lemma fqus_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 @(fqus_ind … H) -L2 -T2
-/3 width=3 by fquq_fwd_fw, transitive_le/
+/3 width=3 by fquq_fwd_fw, nle_trans/
qed-.
(* Advanced inversion lemmas ************************************************)
lemma fqus_inv_refl_atom3: ∀b,I,G,L,X. ❪G,L,⓪[I]❫ ⬂*[b] ❪G,L,X❫ → ⓪[I] = X.
#b #I #G #L #X #H elim (fqus_inv_fqu_sn … H) -H * //
#G0 #L0 #T0 #H1 #H2 lapply (fqu_fwd_fw … H1) lapply (fqus_fwd_fw … H2) -H2 -H1
-#H2 #H1 lapply (le_to_lt_to_lt … H2 H1) -G0 -L0 -T0
-#H elim (lt_le_false … H) -H /2 width=1 by monotonic_le_plus_r/
+#H2 #H1 lapply (nle_nlt_trans … H2 H1) -G0 -L0 -T0
+#H elim (nlt_ge_false … H) -H /2 width=1 by nle_plus_bi_sn/
qed-.