(* Properties with length for local environments ****************************)
-lemma fsle_sort_bi: â\88\80L1,L2,s1,s2. |L1| = |L2| â\86\92 â¦\83L1,â\8b\86s1â¦\84 â\8a\86 â¦\83L2,â\8b\86s2â¦\84.
-/3 width=8 by lveq_length_eq, frees_sort, sle_refl, ex4_4_intro/ qed.
+lemma fsle_sort_bi: â\88\80L1,L2,s1,s2. |L1| = |L2| â\86\92 â\9dªL1,â\8b\86s1â\9d« â\8a\86 â\9dªL2,â\8b\86s2â\9d«.
+/3 width=8 by lveq_length_eq, frees_sort, pr_sle_refl, ex4_4_intro/ qed.
-lemma fsle_gref_bi: â\88\80L1,L2,l1,l2. |L1| = |L2| â\86\92 â¦\83L1,§l1â¦\84 â\8a\86 â¦\83L2,§l2â¦\84.
-/3 width=8 by lveq_length_eq, frees_gref, sle_refl, ex4_4_intro/ qed.
+lemma fsle_gref_bi: â\88\80L1,L2,l1,l2. |L1| = |L2| â\86\92 â\9dªL1,§l1â\9d« â\8a\86 â\9dªL2,§l2â\9d«.
+/3 width=8 by lveq_length_eq, frees_gref, pr_sle_refl, ex4_4_intro/ qed.
-lemma fsle_pair_bi: â\88\80K1,K2. |K1| = |K2| â\86\92 â\88\80V1,V2. â¦\83K1,V1â¦\84 â\8a\86 â¦\83K2,V2â¦\84 →
- â\88\80I1,I2. â¦\83K1.â\93\91{I1}V1,#Oâ¦\84 â\8a\86 â¦\83K2.â\93\91{I2}V2,#Oâ¦\84.
+lemma fsle_pair_bi: â\88\80K1,K2. |K1| = |K2| â\86\92 â\88\80V1,V2. â\9dªK1,V1â\9d« â\8a\86 â\9dªK2,V2â\9d« →
+ â\88\80I1,I2. â\9dªK1.â\93\91[I1]V1,#Oâ\9d« â\8a\86 â\9dªK2.â\93\91[I2]V2,#Oâ\9d«.
#K1 #K2 #HK #V1 #V2
* #n1 #n2 #f1 #f2 #Hf1 #Hf2 #HK12 #Hf12
#I1 #I2
elim (lveq_inj_length … HK12) // -HK #H1 #H2 destruct
-/3 width=12 by frees_pair, lveq_bind, sle_next, ex4_4_intro/
+/3 width=12 by frees_pair, lveq_bind, pr_sle_next, ex4_4_intro/
qed.
lemma fsle_unit_bi: ∀K1,K2. |K1| = |K2| →
- â\88\80I1,I2. â¦\83K1.â\93¤{I1},#Oâ¦\84 â\8a\86 â¦\83K2.â\93¤{I2},#Oâ¦\84.
-/3 width=8 by frees_unit, lveq_length_eq, sle_refl, ex4_4_intro/
+ â\88\80I1,I2. â\9dªK1.â\93¤[I1],#Oâ\9d« â\8a\86 â\9dªK2.â\93¤[I2],#Oâ\9d«.
+/3 width=8 by frees_unit, lveq_length_eq, pr_sle_refl, ex4_4_intro/
qed.