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Cleanup unused definitions and cheated lemmas...
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binghe committed Dec 5, 2023
1 parent 322cb39 commit c6e0300
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41 changes: 0 additions & 41 deletions examples/lambda/barendregt/boehmScript.sml
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Expand Up @@ -737,47 +737,6 @@ Proof
>> rw [Abbr ‘p3’]
QED

(* Definition 10.3.10 (ii) *)
Definition is_faithful_def :
is_faithful p Fs pi =
!M N. M IN Fs /\ N IN Fs ==>
(subterm_eta_equiv p M N <=> equivalent (apply pi M) (apply pi N)) /\
(!X. IS_SOME (ltree_lookup (BT X M) p) <=>
solvable (apply pi M))
End

Definition term_agrees_upto_def :
term_agrees_upto M N p <=>
!q. q <<= p ==> !X. ltree_el (BT X M) q = ltree_el (BT X N) q
End

(* Definition 10.3.10 (iv) *)
val _ = set_fixity "agrees_upto" (Infixr 490);
Definition agrees_upto_def :
$agrees_upto Fs p = !M N. M IN Fs /\ N IN Fs ==> term_agrees_upto M N p
End

(* Lemma 10.3.11 (3) [1. p.251] *)
Theorem agrees_upto_lemma :
!Fs p. Fs agrees_upto p ==>
?pi. Boehm_transform pi /\
!M N. M IN Fs /\ N IN Fs ==>
(subterm_eta_equiv p M N <=>
subterm_eta_equiv p (apply pi M) (apply pi N))
Proof
cheat
QED

(* Proposition 10.3.13 [1, p.253]
Used by separability_thm
*)
Theorem agrees_upto_thm :
!Fs p. Fs agrees_upto p ==> ?pi. Boehm_transform pi /\ is_faithful p Fs pi
Proof
cheat
QED

(*---------------------------------------------------------------------------*
* Separability of terms
*---------------------------------------------------------------------------*)
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