matita/matita/contribs/lambdadelta/delayed_updating/syntax/preterm.ma

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  14
  15 include "delayed_updating/syntax/prototerm.ma".
  16 include "delayed_updating/syntax/path_structure.ma".
  17 include "delayed_updating/notation/relations/predicate_t_hook_1.ma".
  18
  19 (* PRETERM ******************************************************************)
  20
  21 (* Note: different root paths have different structure *)
  22 definition structure_injective: predicate prototerm ≝
  23            λt. ∀p1,p2. p1 ϵ ▵t → p2 ϵ ▵t → ⊗p1 = ⊗p2 → p1 = p2
  24 .
  25
  26 (* Note: a preterm is a prototerm satislying the conditions above *)
  27 record is_preterm (t): Prop ≝
  28 {
  29   is_pt_injective: structure_injective t
  30 }.
  31
  32 interpretation
  33   "preterm condition (prototerm)"
  34   'PredicateTHook t = (is_preterm t).