(* Inversions with pr_eq ****************************************************)
(*** uni_inv_push_dx *)
-lemma pr_eq_inv_uni_push (n) (g): ð\9d\90®â\9d¨nâ\9d© â\89¡ ⫯g â\86\92 â\88§â\88§ ð\9d\9f\8e = n & ð\9d\90¢ â\89¡ g.
+lemma pr_eq_inv_uni_push (n) (g): ð\9d\90®â\9d¨nâ\9d© â\89\90 ⫯g â\86\92 â\88§â\88§ ð\9d\9f\8e = n & ð\9d\90¢ â\89\90 g.
#n @(nat_ind_succ … n) -n
[ /3 width=5 by pr_eq_inv_push_bi, conj/
| #n #_ #f <pr_uni_succ #H elim (pr_eq_inv_next_push … H) -H //
qed-.
(*** uni_inv_push_sn *)
-lemma pr_eq_inv_push_uni (n) (g): ⫯g â\89¡ ð\9d\90®â\9d¨nâ\9d© â\86\92 â\88§â\88§ ð\9d\9f\8e = n & ð\9d\90¢ â\89¡ g.
+lemma pr_eq_inv_push_uni (n) (g): ⫯g â\89\90 ð\9d\90®â\9d¨nâ\9d© â\86\92 â\88§â\88§ ð\9d\9f\8e = n & ð\9d\90¢ â\89\90 g.
/3 width=1 by pr_eq_inv_uni_push, pr_eq_sym/ qed-.
(*** uni_inv_next_dx *)
-lemma pr_eq_inv_uni_next (n) (g): ð\9d\90®â\9d¨nâ\9d© â\89¡ â\86\91g â\86\92 â\88§â\88§ ð\9d\90®â\9d¨â\86\93nâ\9d© â\89¡ g & ↑↓n = n.
+lemma pr_eq_inv_uni_next (n) (g): ð\9d\90®â\9d¨nâ\9d© â\89\90 â\86\91g â\86\92 â\88§â\88§ ð\9d\90®â\9d¨â\86\93nâ\9d© â\89\90 g & ↑↓n = n.
#n @(nat_ind_succ … n) -n
[ #g <pr_uni_zero <pr_id_unfold #H elim (pr_eq_inv_push_next … H) -H //
| #n #_ #g <pr_uni_succ /3 width=5 by pr_eq_inv_next_bi, conj/
qed-.
(*** uni_inv_next_sn *)
-lemma pr_eq_inv_next_uni (n) (g): â\86\91g â\89¡ ð\9d\90®â\9d¨nâ\9d© â\86\92 â\88§â\88§ ð\9d\90®â\9d¨â\86\93nâ\9d© â\89¡ g & ↑↓n = n.
+lemma pr_eq_inv_next_uni (n) (g): â\86\91g â\89\90 ð\9d\90®â\9d¨nâ\9d© â\86\92 â\88§â\88§ ð\9d\90®â\9d¨â\86\93nâ\9d© â\89\90 g & ↑↓n = n.
/3 width=1 by pr_eq_inv_uni_next, pr_eq_sym/ qed-.
(* Inversions with pr_id and pr_eq ******************************************)
(*** uni_inv_id_dx *)
-lemma pr_eq_inv_uni_id (n): ð\9d\90®â\9d¨nâ\9d© â\89¡ 𝐢 → 𝟎 = n.
+lemma pr_eq_inv_uni_id (n): ð\9d\90®â\9d¨nâ\9d© â\89\90 𝐢 → 𝟎 = n.
#n <pr_id_unfold #H elim (pr_eq_inv_uni_push … H) -H //
qed-.
(*** uni_inv_id_sn *)
-lemma pr_eq_inv_id_uni (n): ð\9d\90¢ â\89¡ 𝐮❨n❩ → 𝟎 = n.
+lemma pr_eq_inv_id_uni (n): ð\9d\90¢ â\89\90 𝐮❨n❩ → 𝟎 = n.
/3 width=1 by pr_eq_inv_uni_id, pr_eq_sym/ qed-.