(* Forward lemmas with weight for closures **********************************)
-lemma fqus_fwd_fw: â\88\80b,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â\8a\90*[b] â¦\83G2,L2,T2â¦\84 →
- ♯{G2,L2,T2} ≤ ♯{G1,L1,T1}.
+lemma fqus_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 @(fqus_ind … H) -L2 -T2
/3 width=3 by fquq_fwd_fw, transitive_le/
qed-.
(* Advanced inversion lemmas ************************************************)
-lemma fqus_inv_refl_atom3: â\88\80b,I,G,L,X. â¦\83G,L,â\93ª{I}â¦\84 â\8a\90*[b] â¦\83G,L,Xâ¦\84 â\86\92 â\93ª{I} = X.
+lemma fqus_inv_refl_atom3: â\88\80b,I,G,L,X. â\9dªG,L,â\93ª[I]â\9d« â¬\82*[b] â\9dªG,L,Xâ\9d« â\86\92 â\93ª[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/
-qed-.
+qed-.