(* Forward lemmas with length for local environments ************************)
-fact fqu_fwd_length_lref1_aux: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ →
+fact fqu_fwd_length_lref1_aux: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⊐[b] ⦃G2,L2,T2⦄ →
∀i. T1 = #i → |L2| < |L1|.
#b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 // [2,3: #p]
#I #G #L #V #T [2: #_ ] #j #H destruct
qed-.
-lemma fqu_fwd_length_lref1: ∀b,G1,G2,L1,L2,T2,i. ⦃G1, L1, #i⦄ ⊐[b] ⦃G2, L2, T2⦄ →
+lemma fqu_fwd_length_lref1: ∀b,G1,G2,L1,L2,T2,i. ⦃G1,L1,#i⦄ ⊐[b] ⦃G2,L2,T2⦄ →
|L2| < |L1|.
/2 width=8 by fqu_fwd_length_lref1_aux/
qed-.