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Add better heading to Postponement
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yfyf committed Feb 11, 2014
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Expand Up @@ -13,15 +13,24 @@ Require Import Rels.
Require Import Beta.
Require Import Eta.

(** * Postponement theorem in Untyped Lambda Calculus *)

Module Export Postpone.

(** In this module, we prove the eta postponement theorem.
(** This module contains a formalised proof of the ($\eta$#η#-)Postponement
Theorem for the untyped lambda calculus.
The formalisation is based on an ``informal'' proof due to Masako Takahashi
in ``Parallel Reductions in Lambda-calculus'' (Information and Computation,
Volume 118, 1995).
We (continue to) follow the proof of Masako Takahashi from
"Parallel Reductions in Lambda-calculus" (1995).
Except for the gymnastics related to working with de Bruijn indices, the
translation of the Takashi's proof is rather straightforward.
**)

(** We now prove various properties about the relation between [beta_par]
(** ** Preliminaries *)

(** We at first prove various properties about the relation between [beta_par]
and the eta-expansion [lam_k]. (This is Lemma 3.3 in Takahashi).
We however do it in in a slightly different order than in the paper,
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