some restyling ...

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

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_istot.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_istot.ma
index d4e80390ff447878ad9ae93bc2cb7e001644874c..87087b273bfb4b5382ddd32e314017c709129956 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_istot.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_istot.ma
@@ -17,19 +17,19 @@ include "ground_2/relocation/rtmap_at.ma".
 
 (* RELOCATION MAP ***********************************************************)
 
-definition istot: predicate rtmap ≝ λf. ∀i. ∃j. @⦃i, f⦄ ≡ j.
+definition istot: predicate rtmap ≝ λf. ∀i. ∃j. @⦃i,f⦄ ≘ j.
 
 interpretation "test for totality (rtmap)"
    'IsTotal f = (istot f).
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma istot_inv_push: â\88\80g. ð\9d\90\93â¦\83gâ¦\84 â\86\92 â\88\80f. â\86\91f = g → 𝐓⦃f⦄.
-#g #Hg #f #H #i elim (Hg (⫯i)) -Hg
+lemma istot_inv_push: â\88\80g. ð\9d\90\93â¦\83gâ¦\84 â\86\92 â\88\80f. ⫯f = g → 𝐓⦃f⦄.
+#g #Hg #f #H #i elim (Hg (â\86\91i)) -Hg
 #j #Hg elim (at_inv_npx … Hg … H) -Hg -H /2 width=3 by ex_intro/
 qed-.
 
-lemma istot_inv_next: â\88\80g. ð\9d\90\93â¦\83gâ¦\84 â\86\92 â\88\80f. ⫯f = g → 𝐓⦃f⦄.
+lemma istot_inv_next: â\88\80g. ð\9d\90\93â¦\83gâ¦\84 â\86\92 â\88\80f. â\86\91f = g → 𝐓⦃f⦄.
 #g #Hg #f #H #i elim (Hg i) -Hg
 #j #Hg elim (at_inv_xnx … Hg … H) -Hg -H /2 width=2 by ex_intro/
 qed-.
@@ -47,15 +47,16 @@ lemma istot_tls: ∀n,f. 𝐓⦃f⦄ → 𝐓⦃⫱*[n]f⦄.
 #n elim n -n /3 width=1 by istot_tl/
 qed.
 
-(* Advanced forward lemmas on at ********************************************)
+(* Main forward lemmas on at ************************************************)
 
-let corec at_ext: ∀f1,f2. 𝐓⦃f1⦄ → 𝐓⦃f2⦄ →
-                  (∀i,i1,i2. @⦃i, f1⦄ ≡ i1 → @⦃i, f2⦄ ≡ i2 → i1 = i2) → f1 ≗ f2 ≝ ?.
+corec theorem at_ext: ∀f1,f2. 𝐓⦃f1⦄ → 𝐓⦃f2⦄ →
+                      (∀i,i1,i2. @⦃i,f1⦄ ≘ i1 → @⦃i,f2⦄ ≘ i2 → i1 = i2) →
+                      f1 ≡ f2.
 #f1 cases (pn_split f1) * #g1 #H1
 #f2 cases (pn_split f2) * #g2 #H2
 #Hf1 #Hf2 #Hi
 [ @(eq_push … H1 H2) @at_ext -at_ext /2 width=3 by istot_inv_push/ -Hf1 -Hf2
-  #i #i1 #i2 #Hg1 #Hg2 lapply (Hi (⫯i) (⫯i1) (⫯i2) ??) /2 width=7 by at_push/
+  #i #i1 #i2 #Hg1 #Hg2 lapply (Hi (â\86\91i) (â\86\91i1) (â\86\91i2) ??) /2 width=7 by at_push/
 | cases (Hf2 0) -Hf1 -Hf2 -at_ext
   #j2 #Hf2 cases (at_increasing_strict … Hf2 … H2) -H2
   lapply (Hi 0 0 j2 … Hf2) /2 width=2 by at_refl/ -Hi -Hf2 -H1
@@ -65,13 +66,13 @@ let corec at_ext: ∀f1,f2. 𝐓⦃f1⦄ → 𝐓⦃f2⦄ →
   lapply (Hi 0 j1 0 Hf1 ?) /2 width=2 by at_refl/ -Hi -Hf1 -H2
   #H1 #H cases (lt_le_false … H) -H //
 | @(eq_next … H1 H2) @at_ext -at_ext /2 width=3 by istot_inv_next/ -Hf1 -Hf2
-  #i #i1 #i2 #Hg1 #Hg2 lapply (Hi i (⫯i1) (⫯i2) ??) /2 width=5 by at_next/
+  #i #i1 #i2 #Hg1 #Hg2 lapply (Hi i (â\86\91i1) (â\86\91i2) ??) /2 width=5 by at_next/
 ]
 qed-.
 
