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 f5103e257aeef7cf8d432d309e118400ed48c6f1..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
@@ -13,141 +13,21 @@
 (**************************************************************************)
 
 include "ground_2/notation/functions/identity_0.ma".
-include "ground_2/notation/relations/isidentity_1.ma".
-include "ground_2/relocation/nstream_after.ma".
+include "ground_2/relocation/rtmap_eq.ma".
 
 (* RELOCATION N-STREAM ******************************************************)
 
-let corec id: rtmap ≝ ↑id.
+corec definition id: rtmap ≝ ⫯id.
 
 interpretation "identity (nstream)"
    'Identity = (id).
 
-definition isid: predicate rtmap ≝ λf. f ≐ 𝐈𝐝.
+(* Basic properties *********************************************************)
 
-interpretation "test for identity (trace)"
-   'IsIdentity f = (isid f).
-
-(* Basic properties on id ***************************************************)
-
-lemma id_unfold: 𝐈𝐝 = ↑𝐈𝐝.
->(stream_expand … (𝐈𝐝)) in ⊢ (??%?); normalize //
-qed.
-
-(* Basic properties on isid *************************************************)
-
-lemma isid_eq_repl_back: eq_stream_repl_back … isid.
-/2 width=3 by eq_stream_canc_sn/ qed-.
-
-lemma isid_eq_repl_fwd: eq_stream_repl_fwd … isid.
-/3 width=3 by isid_eq_repl_back, eq_stream_repl_sym/ qed-.
-
-lemma isid_id: 𝐈⦃𝐈𝐝⦄.
-// qed.
-
-lemma isid_push: ∀f. 𝐈⦃f⦄ → 𝐈⦃↑f⦄.
-#f #H normalize >id_unfold /2 width=1 by eq_seq/
-qed.
-
-(* Basic inversion lemmas on isid *******************************************)
-
-lemma isid_inv_seq: ∀f,n.  𝐈⦃n@f⦄ → 𝐈⦃f⦄ ∧ n = 0.
-#f #n normalize >id_unfold in ⊢ (???%→?);
-#H elim (eq_stream_inv_seq ????? H) -H /2 width=1 by conj/
-qed-.
-
-lemma isid_inv_push: ∀f. 𝐈⦃↑f⦄ → 𝐈⦃f⦄.
-* #n #f #H elim (isid_inv_seq … H) -H //
-qed-.
-
-lemma isid_inv_next: ∀f. 𝐈⦃⫯f⦄ → ⊥.
-* #n #f #H elim (isid_inv_seq … H) -H
-#_ #H destruct
-qed-.
-
-lemma isid_inv_gen: ∀f. 𝐈⦃f⦄ → ∃∃g. 𝐈⦃g⦄ & f = ↑g.
-* #n #f #H elim (isid_inv_seq … H) -H
-#Hf #H destruct /2 width=3 by ex2_intro/
-qed-.
-
-lemma isid_inv_eq_repl: ∀f1,f2. 𝐈⦃f1⦄ → 𝐈⦃f2⦄ → f1 ≐ f2.
-/2 width=3 by eq_stream_canc_dx/ qed-.
-
-(* inversion lemmas on at ***************************************************)
-
-let corec id_inv_at: ∀f. (∀i. @⦃i, f⦄ ≡ i) → f ≐ 𝐈𝐝 ≝ ?.
-* #n #f #Ht lapply (Ht 0)
-#H lapply (at_inv_O1 … H) -H
-#H0 >id_unfold @eq_seq
-[ cases H0 -n //
-| @id_inv_at -id_inv_at
-  #i lapply (Ht (⫯i)) -Ht cases H0 -n
-  #H elim (at_inv_SOx … H) -H //
-]
-qed-.
-
-lemma isid_inv_at: ∀i,f. 𝐈⦃f⦄ → @⦃i, f⦄ ≡ i.
-#i elim i -i
-[ * #n #f #H elim (isid_inv_seq … H) -H //
-| #i #IH * #n #f #H elim (isid_inv_seq … H) -H
-  /3 width=1 by at_S1/
-]
-qed-.
-
-lemma isid_inv_at_mono: ∀f,i1,i2. 𝐈⦃f⦄ → @⦃i1, f⦄ ≡ 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: ∀f. (∀i. @⦃i, f⦄ ≡ i) → 𝐈⦃f⦄.
-/2 width=1 by id_inv_at/ qed.
-
-lemma isid_at_total: ∀f. (∀i1,i2. @⦃i1, f⦄ ≡ i2 → i1 = i2) → 𝐈⦃f⦄.
-#f #Ht @isid_at
-#i lapply (at_total i f)
-#H >(Ht … H) in ⊢ (???%); -Ht //
-qed.
-
-(* Properties on after ******************************************************)
-
-lemma after_isid_dx: ∀f2,f1,f. f2 ⊚ f1 ≡ f → f2 ≐ f → 𝐈⦃f1⦄.
-#f2 #f1 #f #Ht #H2 @isid_at_total
-#i1 #i2 #Hi12 elim (after_at1_fwd … Hi12 … Ht) -f1
-/3 width=6 by at_inj, eq_stream_sym/
+lemma id_rew: ⫯𝐈𝐝 = 𝐈𝐝.
+<(stream_rew … (𝐈𝐝)) in ⊢ (???%); normalize //
 qed.
 
-lemma after_isid_sn: ∀f2,f1,f. f2 ⊚ f1 ≡ f → f1 ≐ f → 𝐈⦃f2⦄.
-#f2 #f1 #f #Ht #H1 @isid_at_total
-#i2 #i #Hi2 lapply (at_total i2 f1)
-#H0 lapply (at_increasing … H0)
-#Ht1 lapply (after_fwd_at2 … (f1@❴i2❵) … H0 … Ht)
-/3 width=7 by at_eq_repl_back, at_mono, at_id_le/
+lemma id_eq_rew: ⫯𝐈𝐝 ≡ 𝐈𝐝.
+cases id_rew in ⊢ (??%); //
 qed.
-
-(* Inversion lemmas on after ************************************************)
-
-let corec isid_after_sn: ∀f1,f2. 𝐈⦃f1⦄ → f1 ⊚ f2 ≡ f2 ≝ ?.
-* #n1 #f1 * * [ | #n2 ] #f2 #H cases (isid_inv_seq … H) -H
-/3 width=7 by after_push, after_refl/
-qed-.
-
-let corec isid_after_dx: ∀f2,f1. 𝐈⦃f2⦄ → f1 ⊚ f2 ≡ f1 ≝ ?.
-* #n2 #f2 * *
-[ #f1 #H cases (isid_inv_seq … H) -H
-  /3 width=7 by after_refl/
-| #n1 #f1 #H @after_next [4,5: // |1,2: skip ] /2 width=1 by/
-]
-qed-.
-
-lemma after_isid_inv_sn: ∀f1,f2,f. f1 ⊚ f2 ≡ f →  𝐈⦃f1⦄ → f2 ≐ f.
-/3 width=8 by isid_after_sn, after_mono/
-qed-.
-
-lemma after_isid_inv_dx: ∀f1,f2,f. f1 ⊚ f2 ≡ f →  𝐈⦃f2⦄ → f1 ≐ f.
-/3 width=8 by isid_after_dx, after_mono/
-qed-.
-
-axiom after_inv_isid3: ∀f1,f2,f. f1 ⊚ f2 ≡ f → 𝐈⦃f⦄ → 𝐈⦃f1⦄ ∧ 𝐈⦃f2⦄.