include "basic_2/notation/relations/supterm_6.ma".
include "basic_2/grammar/cl_weight.ma".
-include "basic_2/grammar/bteq.ma".
include "basic_2/relocation/ldrop.ma".
(* SUPCLOSURE ***************************************************************)
(* Basic properties *********************************************************)
lemma fqu_drop_lt: ∀G,L,K,T,U,e. 0 < e →
- ⇩[0, e] L ≡ K → ⇧[0, e] T ≡ U → fqu G L U G K T.
+ ⇩[0, e] L ≡ K → ⇧[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.
/2 width=7 by fqu_fwd_length_lref1_aux/
qed-.
-lemma fqu_fwd_bteq: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ →
- ⦃G1, L1, T1⦄ ⋕ ⦃G2, L2, T2⦄ → ⊥.
-#G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
-[ #I #G #L #V * #_ #H elim (plus_xSy_x_false … H)
-| #I #G #L #V #T * #_ #_ #H elim (discr_tpair_xy_x … H)
-| #a #I #G #L #V #T * #_ #_ #H elim (discr_tpair_xy_y … H)
-| #I #G #L #V #T * #_ #_ #H elim (discr_tpair_xy_y … H)
-| #G #L #K #T #U #e #HLK #_ * #_ #H
- lapply (ldrop_fwd_length_lt4 … HLK ?) // >H -L #H
- elim (lt_refl_false … H)
-]
-qed-.
-
(* Advanced eliminators *****************************************************)
lemma fqu_wf_ind: ∀R:relation3 …. (