| fqu_pair_sn: ∀I,G,L,V,T. fqu G L (②{I}V.T) G L V
| fqu_bind_dx: ∀a,I,G,L,V,T. fqu G L (ⓑ{a,I}V.T) G (L.ⓑ{I}V) T
| fqu_flat_dx: ∀I,G,L,V,T. fqu G L (ⓕ{I}V.T) G L T
-| fqu_drop : ∀G,L,K,T,U,e.
- ⬇[e+1] L ≡ K → ⬆[0, e+1] T ≡ U → fqu G L U G K T
+| fqu_drop : ∀G,L,K,T,U,m.
+ ⬇[m+1] L ≡ K → ⬆[0, m+1] T ≡ U → fqu G L U G K T
.
interpretation
(* Basic properties *********************************************************)
-lemma fqu_drop_lt: ∀G,L,K,T,U,e. 0 < e →
- ⬇[e] L ≡ K → ⬆[0, e] T ≡ U → ⦃G, L, U⦄ ⊐ ⦃G, K, T⦄.
-#G #L #K #T #U #e #He >(plus_minus_m_m e 1) /2 width=3 by fqu_drop/
+lemma fqu_drop_lt: ∀G,L,K,T,U,m. 0 < m →
+ ⬇[m] L ≡ K → ⬆[0, m] T ≡ U → ⦃G, L, U⦄ ⊐ ⦃G, K, T⦄.
+#G #L #K #T #U #m #Hm >(plus_minus_m_m m 1) /2 width=3 by fqu_drop/
qed.
lemma fqu_lref_S_lt: ∀I,G,L,V,i. 0 < i → ⦃G, L.ⓑ{I}V, #i⦄ ⊐ ⦃G, L, #(i-1)⦄.
lemma fqu_fwd_fw: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → ♯{G2, L2, T2} < ♯{G1, L1, T1}.
#G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 //
-#G #L #K #T #U #e #HLK #HTU
+#G #L #K #T #U #m #HLK #HTU
lapply (drop_fwd_lw_lt … HLK ?) -HLK // #HKL
-lapply (lift_fwd_tw … HTU) -e #H
+lapply (lift_fwd_tw … HTU) -m #H
normalize in ⊢ (?%%); /2 width=1 by lt_minus_to_plus/
qed-.
G1 = G2 → |L1| = |L2| → T1 = T2 → ⊥.
#G1 #G2 #L1 #L2 #T1 #T2 * -G1 -G2 -L1 -L2 -T1 -T2 normalize
/2 width=4 by discr_tpair_xy_y, discr_tpair_xy_x, plus_xSy_x_false/
-#G #L #K #T #U #e #HLK #_ #_ #H #_ -G -T -U >(drop_fwd_length … HLK) in H; -L
+#G #L #K #T #U #m #HLK #_ #_ #H #_ -G -T -U >(drop_fwd_length … HLK) in H; -L
/2 width=4 by plus_xySz_x_false/
qed-.