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15 include "basic_2/rt_transition/cpx_simple.ma".
16 include "basic_2/rt_computation/csx_csx.ma".
18 (* STRONGLY NORMALIZING TERMS FOR UNBOUND PARALLEL RT-TRANSITION ************)
20 (* Properties with simple terms *********************************************)
22 lemma csx_appl_simple (h) (G) (L):
23 ∀V. ❪G,L❫ ⊢ ⬈*𝐒[h] V → ∀T1.
24 (∀T2. ❪G,L❫ ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → ❪G,L❫ ⊢ ⬈*𝐒[h] ⓐV.T2) →
25 𝐒❪T1❫ → ❪G,L❫ ⊢ ⬈*𝐒[h] ⓐV.T1.
26 #h #G #L #V #H @(csx_ind … H) -V
27 #V #_ #IHV #T1 #IHT1 #HT1
29 elim (cpx_inv_appl1_simple … H1) // -H1
30 #V0 #T0 #HLV0 #HLT10 #H destruct
31 elim (tneqx_inv_pair … H2) -H2
33 | #HV0 @(csx_cpx_trans … (ⓐV0.T1)) /2 width=1 by cpx_flat/ -HLT10
34 @(IHV … HLV0 … HV0) -HV0 /4 width=5 by csx_cpx_trans, cpx_pair_sn/ (**) (* full auto too slow *)
35 | -IHV -HT1 /4 width=3 by csx_cpx_trans, cpx_pair_sn/