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((S formal-const-decl "second_countable" lindelof nil)
(second_countable type-eq-decl nil topology_def nil)
(second_countable? const-decl "bool" topology_def nil)
(setofsets type-eq-decl nil sets nil)
(setof type-eq-decl nil defined_types nil)
(T formal-type-decl nil lindelof nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(synthetic_base_is_base formula-decl nil basis nil)
(synthetic_base? const-decl "bool" basis nil)
(synthetic_base type-eq-decl nil basis nil)
(base? const-decl "bool" basis nil)
(subcover? const-decl "bool" topology_prelim nil)
(Union_surjective name-judgement
"(surjective?[setofsets[T], set[T]])" sets_lemmas nil)
(fullset_is_clopen name-judgement "clopen" lindelof nil)
(synthetic_basis_is_topology application-judgement "topology[T]"
lindelof nil)
(subset_is_partial_order name-judgement "(partial_order?[set[T]])"
sets_lemmas nil)
(set type-eq-decl nil sets nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(nonempty? const-decl "bool" sets nil)
(U!1 skolem-const-decl "setofsets[T]" lindelof nil)
(a!1 skolem-const-decl "(U!1)" lindelof nil)
(subset? const-decl "bool" sets nil)
(choose const-decl "(p)" sets nil)
(empty? const-decl "bool" sets nil)
(image const-decl "set[R]" function_image nil)
(restrict const-decl "R" restrict nil)
(image const-decl "set[R]" function_image nil)
(VV skolem-const-decl "set[set[T]]" lindelof nil)
(F skolem-const-decl
"[x: (BB) -> ({y: set[T] | UU(y) & subset?(x, y)})]" lindelof nil)
(TRUE const-decl "bool" booleans nil)
(a!2 skolem-const-decl "(V!1)" lindelof nil)
(V!1 skolem-const-decl "setofsets[T]" lindelof nil)
(BB skolem-const-decl "[set[T] -> boolean]" lindelof nil)
(a!1 skolem-const-decl "(UU)" lindelof nil)
(countable_image formula-decl nil countable_image "sets_aux/")
(countable_set nonempty-type-eq-decl nil countability "sets_aux/")
(countable_subset formula-decl nil countability "sets_aux/")
(UU skolem-const-decl "[set[T] -> boolean]" lindelof nil)
(member const-decl "bool" sets nil)
(fullset const-decl "set" sets nil)
(is_countable const-decl "bool" countability "sets_aux/")
(Union const-decl "set" sets nil)
(cover? const-decl "bool" topology_prelim nil)
(open_cover? const-decl "bool" topology_prelim nil)
(has_countable_basis? const-decl "bool" topology_def nil))
shostak)))
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