(* *)
(**************************************************************************)
-include "basic_2/grammar/cl_weight.ma".
+include "basic_2/syntax/cl_weight.ma".
include "basic_2/relocation/lifts_weight.ma".
include "basic_2/s_transition/fqu.ma".
(* Forward lemmas with weight for closures **********************************)
-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 //
-#I #G #L #V #T #U #HTU normalize in ⊢ (?%%); -I
-<(lifts_fwd_tw … HTU) -U /3 width=1 by monotonic_lt_plus_r, monotonic_lt_plus_l/
+lemma fqu_fwd_fw: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ →
+ ♯{G2, L2, T2} < ♯{G1, L1, T1}.
+#b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 //
+#I #I1 #I2 #G #L #HI12 normalize in ⊢ (?%%); -I1
+<(lifts_fwd_tw … HI12) /3 width=1 by monotonic_lt_plus_r, monotonic_lt_plus_l/
qed-.
(* 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) #x #IHx #G1 #L1 #T1 #H destruct /4 width=1 by fqu_fwd_fw/
+lemma fqu_wf_ind: ∀b. ∀Q:relation3 …. (
+ ∀G1,L1,T1. (∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ → Q G2 L2 T2) →
+ Q G1 L1 T1
+ ) → ∀G1,L1,T1. Q G1 L1 T1.
+#b #Q #HQ @(f3_ind … fw) #x #IHx #G1 #L1 #T1 #H destruct /4 width=2 by fqu_fwd_fw/
qed-.