(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 )))
quality 100%
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