(* *)
(**************************************************************************)
-include "basic_2/grammar/cl_restricted_weight.ma".
-include "basic_2/relocation/lifts_weight.ma".
+include "basic_2/syntax/cl_restricted_weight.ma".
+include "basic_2/relocation/lifts_weight_bind.ma".
include "basic_2/relocation/drops.ma".
(* GENERIC SLICING FOR LOCAL ENVIRONMENTS ***********************************)
(* Forward lemmas with weight for local environments ************************)
(* Basic_2A1: includes: drop_fwd_lw *)
-lemma drops_fwd_lw: â\88\80b,f,L1,L2. â¬\87*[b, f] L1 â\89¡ L2 → ♯{L2} ≤ ♯{L1}.
+lemma drops_fwd_lw: â\88\80b,f,L1,L2. â¬\87*[b, f] L1 â\89\98 L2 → ♯{L2} ≤ ♯{L1}.
#b #f #L1 #L2 #H elim H -f -L1 -L2 //
[ /2 width=3 by transitive_le/
-| #f #I #L1 #L2 #V1 #V2 #_ #HV21 #IHL12 normalize
- >(lifts_fwd_tw … HV21) -HV21 /2 width=1 by monotonic_le_plus_l/
+| #f #I1 #I2 #L1 #L2 #_ #HI21 #IHL12 normalize
+ >(liftsb_fwd_bw … HI21) -HI21 /2 width=1 by monotonic_le_plus_l/
]
qed-.
(* Basic_2A1: includes: drop_fwd_lw_lt *)
-lemma drops_fwd_lw_lt: â\88\80f,L1,L2. â¬\87*[â\93\89, f] L1 â\89¡ L2 →
+lemma drops_fwd_lw_lt: â\88\80f,L1,L2. â¬\87*[â\93\89, f] L1 â\89\98 L2 →
(𝐈⦃f⦄ → ⊥) → ♯{L2} < ♯{L1}.
#f #L1 #L2 #H elim H -f -L1 -L2
[ #f #Hf #Hnf elim Hnf -Hnf /2 width=1 by/
| /3 width=3 by drops_fwd_lw, le_to_lt_to_lt/
-| #f #I #L1 #L2 #V1 #V2 #_ #HV21 #IHL12 #H normalize in ⊢ (?%%); -I
- >(lifts_fwd_tw … HV21) -V2 /5 width=3 by isid_push, monotonic_lt_plus_l/
+| #f #I1 #I2 #L1 #L2 #_ #HI21 #IHL12 #H normalize in ⊢ (?%%);
+ >(liftsb_fwd_bw … HI21) -I2 /5 width=3 by isid_push, monotonic_lt_plus_l/
]
qed-.
(* Forward lemmas with restricted weight for closures ***********************)
(* Basic_2A1: includes: drop_fwd_rfw *)
-lemma drops_pair2_fwd_rfw: ∀b,f,I,L,K,V. ⬇*[b, f] L ≡ K.ⓑ{I}V → ∀T. ♯{K, V} < ♯{L, T}.
+lemma drops_bind2_fwd_rfw: ∀b,f,I,L,K,V. ⬇*[b, f] L ≘ K.ⓑ{I}V → ∀T. ♯{K, V} < ♯{L, T}.
#b #f #I #L #K #V #HLK lapply (drops_fwd_lw … HLK) -HLK
-normalize in ⊢ (%→?→?%%); /3 width=3 by le_to_lt_to_lt/
+normalize in ⊢ (%→?→?%%); /3 width=3 by le_to_lt_to_lt, monotonic_lt_plus_r/
qed-.
(* Advanced inversion lemma *************************************************)
-lemma drops_inv_x_pair_xy: ∀b,f,I,L,V. ⬇*[b,f] L ≡ L.ⓑ{I}V → ⊥.
-#b #f #I #L #V #H lapply (drops_fwd_lw … H) -b -f
+lemma drops_inv_x_bind_xy: ∀b,f,I,L. ⬇*[b, f] L ≘ L.ⓘ{I} → ⊥.
+#b #f #I #L #H lapply (drops_fwd_lw … H) -b -f
/2 width=4 by lt_le_false/ (**) (* full auto is a bit slow: 19s *)
qed-.