berghofe [Wed, 07 May 2008 10:56:52 +0200] rev 26803
- 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
berghofe [Wed, 07 May 2008 10:56:50 +0200] rev 26802
Deleted instantiation "set :: (type) itself".
berghofe [Wed, 07 May 2008 10:56:49 +0200] rev 26801
- 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.
berghofe [Wed, 07 May 2008 10:56:43 +0200] rev 26800
- 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
berghofe [Wed, 07 May 2008 10:56:41 +0200] rev 26799
Deleted instance "set :: (type) power" and moved instance "fun :: (type, type) power" to the beginning of the theory
berghofe [Wed, 07 May 2008 10:56:40 +0200] rev 26798
split_beta is now declared as monotonicity rule, to allow bounded quantifiers in introduction rules of inductive predicates.
berghofe [Wed, 07 May 2008 10:56:39 +0200] rev 26797
- 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
berghofe [Wed, 07 May 2008 10:56:38 +0200] rev 26796
- Now imports Code_Setup, rather than Set and Fun, since the theorems about orderings are already needed in Set - Moved "Dense orders" section to Set, since it requires set notation. - The "Order on sets" section is no longer necessary, since it is subsumed by the order on functions and booleans. - Moved proofs of Least_mono and Least_equality to Set, since they require set notation. - In proof of "instance fun :: (type, order) order", use ext instead of expand_fun_eq, since the latter is not yet available. - predicate1I is no longer declared as introduction rule, since it interferes with subsetI
berghofe [Wed, 07 May 2008 10:56:37 +0200] rev 26795
- Explicitely applied predicate1I in a few proofs, because it is no longer part of the claset - Explicitely passed pred_subset_eq and pred_equals_eq as an argument to the to_set attribute, because it is no longer applied automatically
berghofe [Wed, 07 May 2008 10:56:36 +0200] rev 26794
- Now imports Fun rather than Orderings - Moved "Set as lattice" section behind "Fun as lattice" section, since sets are just functions. - The instantiations instantiation set :: (type) distrib_lattice instantiation set :: (type) complete_lattice are no longer needed, and the former definitions inf_set_eq, sup_set_eq, Inf_set_def, and Sup_set_def can now be derived from abstract properties of sup, inf, etc.