(* Forward lemmas with weight for closures **********************************)
-lemma fqup_fwd_fw: â\88\80b,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â\8a\90+[b] ⦃G2,L2,T2⦄ →
+lemma fqup_fwd_fw: â\88\80b,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â¬\82+[b] ⦃G2,L2,T2⦄ →
♯{G2,L2,T2} < ♯{G1,L1,T1}.
#b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
/3 width=3 by fqu_fwd_fw, transitive_lt/
(* Advanced eliminators *****************************************************)
lemma fqup_wf_ind: ∀b. ∀Q:relation3 …. (
- â\88\80G1,L1,T1. (â\88\80G2,L2,T2. â¦\83G1,L1,T1â¦\84 â\8a\90+[b] ⦃G2,L2,T2⦄ → Q G2 L2 T2) →
+ â\88\80G1,L1,T1. (â\88\80G2,L2,T2. â¦\83G1,L1,T1â¦\84 â¬\82+[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
qed-.
lemma fqup_wf_ind_eq: ∀b. ∀Q:relation3 …. (
- â\88\80G1,L1,T1. (â\88\80G2,L2,T2. â¦\83G1,L1,T1â¦\84 â\8a\90+[b] ⦃G2,L2,T2⦄ → Q G2 L2 T2) →
+ â\88\80G1,L1,T1. (â\88\80G2,L2,T2. â¦\83G1,L1,T1â¦\84 â¬\82+[b] ⦃G2,L2,T2⦄ → Q G2 L2 T2) →
∀G2,L2,T2. G1 = G2 → L1 = L2 → T1 = T2 → Q G2 L2 T2
) → ∀G1,L1,T1. Q G1 L1 T1.
#b #Q #HQ @(f3_ind … fw) #x #IHx #G1 #L1 #T1 #H destruct