thom.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/grammar/thom.ma
@@ -28,27 +28,54 @@ 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: ∀T1,T2. T1 ≈ T2 → 𝕊[T1] → 𝕊[T2].
-#T1 #T2 #H elim H -H T1 T2 //
+#T1 #T2 #H elim H -T1 -T2 //
 #V1 #V2 #T1 #T2 #H
 elim (simple_inv_bind … H)
 qed. (**) (* remove from index *)
 
 lemma simple_thom_repl_sn: ∀T1,T2. T1 ≈ T2 → 𝕊[T2] → 𝕊[T1].
-/3/ qed-.
+/3 width=3/ qed-.
 
 (* Basic inversion lemmas ***************************************************)
 
+fact thom_inv_bind1_aux: ∀T1,T2. T1 ≈ T2 → ∀I,W1,U1. T1 = 𝕓{I}W1.U1 →
+                         ∃∃W2,U2. I = Abst & T2 = 𝕔{Abst} 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. 𝕓{I}W1.U1 ≈ T2 →
+                      ∃∃W2,U2. I = Abst & T2 = 𝕔{Abst} W2. U2.
+/2 width=5/ qed-.
+
+fact thom_inv_flat1_aux: ∀T1,T2. T1 ≈ T2 → ∀I,W1,U1. T1 = 𝕗{I}W1.U1 →
+                         ∃∃W2,U2. U1 ≈ U2 & 𝕊[U1] & 𝕊[U2] &
+                                  I = Appl & T2 = 𝕔{Appl} 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.
+
+lemma thom_inv_flat1: ∀I,W1,U1,T2. 𝕗{I}W1.U1 ≈ T2 →
+                      ∃∃W2,U2. U1 ≈ U2 & 𝕊[U1] & 𝕊[U2] &
+                               I = Appl & T2 = 𝕔{Appl} W2. U2.
+/2 width=4/ qed-.
 
 (* Basic_1: removed theorems 7:
             iso_gen_sort iso_gen_lref iso_gen_head iso_refl iso_trans