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4 (* ||A|| A project by Andrea Asperti *)
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15 include "static_2/syntax/term_simple.ma".
16 include "basic_2/rt_transition/cpg.ma".
18 (* BOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS *****************)
20 (* Properties with simple terms *********************************************)
22 (* Note: the main property of simple terms *)
23 lemma cpg_inv_appl1_simple: ∀Rt,c,h,G,L,V1,T1,U. ⦃G, L⦄ ⊢ ⓐV1.T1 ⬈[Rt, c, h] U → 𝐒⦃T1⦄ →
24 ∃∃cV,cT,V2,T2. ⦃G, L⦄ ⊢ V1 ⬈[Rt, cV, h] V2 & ⦃G, L⦄ ⊢ T1 ⬈[Rt, cT, h] T2 &
25 U = ⓐV2.T2 & c = ((↕*cV)∨cT).
26 #Rt #c #h #G #L #V1 #T1 #U #H #HT1 elim (cpg_inv_appl1 … H) -H *
27 [ /2 width=8 by ex4_4_intro/
28 | #cV #cW #cT #p #V2 #W1 #W2 #U1 #U2 #_ #_ #_ #H destruct
29 elim (simple_inv_bind … HT1)
30 | #cV #cW #cT #p #V #V2 #W1 #W2 #U1 #U2 #_ #_ #_ #_ #H destruct
31 elim (simple_inv_bind … HT1)