#b1 #f1 #L1 #L #H elim H -f1 -L1 -L
[ #f1 #_ #b2 #f #L2 #HL2 #f2 #Hf12 elim (drops_inv_atom1 … HL2) -b1 -HL2
#H #Hf destruct @drops_atom
- #H elim (after_inv_isid3 … Hf12) -Hf12 /2 width=1 by/
-| #f1 #I1 #K1 #K #_ #IH #b2 #f #L2 #HL2 #f2 #Hf elim (after_inv_nxx … Hf) -Hf [2,3: // ]
+ #H elim (pr_after_inv_isi … Hf12) -Hf12 /2 width=1 by/
+| #f1 #I1 #K1 #K #_ #IH #b2 #f #L2 #HL2 #f2 #Hf elim (pr_after_inv_next_sn … Hf) -Hf [2,3: // ]
#g #Hg #H destruct /3 width=3 by drops_inv_drop1/
-| #f1 #I1 #I #K1 #K #_ #HI1 #IH #b2 #f #L2 #HL2 #f2 #Hf elim (after_inv_pxx … Hf) -Hf [1,3: * |*:// ]
+| #f1 #I1 #I #K1 #K #_ #HI1 #IH #b2 #f #L2 #HL2 #f2 #Hf elim (pr_after_inv_push_sn … Hf) -Hf [1,3: * |*:// ]
#g2 #g #Hf #H1 #H2 destruct
[ elim (drops_inv_skip1 … HL2) -HL2 /3 width=6 by drops_skip, liftsb_div3/
| /4 width=3 by drops_inv_drop1, drops_drop/
#b1 #f1 #L1 #L #H elim H -f1 -L1 -L
[ #f1 #Hf1 #b2 #f2 #L2 #HL2 #f #Hf elim (drops_inv_atom1 … HL2) -HL2
#H #Hf2 destruct @drops_atom #H elim (andb_inv_true_dx … H) -H
- #H1 #H2 lapply (after_isid_inv_sn … Hf ?) -Hf
- /3 width=3 by isid_eq_repl_back/
-| #f1 #I1 #K1 #K #_ #IH #b2 #f2 #L2 #HL2 #f #Hf elim (after_inv_nxx … Hf) -Hf
+ #H1 #H2 lapply (pr_after_isi_inv_sn … Hf ?) -Hf
+ /3 width=3 by pr_isi_eq_repl_back/
+| #f1 #I1 #K1 #K #_ #IH #b2 #f2 #L2 #HL2 #f #Hf elim (pr_after_inv_next_sn … Hf) -Hf
/3 width=3 by drops_drop/
-| #f1 #I1 #I #K1 #K #_ #HI1 #IH #b2 #f2 #L2 #HL2 #f #Hf elim (after_inv_pxx … Hf) -Hf [1,3: * |*: // ]
+| #f1 #I1 #I #K1 #K #_ #HI1 #IH #b2 #f2 #L2 #HL2 #f #Hf elim (pr_after_inv_push_sn … Hf) -Hf [1,3: * |*: // ]
#g2 #g #Hg #H1 #H2 destruct
[ elim (drops_inv_skip1 … HL2) -HL2 /3 width=6 by drops_skip, liftsb_trans/
| /4 width=3 by drops_inv_drop1, drops_drop/
𝐔❪f1❫ → 𝐔❪f2❫ → f1 ≡ f2.
#f1 #L #K #H elim H -f1 -L -K
[ #f1 #Hf1 #f2 #Hf2 elim (drops_inv_atom1 … Hf2) -Hf2
- /3 width=1 by isid_inv_eq_repl/
-| #f1 #I #L #K #Hf1 #IH #f2 elim (pn_split f2) *
+ /3 width=1 by pr_isi_inv_eq_repl/
+| #f1 #I #L #K #Hf1 #IH #f2 elim (pr_map_split_tl f2) *
#g2 #H2 #Hf2 #HU1 #HU2 destruct
[ elim (drops_inv_skip1 … Hf2) -IH -HU1 -Hf2 #Y2 #X2 #HY2 #_ #H destruct
- lapply (drops_fwd_isid … HY2 ?) -HY2 /2 width=3 by isuni_inv_push/ -HU2
+ lapply (drops_fwd_isid … HY2 ?) -HY2 /2 width=3 by pr_isu_inv_push/ -HU2
#H destruct elim (drops_inv_x_bind_xy … Hf1)
- | /4 width=5 by drops_inv_drop1, isuni_inv_next, eq_next/
+ | /4 width=5 by drops_inv_drop1, pr_isu_inv_next, pr_eq_next/
]
-| #f1 #I1 #I2 #L #K #Hf1 #_ #IH #f2 elim (pn_split f2) *
+| #f1 #I1 #I2 #L #K #Hf1 #_ #IH #f2 elim (pr_map_split_tl f2) *
#g2 #H2 #Hf2 #HU1 #HU2 destruct
[ elim (drops_inv_skip1 … Hf2) -Hf2 #Y2 #X2 #HY2 #_ #H destruct -Hf1
- /4 width=5 by isuni_fwd_push, eq_push/
+ /4 width=5 by pr_isu_fwd_push, pr_eq_push/
| lapply (drops_inv_drop1 … Hf2) -Hf2 -IH -HU2 #Hg2
- lapply (drops_fwd_isid … Hf1 ?) -Hf1 /2 width=3 by isuni_inv_push/ -HU1
+ lapply (drops_fwd_isid … Hf1 ?) -Hf1 /2 width=3 by pr_isu_inv_push/ -HU1
#H destruct elim (drops_inv_x_bind_xy … Hg2)
]
]
(* Basic_2A1: includes: drop_mono *)
lemma drops_mono: ∀b1,f,L,L1. ⇩*[b1,f] L ≘ L1 →
∀b2,L2. ⇩*[b2,f] L ≘ L2 → L1 = L2.
-#b1 #f #L #L1 lapply (after_isid_dx 𝐢 … f)
+#b1 #f #L #L1 lapply (pr_after_isi_dx 𝐢 … f)
/3 width=8 by drops_conf, drops_fwd_isid/
qed-.
#f1 #f2 #I1 #I2 #L #K #Hf1 #Hf2 #HU1 #HU2
lapply (drops_isuni_fwd_drop2 … Hf1) // #H1
lapply (drops_isuni_fwd_drop2 … Hf2) // #H2
-lapply (drops_conf_div_isuni … H1 … H2 ??) /2 width=3 by isuni_next/ -H1 -H2 -HU1 -HU2 #H
+lapply (drops_conf_div_isuni … H1 … H2 ??) /2 width=3 by pr_isu_next/ -H1 -H2 -HU1 -HU2 #H
lapply (eq_inv_nn … H ????) -H [5: |*: // ] #H12
lapply (drops_eq_repl_back … Hf1 … H12) -Hf1 #H0
lapply (drops_mono … H0 … Hf2) -L #H