lemma fqu_sort: ∀b,I,G,L,s. ⦃G, L.ⓘ{I}, ⋆s⦄ ⊐[b] ⦃G, L, ⋆s⦄.
/2 width=1 by fqu_drop/ qed.
-lemma fqu_lref_S: â\88\80b,I,G,L,i. â¦\83G, L.â\93\98{I}, #⫯i⦄ ⊐[b] ⦃G, L, #i⦄.
+lemma fqu_lref_S: â\88\80b,I,G,L,i. â¦\83G, L.â\93\98{I}, #â\86\91i⦄ ⊐[b] ⦃G, L, #i⦄.
/2 width=1 by fqu_drop/ qed.
lemma fqu_gref: ∀b,I,G,L,l. ⦃G, L.ⓘ{I}, §l⦄ ⊐[b] ⦃G, L, §l⦄.
fact fqu_inv_lref1_aux: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ →
∀i. T1 = #i →
(∃∃J,V. G1 = G2 & L1 = L2.ⓑ{J}V & T2 = V & i = 0) ∨
- â\88\83â\88\83J,j. G1 = G2 & L1 = L2.â\93\98{J} & T2 = #j & i = ⫯j.
+ â\88\83â\88\83J,j. G1 = G2 & L1 = L2.â\93\98{J} & T2 = #j & i = â\86\91j.
#b #G1 #G2 #L1 #L2 #T1 #T2 * -G1 -G2 -L1 -L2 -T1 -T2
[ #I #G #L #T #i #H destruct /3 width=4 by ex4_2_intro, or_introl/
| #I #G #L #V #T #i #H destruct
lemma fqu_inv_lref1: ∀b,G1,G2,L1,L2,T2,i. ⦃G1, L1, #i⦄ ⊐[b] ⦃G2, L2, T2⦄ →
(∃∃J,V. G1 = G2 & L1 = L2.ⓑ{J}V & T2 = V & i = 0) ∨
- â\88\83â\88\83J,j. G1 = G2 & L1 = L2.â\93\98{J} & T2 = #j & i = ⫯j.
+ â\88\83â\88\83J,j. G1 = G2 & L1 = L2.â\93\98{J} & T2 = #j & i = â\86\91j.
/2 width=4 by fqu_inv_lref1_aux/ qed-.
fact fqu_inv_gref1_aux: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ →
#Z #X #H1 #H2 #H3 #H4 destruct /2 width=1 by and3_intro/
qed-.
-lemma fqu_inv_lref1_bind: â\88\80b,I,G1,G2,K,L2,T2,i. â¦\83G1, K.â\93\98{I}, #(⫯i)⦄ ⊐[b] ⦃G2, L2, T2⦄ →
+lemma fqu_inv_lref1_bind: â\88\80b,I,G1,G2,K,L2,T2,i. â¦\83G1, K.â\93\98{I}, #(â\86\91i)⦄ ⊐[b] ⦃G2, L2, T2⦄ →
∧∧ G1 = G2 & L2 = K & T2 = #i.
#b #I #G1 #G2 #K #L2 #T2 #i #H elim (fqu_inv_lref1 … H) -H *
#Z #X #H1 #H2 #H3 #H4 destruct /2 width=1 by and3_intro/