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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "basic_2/grammar/cl_weight.ma".
16 include "basic_2/relocation/lifts_weight.ma".
17 include "basic_2/s_transition/fqu.ma".
19 (* SUPCLOSURE ***************************************************************)
21 (* Forward lemmas with weight for closures **********************************)
23 lemma fqu_fwd_fw: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → ♯{G2, L2, T2} < ♯{G1, L1, T1}.
24 #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 //
25 #I #G #L #V #T #U #HTU normalize in ⊢ (?%%); -I
26 <(lifts_fwd_tw … HTU) -U /3 width=1 by monotonic_lt_plus_r, monotonic_lt_plus_l/
29 (* Advanced eliminators *****************************************************)
31 lemma fqu_wf_ind: ∀R:relation3 …. (
32 ∀G1,L1,T1. (∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → R G2 L2 T2) →
34 ) → ∀G1,L1,T1. R G1 L1 T1.
35 #R #HR @(f3_ind … fw) #x #IHx #G1 #L1 #T1 #H destruct /4 width=1 by fqu_fwd_fw/