matita/matita/contribs/lambdadelta/basic_2/etc/csup/csup_csup.etc

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   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
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  14
  15 include "basic_2/substitution/ldrop_ldrop.ma".
  16 include "basic_2/substitution/csup.ma".
  17
  18 (* SUPCLOSURE ***************************************************************)
  19
  20 (* Main forward lemmas ******************************************************)
  21
  22 theorem csup_trans_fwd_refl: ∀L,L0,T1,T2. ⦃L, T1⦄ > ⦃L0, T2⦄ →
  23                              ∀T3. ⦃L0, T2⦄ > ⦃L, T3⦄ →
  24                              L = L0 ∨ ⦃L, T1⦄ > ⦃L, T3⦄.
  25 #L #L0 #T1 #T2 * -L -L0 -T1 -T2 /2 width=1/
  26 [ #I #L0 #K0 #V0 #i #HLK0 #T3 #H
  27   lapply (ldrop_pair2_fwd_cw … HLK0 T3) -HLK0 #H1
  28   lapply (csup_fwd_cw … H) -H #H2
  29   lapply (transitive_lt … H1 H2) -H1 -H2 #H
  30   elim (lt_refl_false … H)
  31 | #a #I #L0 #V2 #T2 #T3 #HT23
  32   elim (csup_inv_ldrop … HT23 I V2 0 ?) -HT23 // #H1 #H2 destruct /2 width=1/
  33   qed-.