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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "basic_2/syntax/tdeq_tdeq.ma".
16 include "basic_2/rt_transition/lfpx_lfdeq.ma".
17 include "basic_2/rt_computation/csx.ma".
19 (* STRONGLY NORMALIZING TERMS FOR UNCOUNTED PARALLEL RT-TRANSITION **********)
21 (* Advanced properties ******************************************************)
23 lemma csx_tdeq_trans: ∀h,o,G,L,T1. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃T1⦄ →
24 ∀T2. T1 ≡[h, o] T2 → ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃T2⦄.
25 #h #o #G #L #T1 #H @(csx_ind … H) -T1 #T #_ #IH #T2 #HT2
26 @csx_intro #T1 #HT21 #HnT21 elim (tdeq_cpx_trans … HT2 … HT21) -HT21
27 /4 width=5 by tdeq_repl/
30 lemma csx_cpx_trans: ∀h,o,G,L,T1. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃T1⦄ →
31 ∀T2. ⦃G, L⦄ ⊢ T1 ⬈[h] T2 → ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃T2⦄.
32 #h #o #G #L #T1 #H @(csx_ind … H) -T1 #T1 #HT1 #IHT1 #T2 #HLT12
33 elim (tdeq_dec h o T1 T2) /3 width=4 by csx_tdeq_trans/
36 (* Basic_1: was just: sn3_cast *)
37 lemma csx_cast: ∀h,o,G,L,W. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃W⦄ →
38 ∀T. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃T⦄ → ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃ⓝW.T⦄.
39 #h #o #G #L #W #HW @(csx_ind … HW) -W
40 #W #HW #IHW #T #HT @(csx_ind … HT) -T
41 #T #HT #IHT @csx_intro
42 #X #H1 #H2 elim (cpx_inv_cast1 … H1) -H1
43 [ * #W0 #T0 #HLW0 #HLT0 #H destruct
44 elim (tdeq_false_inv_pair … H2) -H2
45 [ -W -T #H elim H -H //
46 | -HW -IHT /3 width=3 by csx_cpx_trans/
47 | -HW -HT -IHW /4 width=3 by csx_cpx_trans, cpx_pair_sn/
49 |*: /3 width=3 by csx_cpx_trans/