matita/matita/contribs/lambdadelta/basic_2/examples/ex_cpr_omega.ma

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  14
  15 include "basic_2/reduction/cpr.ma".
  16
  17 (* EXAMPLES *****************************************************************)
  18
  19 (* A reduction cycle in two steps: the term Omega ***************************)
  20
  21 definition Delta: term ≝ +ⓛ⋆0.ⓐ#0.#0.
  22
  23 definition Omega1: term ≝ ⓐDelta.Delta.
  24
  25 definition Omega2: term ≝ +ⓓⓝ⋆0.Delta.ⓐ#0.#0.
  26
  27 (* Basic properties *********************************************************)
  28
  29 lemma Delta_lift: ∀d,e. ⇧[d, e] Delta ≡ Delta.
  30 /4 width=1 by lift_flat, lift_bind, lift_lref_lt/ qed.
  31
  32 (* Main properties **********************************************************)
  33
  34 theorem cpr_Omega_12: ⦃⋆, ⋆⦄ ⊢ Omega1 ➡ Omega2.
  35 /2 width=1 by cpr_beta/ qed.
  36
  37 theorem cpr_Omega_21: ⦃⋆, ⋆⦄ ⊢ Omega2 ➡ Omega1.
  38 @(cpr_zeta … Omega1) /2 width=1 by lift_flat/
  39 @cpr_flat @(cpr_delta … Delta ? 0)
  40 [3,5,8,10: // |4,9: /2 width=1 by cpr_eps/ |*: skip ]
  41 qed.