(pointwise_orders_aux
(continuous_pointwise_preserves_directed_complete_partial_order 0
(continuous_pointwise_preserves_directed_complete_partial_order-1 nil
3353820348
("" (skosimp*)
(("" (lemma "scott_continuous_dcpo[T1, T2, d1!1, d2!1]")
(("" (expand "continuous_pointwise")
(("" (expand "restrict") (("" (propax) nil nil)) nil)) nil))
nil))
nil)
((directed_complete_partial_order? const-decl "bool" directed_orders
"orders/")
(pred type-eq-decl nil defined_types nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(T2 formal-type-decl nil pointwise_orders_aux nil)
(T1 formal-type-decl nil pointwise_orders_aux nil)
(scott_continuous_dcpo formula-decl nil scott_continuity nil)
(restrict const-decl "R" restrict nil)
(continuous_pointwise const-decl "bool" pointwise_orders_aux nil))
nil))
(continuous_pointwise_preserves_pointed_directed_complete_partial_order
0
(continuous_pointwise_preserves_pointed_directed_complete_partial_order-1
nil 3353820559
("" (skosimp)
(("" (typepred "p1!1")
(("" (typepred "p2!1")
(("" (expand "pointed_directed_complete_partial_order?")
(("" (flatten)
(("" (expand "has_least?")
(("" (expand "fullset")
(("" (skosimp*)
(("" (inst + "LAMBDA (x:T1): t!1")
(("1" (expand "least?")
(("1" (expand "lower_bound?")
(("1" (skosimp)
(("1" (expand "continuous_pointwise")
(("1" (expand "pointwise")
(("1"
(skosimp)
(("1" (inst -2 "r!1(x!1)") nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(lemma
"const_continuous[T1,scott_open_sets[T1,p1!1],
T2,scott_open_sets[T2,p2!1]]")
(("1" (inst - "t!1")
(("1" (expand "const_fun")
(("1"
(rewrite
"scott_continuous_def[T1, T2, p1!1, p2!1]")
nil nil))
nil))
nil)
("2" (rewrite "scott_topology[T2,p2!1]") nil
nil)
("3" (lemma "scott_topology[T1,p1!1]")
(("3" (propax) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((pointed_directed_complete_partial_order? const-decl "bool"
directed_orders "orders/")
(pred type-eq-decl nil defined_types nil)
(T1 formal-type-decl nil pointwise_orders_aux nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(continuous_pointwise_preserves_directed_complete_partial_order
application-judgement
"(directed_complete_partial_order?[(scott_continuous?[T1, T2, (d1), (d2)])])"
pointwise_orders_aux nil)
(has_least? const-decl "bool" minmax_orders "orders/")
(const_continuous formula-decl nil constant_continuity "topology/")
(setof type-eq-decl nil defined_types nil)
(setofsets type-eq-decl nil sets nil)
(scott_open_sets const-decl "setofsets[T]" scott nil)
(topology? const-decl "bool" topology_prelim "topology/")
(const_fun const-decl "[S -> T]" const_fun_def "structures/")
(scott_continuous_def formula-decl nil scott_continuity nil)
(scott_topology formula-decl nil scott nil)
(least? const-decl "bool" minmax_orders "orders/")
(pointwise const-decl "bool" pointwise_orders "orders/")
(TRUE const-decl "bool" booleans nil)
(continuous_pointwise const-decl "bool" pointwise_orders_aux nil)
(lower_bound? const-decl "bool" bounded_orders "orders/")
(p1!1 skolem-const-decl
"(pointed_directed_complete_partial_order?[T1])"
pointwise_orders_aux nil)
(p2!1 skolem-const-decl
"(pointed_directed_complete_partial_order?[T2])"
pointwise_orders_aux nil)
(scott_continuous? const-decl "bool" scott_continuity nil)
(t!1 skolem-const-decl "T2" pointwise_orders_aux nil)
(fullset const-decl "set" sets nil)
(T2 formal-type-decl nil pointwise_orders_aux nil))
nil)))
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