-(* Main properties on at ****************************************************)
+(* Advanced properties on at ************************************************)
 
-lemma at_dec: ∀f,i1,i2. 𝐓⦃f⦄ → Decidable (@⦃i1, f⦄ ≡ i2).
+lemma at_dec: ∀f,i1,i2. 𝐓⦃f⦄ → Decidable (@⦃i1,f⦄ ≘ i2).
 #f #i1 #i2 #Hf lapply (Hf i1) -Hf *
 #j2 #Hf elim (eq_nat_dec i2 j2)
 [ #H destruct /2 width=1 by or_introl/
@@ -79,7 +80,8 @@ lemma at_dec: ∀f,i1,i2. 𝐓⦃f⦄ → Decidable (@⦃i1, f⦄ ≡ i2).
 ]
 qed-.
 
-lemma is_at_dec_le: ∀f,i2,i. 𝐓⦃f⦄ → (∀i1. i1 + i ≤ i2 → @⦃i1, f⦄ ≡ i2 → ⊥) → Decidable (∃i1. @⦃i1, f⦄ ≡ i2).
+lemma is_at_dec_le: ∀f,i2,i. 𝐓⦃f⦄ → (∀i1. i1 + i ≤ i2 → @⦃i1,f⦄ ≘ i2 → ⊥) →
+                    Decidable (∃i1. @⦃i1,f⦄ ≘ i2).
 #f #i2 #i #Hf elim i -i
 [ #Ht @or_intror * /3 width=3 by at_increasing/
 | #i #IH #Ht elim (at_dec f (i2-i) i2) /3 width=2 by ex_intro, or_introl/
@@ -88,13 +90,13 @@ lemma is_at_dec_le: ∀f,i2,i. 𝐓⦃f⦄ → (∀i1. i1 + i ≤ i2 → @⦃i1,
 ]
 qed-.
 
-lemma is_at_dec: ∀f,i2. 𝐓⦃f⦄ → Decidable (∃i1. @⦃i1, f⦄ ≡ i2).
-#f #i2 #Hf @(is_at_dec_le ?? (⫯i2)) /2 width=4 by lt_le_false/
+lemma is_at_dec: ∀f,i2. 𝐓⦃f⦄ → Decidable (∃i1. @⦃i1,f⦄ ≘ i2).
+#f #i2 #Hf @(is_at_dec_le ?? (â\86\91i2)) /2 width=4 by lt_le_false/
 qed-.
 
 (* Advanced properties on isid **********************************************)
 
-lemma isid_at_total: ∀f. 𝐓⦃f⦄ → (∀i1,i2. @⦃i1, f⦄ ≡ i2 → i1 = i2) → 𝐈⦃f⦄.
+lemma isid_at_total: ∀f. 𝐓⦃f⦄ → (∀i1,i2. @⦃i1,f⦄ ≘ i2 → i1 = i2) → 𝐈⦃f⦄.
 #f #H1f #H2f @isid_at
 #i lapply (H1f i) -H1f *
 #j #Hf >(H2f … Hf) in ⊢ (???%); -H2f //