(* Forward lemmas with length for local environments ************************)
(* Note: "#f #I1 #I2 #L1 #L2 >length_bind >length_bind //" was needed to conclude *)
-lemma sex_fwd_length: ∀RN,RP,f,L1,L2. L1 ⪤[RN, RP, f] L2 → |L1| = |L2|.
+lemma sex_fwd_length: ∀RN,RP,f,L1,L2. L1 ⪤[RN,RP,f] L2 → |L1| = |L2|.
#RN #RP #f #L1 #L2 #H elim H -f -L1 -L2 //
qed-.
(* Properties with length for local environments ****************************)
-lemma sex_length_cfull: ∀L1,L2. |L1| = |L2| → ∀f. L1 ⪤[cfull, cfull, f] L2.
+lemma sex_length_cfull: ∀L1,L2. |L1| = |L2| → ∀f. L1 ⪤[cfull,cfull,f] L2.
#L1 elim L1 -L1
[ #Y2 #H >(length_inv_zero_sn … H) -Y2 //
| #L1 #I1 #IH #Y2 #H #f
elim (length_inv_succ_sn … H) -H #I2 #L2 #HL12 #H destruct
- elim (pn_split f) * #g #H destruct /3 width=1 by sex_next, sex_push/
+ elim (pr_map_split_tl f) * #g #H destruct /3 width=1 by sex_next, sex_push/
]
qed.
lemma sex_length_isid: ∀R,L1,L2. |L1| = |L2| →
- â\88\80f. ð\9d\90\88â¦\83fâ¦\84 â\86\92 L1 ⪤[R, cfull, f] L2.
+ â\88\80f. ð\9d\90\88â\9d¨fâ\9d© â\86\92 L1 ⪤[R,cfull,f] L2.
#R #L1 elim L1 -L1
[ #Y2 #H >(length_inv_zero_sn … H) -Y2 //
| #L1 #I1 #IH #Y2 #H #f #Hf
elim (length_inv_succ_sn … H) -H #I2 #L2 #HL12 #H destruct
- elim (isid_inv_gen … Hf) -Hf #g #Hg #H destruct /3 width=1 by sex_push/
+ elim (pr_isi_inv_gen … Hf) -Hf #g #Hg #H destruct /3 width=1 by sex_push/
]
qed.