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4 (* ||A|| A project by Andrea Asperti *)
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15 include "static_2/s_transition/fqu_weight.ma".
16 include "static_2/s_computation/fqup.ma".
18 (* PLUS-ITERATED SUPCLOSURE *************************************************)
20 (* Forward lemmas with weight for closures **********************************)
22 lemma fqup_fwd_fw: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ →
23 ♯{G2, L2, T2} < ♯{G1, L1, T1}.
24 #b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
25 /3 width=3 by fqu_fwd_fw, transitive_lt/
28 (* Advanced eliminators *****************************************************)
30 lemma fqup_wf_ind: ∀b. ∀Q:relation3 …. (
31 ∀G1,L1,T1. (∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ → Q G2 L2 T2) →
33 ) → ∀G1,L1,T1. Q G1 L1 T1.
34 #b #Q #HQ @(f3_ind … fw) #x #IHx #G1 #L1 #T1 #H destruct
35 /4 width=2 by fqup_fwd_fw/
38 lemma fqup_wf_ind_eq: ∀b. ∀Q:relation3 …. (
39 ∀G1,L1,T1. (∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ → Q G2 L2 T2) →
40 ∀G2,L2,T2. G1 = G2 → L1 = L2 → T1 = T2 → Q G2 L2 T2
41 ) → ∀G1,L1,T1. Q G1 L1 T1.
42 #b #Q #HQ @(f3_ind … fw) #x #IHx #G1 #L1 #T1 #H destruct
43 /4 width=7 by fqup_fwd_fw/