Quelle sets_complete_lattices.prf Sprache: Lisp

(sets_complete_lattices
(subset_equals_pointwise_implies 0
  (subset_equals_pointwise_implies-1 nil 3318704900
   ("" (expand* "subset?" "member" "pointwise") nil nil)
   ((pointwise const-decl "bool" pointwise_orders nil)
    (member const-decl "bool" sets nil)
    (subset? const-decl "bool" sets nil))
   shostak))
(subset_is_a_complete_lattice 0
  (subset_is_a_complete_lattice-1 nil 3318704881
   ("" (rewrite "subset_equals_pointwise_implies")
    (("" (rewrite "pointwise_preserves_complete_lattices") nil nil))
    nil)
   ((bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T formal-type-decl nil sets_complete_lattices nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (complete_lattice? const-decl "bool" bounded_orders nil)
    (pred type-eq-decl nil defined_types nil)
    (pointwise_preserves_complete_lattices judgement-tcc nil
     pointwise_orders nil)
    (pointwise_preserves_reflexive application-judgement
     "(reflexive?[[D -> R]])" sets_complete_lattices nil)
    (pointwise_preserves_transitive application-judgement
     "(transitive?[[D -> R]])" sets_complete_lattices nil)
    (pointwise_preserves_preorder application-judgement
     "(preorder?[[D -> R]])" sets_complete_lattices nil)
    (pointwise_preserves_antisymmetric application-judgement
     "(antisymmetric?[[D -> R]])" sets_complete_lattices nil)
    (pointwise_preserves_partial_order application-judgement
     "(partial_order?[[D -> R]])" sets_complete_lattices nil)
    (pointwise_preserves_lower_semilattices application-judgement
     "(lower_semilattice?[[D -> R]])" sets_complete_lattices nil)
    (pointwise_preserves_complete_lower_semilattices
     application-judgement "(complete_lower_semilattice?[[D -> R]])"
     sets_complete_lattices nil)
    (pointwise_preserves_upper_semilattices application-judgement
     "(upper_semilattice?[[D -> R]])" sets_complete_lattices nil)
    (pointwise_preserves_lattices application-judgement
     "(lattice?[[D -> R]])" sets_complete_lattices nil)
    (pointwise_preserves_complete_upper_semilattices
     application-judgement "(complete_upper_semilattice?[[D -> R]])"
     sets_complete_lattices nil)
    (pointwise_preserves_complete_lattices application-judgement
     "(complete_lattice?[[T -> bool]])" sets_complete_lattices nil)
    (implies_is_total_order name-judgement "(total_order?[bool])"
     booleans_are_finite nil)
    (subset_equals_pointwise_implies formula-decl nil
     sets_complete_lattices nil))
   nil)))

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Cephes Mathematical Library

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