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15 include "basic_2/relocation/fqu_lleq.ma".
16 include "basic_2/relocation/fquq_alt.ma".
18 (* OPTIONAL SUPCLOSURE ******************************************************)
20 (* Properties on lazy equivalence for local environments ********************)
22 lemma lleq_fquq_trans: ∀G1,G2,L2,K2,T,U. ⦃G1, L2, T⦄ ⊃⸮ ⦃G2, K2, U⦄ →
24 ∃∃K1. ⦃G1, L1, T⦄ ⊃⸮ ⦃G2, K1, U⦄ & K1 ⋕[0, U] K2.
25 #G1 #G2 #L2 #K2 #T #U #H #L1 #HL12 elim(fquq_inv_gen … H) -H
26 [ #H elim (lleq_fqu_trans … H … HL12) -L2 /3 width=3 by fqu_fquq, ex2_intro/
27 | * #HG #HL #HT destruct /2 width=3 by ex2_intro/