(uniform_continuity
(ds_eq_0 0
(ds_eq_0-1 nil 3459781815
("" (skeep)
(("" (lemma "fullset_S_metric_space") (("" (grind) nil nil)) nil))
nil)
((fullset_S_metric_space formula-decl nil uniform_continuity nil)
(metric_space? const-decl "bool" metric_spaces_def nil)
(space_triangle? const-decl "bool" metric_spaces_def nil)
(space_symmetric? const-decl "bool" metric_spaces_def nil)
(space_zero? const-decl "bool" metric_spaces_def nil)
(S formal-nonempty-type-decl nil uniform_continuity nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(set type-eq-decl nil sets nil)
(fullset const-decl "set" sets nil))
shostak))
(ds_sym 0
(ds_sym-1 nil 3459781852
("" (skeep)
(("" (lemma "fullset_S_metric_space") (("" (grind) nil nil)) nil))
nil)
((fullset_S_metric_space formula-decl nil uniform_continuity nil)
(set type-eq-decl nil sets nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(S formal-nonempty-type-decl nil uniform_continuity nil)
(space_zero? const-decl "bool" metric_spaces_def nil)
(space_symmetric? const-decl "bool" metric_spaces_def nil)
(space_triangle? const-decl "bool" metric_spaces_def nil)
(metric_space? const-decl "bool" metric_spaces_def nil)
(fullset const-decl "set" sets nil))
nil))
(ds_triangle 0
(ds_triangle-1 nil 3459781863
("" (skeep)
(("" (lemma "fullset_S_metric_space") (("" (grind) nil nil)) nil))
nil)
((fullset_S_metric_space formula-decl nil uniform_continuity nil)
(S formal-nonempty-type-decl nil uniform_continuity nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(set type-eq-decl nil sets nil)
(space_zero? const-decl "bool" metric_spaces_def nil)
(space_symmetric? const-decl "bool" metric_spaces_def nil)
(space_triangle? const-decl "bool" metric_spaces_def nil)
(metric_space? const-decl "bool" metric_spaces_def nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(fullset const-decl "set" sets nil))
nil))
(dt_eq_0 0
(dt_eq_0-1 nil 3459781878
("" (skeep)
(("" (lemma "fullset_T_metric_space") (("" (grind) nil nil)) nil))
nil)
((fullset_T_metric_space formula-decl nil uniform_continuity nil)
(metric_space? const-decl "bool" metric_spaces_def nil)
(space_triangle? const-decl "bool" metric_spaces_def nil)
(space_symmetric? const-decl "bool" metric_spaces_def nil)
(space_zero? const-decl "bool" metric_spaces_def nil)
(T formal-nonempty-type-decl nil uniform_continuity nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(set type-eq-decl nil sets nil)
(fullset const-decl "set" sets nil))
nil))
(dt_sym 0
(dt_sym-1 nil 3459781915
("" (skeep)
(("" (lemma "fullset_T_metric_space") (("" (grind) nil nil)) nil))
nil)
((fullset_T_metric_space formula-decl nil uniform_continuity nil)
(set type-eq-decl nil sets nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(T formal-nonempty-type-decl nil uniform_continuity nil)
(space_zero? const-decl "bool" metric_spaces_def nil)
(space_symmetric? const-decl "bool" metric_spaces_def nil)
(space_triangle? const-decl "bool" metric_spaces_def nil)
(metric_space? const-decl "bool" metric_spaces_def nil)
(fullset const-decl "set" sets nil))
nil))
(dt_triangle 0
(dt_triangle-1 nil 3459781926
("" (skeep)
(("" (lemma "fullset_T_metric_space") (("" (grind) nil nil)) nil))
nil)
((fullset_T_metric_space formula-decl nil uniform_continuity nil)
(T formal-nonempty-type-decl nil uniform_continuity nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(set type-eq-decl nil sets nil)
(space_zero? const-decl "bool" metric_spaces_def nil)
(space_symmetric? const-decl "bool" metric_spaces_def nil)
(space_triangle? const-decl "bool" metric_spaces_def nil)
(metric_space? const-decl "bool" metric_spaces_def nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(fullset const-decl "set" sets nil))
nil))
(IMP_continuity_ms_TCC1 0
(IMP_continuity_ms_TCC1-1 nil 3459685573
("" (rewrite "fullset_S_metric_space") nil nil)
((fullset_S_metric_space formula-decl nil uniform_continuity nil))
nil))
(IMP_continuity_ms_TCC2 0
(IMP_continuity_ms_TCC2-1 nil 3459685573
("" (rewrite "fullset_T_metric_space") nil nil)
((fullset_T_metric_space formula-decl nil uniform_continuity nil))
nil))
(unif_cont_implies_cont 0
(unif_cont_implies_cont-1 nil 3460390924
("" (skosimp*)
(("" (expand "continuous?")
