(* 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 #I1 #I2 #L1 #L2 #_ #HI21 #IHL12 normalize
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/
(* Forward lemmas with restricted weight for closures ***********************)
(* Basic_2A1: includes: drop_fwd_rfw *)
-lemma drops_bind2_fwd_rfw: â\88\80b,f,I,L,K,V. â¬\87*[b, f] L â\89¡ K.ⓑ{I}V → ∀T. ♯{K, V} < ♯{L, T}.
+lemma drops_bind2_fwd_rfw: â\88\80b,f,I,L,K,V. â¬\87*[b, f] L â\89\98 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, monotonic_lt_plus_r/
qed-.
(* Advanced inversion lemma *************************************************)
-lemma drops_inv_x_bind_xy: â\88\80b,f,I,L. â¬\87*[b, f] L â\89¡ L.ⓘ{I} → ⊥.
+lemma drops_inv_x_bind_xy: â\88\80b,f,I,L. â¬\87*[b, f] L â\89\98 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-.