milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / relocation / nstream_id.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/nstream_id.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/nstream_id.ma
index d76d129407de9cfdfa75f442e5b30ae5a9dbce37..fcb6cca7208380c55ebe6a51a7cc987882d49284 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/relocation/nstream_id.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/relocation/nstream_id.ma
@@ -13,133 +13,21 @@
 (**************************************************************************)
 
 include "ground_2/notation/functions/identity_0.ma".
-include "ground_2/notation/relations/isidentity_1.ma".
-include "ground_2/relocation/nstream_lift.ma".
-include "ground_2/relocation/nstream_after.ma".
+include "ground_2/relocation/rtmap_eq.ma".
 
 (* RELOCATION N-STREAM ******************************************************)
 
-let corec id: nstream ≝ ↑id.
+corec definition id: rtmap ≝ ⫯id.
 
 interpretation "identity (nstream)"
    'Identity = (id).
 
-definition isid: predicate nstream ≝ λt. t ≐ 𝐈𝐝.
+(* Basic properties *********************************************************)
 
-interpretation "test for identity (trace)"
-   'IsIdentity t = (isid t).
-
-(* Basic properties on id ***************************************************)
-
-lemma id_unfold: 𝐈𝐝 = ↑𝐈𝐝.
->(stream_expand … (𝐈𝐝)) in ⊢ (??%?); normalize //
+lemma id_rew: ⫯𝐈𝐝 = 𝐈𝐝.
+<(stream_rew … (𝐈𝐝)) in ⊢ (???%); normalize //
 qed.
 
-(* Basic properties on isid *************************************************)
-
-lemma isid_id: 𝐈⦃𝐈𝐝⦄.
-// qed.
-
-lemma isid_push: ∀t. 𝐈⦃t⦄ → 𝐈⦃↑t⦄.
-#t #H normalize >id_unfold /2 width=1 by eq_seq/
+lemma id_eq_rew: ⫯𝐈𝐝 ≡ 𝐈𝐝.
+cases id_rew in ⊢ (??%); //
 qed.
-
-(* Basic inversion lemmas on isid *******************************************)
-
-lemma isid_inv_seq: ∀t,a.  𝐈⦃a@t⦄ → 𝐈⦃t⦄ ∧ a = 0.
-#t #a normalize >id_unfold in ⊢ (???%→?);
-#H elim (eq_stream_inv_seq ????? H) -H /2 width=1 by conj/
-qed-.
-
-lemma isid_inv_push: ∀t. 𝐈⦃↑t⦄ → 𝐈⦃t⦄.
-* #a #t #H elim (isid_inv_seq … H) -H //
-qed-.
-
-lemma isid_inv_next: ∀t. 𝐈⦃⫯t⦄ → ⊥.
-* #a #t #H elim (isid_inv_seq … H) -H
-#_ #H destruct
-qed-.
-
-(* inversion lemmas on at ***************************************************)
-
-let corec id_inv_at: ∀t. (∀i. @⦃i, t⦄ ≡ i) → t ≐ 𝐈𝐝 ≝ ?.
-* #a #t #Ht lapply (Ht 0)
-#H lapply (at_inv_O1 … H) -H
-#H0 >id_unfold @eq_seq
-[ cases H0 -a //
-| @id_inv_at -id_inv_at
-  #i lapply (Ht (⫯i)) -Ht cases H0 -a
-  #H elim (at_inv_SOx … H) -H //
-]
-qed-.
-
-lemma isid_inv_at: ∀i,t. 𝐈⦃t⦄ → @⦃i, t⦄ ≡ i.
-#i elim i -i
-[ * #a #t #H elim (isid_inv_seq … H) -H //
-| #i #IH * #a #t #H elim (isid_inv_seq … H) -H
-  /3 width=1 by at_S1/
-]
-qed-.
-
-lemma isid_inv_at_mono: ∀t,i1,i2. 𝐈⦃t⦄ → @⦃i1, t⦄ ≡ i2 → i1 = i2.
-/3 width=6 by isid_inv_at, at_mono/ qed-.
-
-(* Properties on at *********************************************************)
-
-lemma id_at: ∀i. @⦃i, 𝐈𝐝⦄ ≡ i.
-/2 width=1 by isid_inv_at/ qed.
-
-lemma isid_at: ∀t. (∀i. @⦃i, t⦄ ≡ i) → 𝐈⦃t⦄.
-/2 width=1 by id_inv_at/ qed.
-
-lemma isid_at_total: ∀t. (∀i1,i2. @⦃i1, t⦄ ≡ i2 → i1 = i2) → 𝐈⦃t⦄.
-#t #Ht @isid_at
-#i lapply (at_total i t)
-#H >(Ht … H) in ⊢ (???%); -Ht //
-qed.
-
-(* Properties on after ******************************************************)
-
-lemma after_isid_dx: ∀t2,t1,t. t2 ⊚ t1 ≡ t → t2 ≐ t → 𝐈⦃t1⦄.
-#t2 #t1 #t #Ht #H2 @isid_at_total
-#i1 #i2 #Hi12 elim (after_at1_fwd … Hi12 … Ht) -t1
-/3 width=6 by at_inj, eq_stream_sym/
-qed.
-
-lemma after_isid_sn: ∀t2,t1,t. t2 ⊚ t1 ≡ t → t1 ≐ t → 𝐈⦃t2⦄.
-#t2 #t1 #t #Ht #H1 @isid_at_total
-#i2 #i #Hi2 lapply (at_total i2 t1)
-#H0 lapply (at_increasing … H0)
-#Ht1 lapply (after_fwd_at2 … (t1@❴i2❵) … H0 … Ht)
-/3 width=7 by at_repl_back, at_mono, at_id_le/
-qed.
-
-(* Inversion lemmas on after ************************************************)
-
-let corec isid_after_sn: ∀t1,t2. 𝐈⦃t1⦄ → t1 ⊚ t2 ≡ t2 ≝ ?.
-* #a1 #t1 * * [ | #a2 ] #t2 #H cases (isid_inv_seq … H) -H
-#Ht1 #H1
-[ @(after_zero … H1) -H1 /2 width=1 by/
-| @(after_skip … H1) -H1 /2 width=5 by/
-]
-qed-.
-
-let corec isid_after_dx: ∀t2,t1. 𝐈⦃t2⦄ → t1 ⊚ t2 ≡ t1 ≝ ?.
-* #a2 #t2 * *
-[ #t1 #H cases (isid_inv_seq … H) -H
-  #Ht2 #H2 @(after_zero … H2) -H2 /2 width=1 by/
-| #a1 #t1 #H @(after_drop … a1 a1) /2 width=5 by/
-]
-qed-.
-
-lemma after_isid_inv_sn: ∀t1,t2,t. t1 ⊚ t2 ≡ t →  𝐈⦃t1⦄ → t2 ≐ t.
-/3 width=4 by isid_after_sn, after_mono/
-qed-.
-
-lemma after_isid_inv_dx: ∀t1,t2,t. t1 ⊚ t2 ≡ t →  𝐈⦃t2⦄ → t1 ≐ t.
-/3 width=4 by isid_after_dx, after_mono/
-qed-.
-(*
-lemma after_inv_isid3: ∀t1,t2,t. t1 ⊚ t2 ≡ t → 𝐈⦃t⦄ → 𝐈⦃t1⦄ ∧ 𝐈⦃t2⦄.
-qed-.
-*)