matita/matita/contribs/lambdadelta/basic_2/etc/tdpos/cnv_cpms_tdpos.etc

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   3 (*      ||M||                                                             *)
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  14
  15 include "basic_2/dynamic/cnv_cpm_tdpos.ma".
  16
  17 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
  18
  19 (* Forward lemmas with positive rt-computation for terms ********************)
  20
  21 lemma cpms_fwd_tdpos_sn (a) (h) (o) (n) (G) (L):
  22                         ∀T1. ⦃G,L⦄ ⊢ T1 ![a,h] → 𝐏[h,o]⦃T1⦄ →
  23                         ∀T2. ⦃G,L⦄ ⊢ T1 ➡*[n,h] T2 →
  24                         ∨∨ ∧∧ T1 = T2 & 0 = n
  25                          | ∃∃n1,n2,T. ⦃G,L⦄ ⊢ T1 ➡[n1,h] T & (T1 ≛[h,o] T → ⊥) & ⦃G,L⦄ ⊢ T ➡*[n2,h] T2 & n1+n2=n.
  26 #a #h #o #n #G #L #T1 #H1T1 #H2T1 #T2 #H
  27 @(cpms_ind_dx … H) -n -T2
  28 [ /3 width=1 by or_introl, conj/
  29 | #n1 #n2 #T #T2 #HT1 * *
  30   [ #H1 #H2 #HT2 destruct -HT1
  31     elim (cpm_fwd_tdpos_sn … H1T1 H2T1 … HT2) -H1T1 -H2T1
  32     [ * #H1 #H2 destruct -HT2 /3 width=1 by or_introl, conj/
  33     | #HnT2 >commutative_plus in ⊢ (??%); /4 width=7 by ex4_3_intro, or_intror/
  34     ]
  35   | #m1 #m2 #T0 #H1T10 #H2T10 #HT0 #H #HT2 destruct -H1T1 -H2T1 -HT1
  36     >associative_plus in ⊢ (??%); /4 width=7 by cpms_step_dx, ex4_3_intro, or_intror/
  37   ]
  38 ]
  39 qed-.