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4 (* ||A|| A project by Andrea Asperti *)
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15 include "static_2/syntax/term_simple.ma".
16 include "static_2/syntax/theq.ma".
18 (* HEAD EQUIVALENCE FOR TERMS ***********************************************)
20 (* Properies with simple (neutral) terms ************************************)
22 (* Basic_2A1: was: simple_tsts_repl_dx *)
23 lemma simple_theq_repl_dx: ∀T1,T2. T1 ⩳ T2 → 𝐒⦃T1⦄ → 𝐒⦃T2⦄.
26 elim (simple_inv_pair … H) -H #J #H destruct //
29 (* Basic_2A1: was: simple_tsts_repl_sn *)
30 lemma simple_theq_repl_sn: ∀T1,T2. T1 ⩳ T2 → 𝐒⦃T2⦄ → 𝐒⦃T1⦄.
31 /3 width=3 by simple_theq_repl_dx, theq_sym/ qed-.