sets_1 Theory

Introduces family of classes for types with computable equality and inequality relations. Specific classes introduced for quasi, partial, total, and linear orders.

Summary of Definitions


Typed Definitions

poset_sig *1
set_car *1
set_eq *1
set_le *1
dset *1
mk_dset *3
set_leq *1
set_blt *1
set_lt *1
qoset *1
poset *1
loset *1
mk_oset *6
eq_pair *1
set_prod *4
dset_set *4
int_loset *7
atom_dset *3

Main Theorems

assert_of_dset_eq *4
decidable__dset_eq *2
dset_eq_refl *3
decidable__set_leq *1
assert_of_set_leq *1
set_lt_is_sp_of_leq *3
set_lt_is_sp_of_leq_a *3
decidable__set_lt *1
assert_of_set_lt *1
qoset_refl *1
set_leq_weakening_eq *3
qoset_trans *1
set_leq_transitivity *1
set_leq_trans *2
qoset_lt_trans *2
qoset_lt_irrefl *3
set_lt_irreflexivity *2
set_leq_weakening_lt *3
set_lt_transitivity_1 *3
set_lt_transitivity_2 *3
set_blt_functionality_wrt_set_lt_r *3
poset_anti_sym *1
set_leq_antisymmetry *1
set_leq_iff_lt_or_eq *7
loset_connex *1
loset_trichot *13
set_leq_complement *5
set_lt_complement *6
assert_of_eq_pair *8


Listing


Last modified February 4th, 1995

Paul Jackson / jackson@cs.cornell.edu