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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/tshf.ma".
16 include "basic_2/reduction/cpr.ma".
18 (* CONTEXT-SENSITIVE PARALLEL REDUCTION FOR TERMS ***************************)
20 (* Forward lemmas on same head forms for terms ******************************)
22 lemma cpr_fwd_tshf1: ∀L,T1,T2. L ⊢ T1 ➡ T2 → T1 ≈ T1 →
23 T2 ≈ T1 ∨ (L = ⋆ → ⊥).
24 #L #T1 #T2 #H elim H -L -T1 -T2
26 | #L #K #V1 #V2 #W2 #i #HLK #_ #_ #_ #_
27 @or_intror #H destruct
28 lapply (ldrop_inv_atom1 … HLK) -HLK #H destruct
29 | #a #I #L #V1 #V2 #T1 #T2 #_ #_ #_ #_ #H
30 elim (tshf_inv_bind1 … H) -H #W2 #U2 #H1 * #H2 destruct /2 width=1/
31 | #I #L #V1 #V2 #T1 #T2 #_ #_ #_ #IHT12 #H
32 elim (tshf_inv_flat1 … H) -H #W2 #U2 #HT1U2 #HT1 #_ #H1 #H2 destruct
33 lapply (IHT12 HT1U2) -IHT12 -HT1U2 * #HUT2 /3 width=1/
34 lapply (simple_tshf_repl_sn … HUT2 HT1) /3 width=1/
35 | #L #V #T #T1 #T2 #_ #_ #_ #H
36 elim (tshf_inv_bind1 … H) -H #W2 #U2 #H1 * #H2 destruct
37 | #L #V #T1 #T2 #_ #_ #H
38 elim (tshf_inv_flat1 … H) -H #W2 #U2 #_ #_ #_ #H destruct
39 | #a #L #V1 #V2 #W #T1 #T2 #_ #_ #_ #_ #H
40 elim (tshf_inv_flat1 … H) -H #W2 #U2 #_ #H
41 elim (simple_inv_bind … H)
42 | #a #L #V2 #V1 #V #W1 #W2 #T1 #T2 #_ #_ #_ #_ #_ #_ #_ #H
43 elim (tshf_inv_flat1 … H) -H #U1 #U2 #_ #H
44 elim (simple_inv_bind … H)