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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/syntax/term_simple.ma".
16 include "basic_2/syntax/tsts.ma".
18 (* SAME TOP TERM STRUCTURE **************************************************)
20 (* Properies with simple (neutral) terms ************************************)
22 lemma simple_tsts_repl_dx: ∀h,o,T1,T2. T1 ⩳[h, o] T2 → 𝐒⦃T1⦄ → 𝐒⦃T2⦄.
23 #h #o #T1 #T2 * -T1 -T2 //
25 elim (simple_inv_pair … H) -H #J #H destruct //
28 lemma simple_tsts_repl_sn: ∀h,o,T1,T2. T1 ⩳[h, o] T2 → 𝐒⦃T2⦄ → 𝐒⦃T1⦄.
29 /3 width=5 by simple_tsts_repl_dx, tsts_sym/ qed-.