matita/matita/contribs/lambdadelta/basic_2A/substitution/lsuby_lsuby.ma

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  14
  15 include "basic_2A/substitution/lsuby.ma".
  16
  17 (* LOCAL ENVIRONMENT REFINEMENT FOR EXTENDED SUBSTITUTION *******************)
  18
  19 (* Main properties **********************************************************)
  20
  21 theorem lsuby_trans: ∀l,m. Transitive … (lsuby l m).
  22 #l #m #L1 #L2 #H elim H -L1 -L2 -l -m
  23 [ #L1 #l #m #X #H lapply (lsuby_inv_atom1 … H) -H
  24   #H destruct //
  25 | #I1 #I2 #L1 #L #V1 #V #_ #IHL1 #X #H elim (lsuby_inv_zero1 … H) -H //
  26   * #I2 #L2 #V2 #HL2 #H destruct /3 width=1 by lsuby_zero/
  27 | #I1 #I2 #L1 #L2 #V #m #_ #IHL1 #X #H elim (lsuby_inv_pair1 … H) -H //
  28   * #I2 #L2 #HL2 #H destruct /3 width=1 by lsuby_pair/
  29 | #I1 #I2 #L1 #L2 #V1 #V2 #l #m #_ #IHL1 #X #H elim (lsuby_inv_succ1 … H) -H //
  30   * #I2 #L2 #V2 #HL2 #H destruct /3 width=1 by lsuby_succ/
  31 ]
  32 qed-.