(* 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-.
corec theorem at_ext: ∀f1,f2. 𝐓⦃f1⦄ → 𝐓⦃f2⦄ →
(∀i,i1,i2. @⦃i, f1⦄ ≘ i1 → @⦃i, f2⦄ ≘ i2 → i1 = i2) →
- f1 â\89\97 f2.
+ f1 â\89¡ 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
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-.
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/
+#f #i2 #Hf @(is_at_dec_le ?? (â\86\91i2)) /2 width=4 by lt_le_false/
qed-.
(* Advanced properties on isid **********************************************)