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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 "static_2/syntax/toeq_simple.ma".
16 include "static_2/syntax/toeq_toeq.ma".
17 include "basic_2/rt_transition/cpx_simple.ma".
18 include "basic_2/rt_computation/cpxs.ma".
19 include "basic_2/rt_computation/csx_csx.ma".
21 (* STRONGLY NORMALIZING TERMS FOR UNBOUND PARALLEL RT-TRANSITION ************)
23 (* Properties with outer equivalence for terms ******************************)
25 (* Basic_1: was just: sn3_appl_appl *)
26 (* Basic_2A1: was: csx_appl_simple_tsts *)
27 lemma csx_appl_simple_toeq (h) (G) (L):
28 ∀V. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃V⦄ → ∀T1. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T1⦄ →
29 (∀T2. ⦃G,L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ⩳ T2 → ⊥) → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓐV.T2⦄) →
30 𝐒⦃T1⦄ → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓐV.T1⦄.
31 #h #G #L #V #H @(csx_ind … H) -V
32 #V #_ #IHV #T1 #H @(csx_ind … H) -T1
33 #T1 #H1T1 #IHT1 #H2T1 #H3T1
35 elim (cpx_inv_appl1_simple … HL) -HL //
36 #V0 #T0 #HLV0 #HLT10 #H0 destruct
37 elim (tdneq_inv_pair … H) -H
40 @(csx_cpx_trans … (ⓐV0.T1)) /2 width=1 by cpx_flat/ -HLT10
41 @IHV -IHV /4 width=3 by csx_cpx_trans, cpx_pair_sn/
43 @(csx_cpx_trans … (ⓐV.T0)) /2 width=1 by cpx_flat/ -HLV0
44 elim (toeq_dec T1 T0) #H2T10
45 [ @IHT1 -IHT1 /4 width=5 by cpxs_strap2, cpxs_strap1, toeq_canc_sn, simple_toeq_repl_dx/
46 | -IHT1 -H3T1 -H1T10 /3 width=1 by cpx_cpxs/