matita/matita/contribs/lambdadelta/basic_2/grammar/leq_leq.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  14
  15 include "basic_2/grammar/leq.ma".
  16
  17 (* EQUIVALENCE FOR LOCAL ENVIRONMENTS ***************************************)
  18
  19 (* Main properties **********************************************************)
  20
  21 theorem leq_trans: ∀d,e. Transitive … (leq d e).
  22 #d #e #L1 #L2 #H elim H -L1 -L2 -d -e
  23 [ #d #e #X #H lapply (leq_inv_atom1 … H) -H
  24   #H destruct //
  25 | #I1 #I #L1 #L #V1 #V #_ #IHL1 #X #H elim (leq_inv_zero1 … H) -H
  26   #I2 #L2 #V2 #HL2 #H destruct /3 width=1 by leq_zero/
  27 | #I #L1 #L #V #e #_ #IHL1 #X #H elim (leq_inv_pair1 … H) -H //
  28   #L2 #HL2 #H destruct /3 width=1 by leq_pair/
  29 | #I1 #I #L1 #L #V1 #V #d #e #_ #IHL1 #X #H elim (leq_inv_succ1 … H) -H //
  30   #I2 #L2 #V2 #HL2 #H destruct /3 width=1 by leq_succ/
  31 ]
  32 qed-.