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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 UNCOUNTED PARALLEL RT-TRANSITION **********)
20 (* Properties with simple terms *********************************************)
22 lemma csx_appl_simple: ∀h,o,G,L,V. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄ → ∀T1.
23 (∀T2. ⦃G, L⦄ ⊢ T1 ⬈[h] T2 → (T1 ≛[h, o] T2 → ⊥) → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓐV.T2⦄) →
24 𝐒⦃T1⦄ → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓐV.T1⦄.
25 #h #o #G #L #V #H @(csx_ind … H) -V
26 #V #_ #IHV #T1 #IHT1 #HT1
28 elim (cpx_inv_appl1_simple … H1) // -H1
29 #V0 #T0 #HLV0 #HLT10 #H destruct
30 elim (tdneq_inv_pair … H2) -H2
32 | #HV0 @(csx_cpx_trans … (ⓐV0.T1)) /2 width=1 by cpx_flat/ -HLT10
33 @(IHV … HLV0 … HV0) -HV0 /4 width=5 by csx_cpx_trans, cpx_pair_sn/ (**) (* full auto too slow *)
34 | -IHV -HT1 /4 width=3 by csx_cpx_trans, cpx_pair_sn/