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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "basic_2/reducibility/trf.ma".
17 (* CONTEXT-FREE IRREDUCIBLE TERMS *******************************************)
19 definition tif: predicate term โ ฮปT. ๐[T] โ โฅ.
21 interpretation "context-free irreducibility (term)"
22 'NotReducible T = (tif T).
24 (* Basic inversion lemmas ***************************************************)
26 lemma tif_inv_abbr: โV,T. ๐[โV.T] โ โฅ.
29 lemma tif_inv_abst: โV,T. ๐[โV.T] โ ๐[V] โง ๐[T].
32 lemma tif_inv_appl: โV,T. ๐[โV.T] โ โงโง ๐[V] & ๐[T] & ๐[T].
33 #V #T #HVT @and3_intro /3 width=1/
34 generalize in match HVT; -HVT elim T -T //
35 * // * #U #T #_ #_ #H elim (H ?) -H /2 width=1/
38 lemma tif_inv_cast: โV,T. ๐[โฃV.T] โ โฅ.
41 (* Basic properties *********************************************************)
43 lemma tif_atom: โI. ๐[โช{I}].
46 lemma tif_abst: โV,T. ๐[V] โ ๐[T] โ ๐[โV.T].
48 elim (trf_inv_abst โฆ H) -H /2 width=1/
51 lemma tif_appl: โV,T. ๐[V] โ ๐[T] โ ๐[T] โ ๐[โV.T].
53 elim (trf_inv_appl โฆ H) -H /2 width=1/