(* Forward lemmas with weight for closures **********************************)
-lemma fqu_fwd_fw: â\88\80b,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â¬\82[b] â¦\83G2,L2,T2â¦\84 →
- ♯{G2,L2,T2} < ♯{G1,L1,T1}.
+lemma fqu_fwd_fw: â\88\80b,G1,G2,L1,L2,T1,T2. â\9dªG1,L1,T1â\9d« â¬\82[b] â\9dªG2,L2,T2â\9d« →
+ ♯❨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/
(* Advanced eliminators *****************************************************)
lemma fqu_wf_ind: ∀b. ∀Q:relation3 …. (
- â\88\80G1,L1,T1. (â\88\80G2,L2,T2. â¦\83G1,L1,T1â¦\84 â¬\82[b] â¦\83G2,L2,T2â¦\84 → Q G2 L2 T2) →
- Q G1 L1 T1
- ) → ∀G1,L1,T1. Q G1 L1 T1.
+ â\88\80G1,L1,T1. (â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« â¬\82[b] â\9dªG2,L2,T2â\9d« → 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-.