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Adapted to encoding of sets as predicates

Wed, 07 May 2008 10:56:58 +0200
Replaced forward proofs of existential statements by backward proofs

Replaced forward proofs of existential statements by backward proofs
to avoid problems with HO unification

Adapted functions mk_setT and dest_setT to encoding of sets as predicates.

- Explicitely passed pred_subset_eq and pred_equals_eq as an argument to the
to_set and to_pred attributes, because it is no longer applied automatically
- Manually applied predicate1I in proof of accp_subset, because it is no longer
part of the claset
- Replaced psubset_def by less_le

Deleted instantiation "set :: (type) itself".

- Function dec in Trancl_Tac must eta-contract relation before calling
decr, since it is now a function and could therefore be in eta-expanded form
- The trancl prover now does more eta-contraction itself, so eta-contraction
is no longer necessary in Tranclp_tac.

- Now uses Orderings as parent theory
- "'a set" is now just a type abbreviation for "'a => bool"
- The instantiation "set :: (type) ord" and the definition of (p)subset is
no longer needed, since it is subsumed by the order on functions and booleans.
The derived theorems (p)subset_eq can be used as a replacement.
- mem_Collect_eq and Collect_mem_eq can now be derived from the definitions
of mem and Collect.
- Replaced the instantiation "set :: (type) minus" by the two instantiations
"fun :: (type, minus) minus" and "bool :: minus". The theorem set_diff_eq
can be used as a replacement for the definition set_diff_def
- Replaced the instantiation "set :: (type) uminus" by the two instantiations
"fun :: (type, uminus) uminus" and "bool :: uminus". The theorem Compl_eq
can be used as a replacement for the definition Compl_def.
- Variable P in rule split_if must be instantiated manually in proof of
split_if_mem2 due to problems with HO unification
- Moved definition of dense linear orders and proofs about LEAST from
Orderings to Set
- Deleted code setup for sets

Deleted instance "set :: (type) power" and moved instance
"fun :: (type, type) power" to the beginning of the theory

split_beta is now declared as monotonicity rule, to allow bounded
quantifiers in introduction rules of inductive predicates.

- Added mem_def and predicate1I in some of the proofs
- pred_equals_eq and pred_subset_eq are no longer used in the conversion
between sets and predicates, because sets and predicates can no longer
be distinguished