include "basic_2/notation/relations/supterm_6.ma".
include "basic_2/grammar/cl_weight.ma".
-include "basic_2/substitution/ldrop.ma".
+include "basic_2/substitution/drop.ma".
(* SUPCLOSURE ***************************************************************)
| fqu_bind_dx: ∀a,I,G,L,V,T. fqu G L (ⓑ{a,I}V.T) G (L.ⓑ{I}V) T
| fqu_flat_dx: ∀I,G,L,V,T. fqu G L (ⓕ{I}V.T) G L T
| fqu_drop : ∀G,L,K,T,U,e.
- â\87©[e+1] L â\89¡ K â\86\92 â\87§[0, e+1] T ≡ U → fqu G L U G K T
+ â¬\87[e+1] L â\89¡ K â\86\92 â¬\86[0, e+1] T ≡ U → fqu G L U G K T
.
interpretation
(* Basic properties *********************************************************)
lemma fqu_drop_lt: ∀G,L,K,T,U,e. 0 < e →
- â\87©[e] L â\89¡ K â\86\92 â\87§[0, e] T ≡ U → ⦃G, L, U⦄ ⊐ ⦃G, K, T⦄.
+ â¬\87[e] L â\89¡ K â\86\92 â¬\86[0, e] T ≡ U → ⦃G, L, U⦄ ⊐ ⦃G, K, T⦄.
#G #L #K #T #U #e #He >(plus_minus_m_m e 1) /2 width=3 by fqu_drop/
qed.
lemma fqu_lref_S_lt: ∀I,G,L,V,i. 0 < i → ⦃G, L.ⓑ{I}V, #i⦄ ⊐ ⦃G, L, #(i-1)⦄.
-/3 width=3 by fqu_drop, ldrop_drop, lift_lref_ge_minus/
+/3 width=3 by fqu_drop, drop_drop, lift_lref_ge_minus/
qed.
(* Basic forward lemmas *****************************************************)
lemma fqu_fwd_fw: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → ♯{G2, L2, T2} < ♯{G1, L1, T1}.
#G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 //
#G #L #K #T #U #e #HLK #HTU
-lapply (ldrop_fwd_lw_lt … HLK ?) -HLK // #HKL
+lapply (drop_fwd_lw_lt … HLK ?) -HLK // #HKL
lapply (lift_fwd_tw … HTU) -e #H
normalize in ⊢ (?%%); /2 width=1 by lt_minus_to_plus/
qed-.
#G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
[1: normalize //
|3: #a
-|5: /2 width=4 by ldrop_fwd_length_lt4/
+|5: /2 width=4 by drop_fwd_length_lt4/
] #I #G #L #V #T #j #H destruct
qed-.