(* 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_gen: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ →
- |G1| = |G2| → |L1| = |L2| → T1 = 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)
-]
+(* Advanced eliminators *****************************************************)
+
+lemma fqu_wf_ind: ∀R:relation3 …. (
+ ∀G1,L1,T1. (∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ → R G2 L2 T2) →
+ R G1 L1 T1
+ ) → ∀G1,L1,T1. R G1 L1 T1.
+#R #HR @(f3_ind … fw) #n #IHn #G1 #L1 #T1 #H destruct /4 width=1 by fqu_fwd_fw/
qed-.