lemma fquq_refl: tri_reflexive … fquq.
/2 width=3 by fquq_drop/ qed.
-lemma fqu_fquq: â\88\80G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\83 â¦\83G2, L2, T2â¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 â\8a\83⸮ ⦃G2, L2, T2⦄.
+lemma fqu_fquq: â\88\80G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\90 â¦\83G2, L2, T2â¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 â\8a\90⸮ ⦃G2, L2, T2⦄.
#G1 #G2 #L1 #L2 #T1 #T2 #H elim H -L1 -L2 -T1 -T2 /2 width=3 by fquq_drop/
qed.
(* Basic forward lemmas *****************************************************)
-lemma fquq_fwd_fw: â\88\80G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\83⸮ ⦃G2, L2, T2⦄ → ♯{G2, L2, T2} ≤ ♯{G1, L1, T1}.
+lemma fquq_fwd_fw: â\88\80G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\90⸮ ⦃G2, L2, T2⦄ → ♯{G2, L2, T2} ≤ ♯{G1, L1, T1}.
#G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 /2 width=1 by lt_to_le/
#G1 #L1 #K1 #T1 #U1 #e #HLK1 #HTU1
lapply (ldrop_fwd_lw … HLK1) -HLK1
/2 width=1 by le_plus, le_n/
qed-.
-fact fquq_fwd_length_lref1_aux: â\88\80G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\83⸮ ⦃G2, L2, T2⦄ →
+fact fquq_fwd_length_lref1_aux: â\88\80G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\90⸮ ⦃G2, L2, T2⦄ →
∀i. T1 = #i → |L2| ≤ |L1|.
#G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 //
[ #a #I #G #L #V #T #j #H destruct
]
qed-.
-lemma fquq_fwd_length_lref1: â\88\80G1,G2,L1,L2,T2,i. â¦\83G1, L1, #iâ¦\84 â\8a\83⸮ ⦃G2, L2, T2⦄ → |L2| ≤ |L1|.
+lemma fquq_fwd_length_lref1: â\88\80G1,G2,L1,L2,T2,i. â¦\83G1, L1, #iâ¦\84 â\8a\90⸮ ⦃G2, L2, T2⦄ → |L2| ≤ |L1|.
/2 width=7 by fquq_fwd_length_lref1_aux/
qed-.