(("" (expand "uniformly_continuous?")
(("" (skosimp*)
(("" (expand "continuous_at?")
(("" (skosimp*)
(("" (inst - "epsilon!1")
(("" (skosimp*)
(("" (inst + "delta!1")
(("" (skosimp*)
(("" (expand "member")
(("" (expand "ball") (("" (grind) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((continuous? const-decl "bool" continuity_ms_def nil)
(ball const-decl "set[T]" metric_spaces nil)
(set type-eq-decl nil sets nil)
(S formal-nonempty-type-decl nil uniform_continuity nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(member const-decl "bool" sets nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(> const-decl "bool" reals nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(continuous_at? const-decl "bool" continuity_ms_def nil)
(uniformly_continuous? const-decl "bool" uniform_continuity nil))
shostak))
(Hset_def 0
(Hset_def-2 nil 3460196535
("" (skosimp*)
(("" (expand "Hset")
(("" (expand "continuous?")
(("" (expand "restrict")
(("" (inst - "x!1")
(("" (expand "continuous_at?")
(("" (inst - "epsilon!1")
(("" (skosimp*)
(("" (assert)
(("" (inst + "(x!1,delta!1/2)")
(("" (split +)
(("1" (skosimp*)
(("1" (inst?)
(("1" (expand "intersection")
(("1"
(assert)
(("1"
(flatten)
(("1"
(assert)
(("1"
(expand "ball")
(("1"
(assert)
(("1"
(rewrite "dt_sym")
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (expand "intersection")
(("2" (assert) nil nil)) nil))
nil))
nil)
("2" (expand "ball")
(("2" (lemma "ds_eq_0")
(("2" (inst?) (("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((Hset const-decl "set[[S, posreal]]" uniform_continuity nil)
(S formal-nonempty-type-decl nil uniform_continuity nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(set type-eq-decl nil sets nil)
(number nonempty-type-decl nil numbers nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(>= const-decl "bool" reals nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(> const-decl "bool" reals nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(member const-decl "bool" sets nil)
(A!1 skolem-const-decl "set[S]" uniform_continuity nil)
(x!2 skolem-const-decl "S" uniform_continuity nil)
(posreal_times_posreal_is_posreal application-judgement "posreal"
real_types nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(dt_sym formula-decl nil uniform_continuity nil)
(T formal-nonempty-type-decl nil uniform_continuity nil)
(ball const-decl "set[T]" metric_spaces nil)
(intersection const-decl "set" sets nil)
(ds_eq_0 formula-decl nil uniform_continuity nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(/= const-decl "boolean" notequal nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(posreal_div_posreal_is_posreal application-judgement "posreal"
real_types nil)
(continuous_at? const-decl "bool" continuity_ms_def nil)
(continuous? const-decl "bool" continuity_ms_def nil))
nil)
(Hset_def-1 nil 3460108603
("" (skosimp*)
(("" (expand "Hset")
(("" (expand "continuous?")
(("" (expand "restrict")
(("" (inst - "x!1")
(("" (expand "continuous_at?")
(("" (inst - "epsilon!1")
(("" (skosimp*)
(("" (assert)
(("" (inst + "(x!1,delta!1)")
(("" (split +)
(("1" (skosimp*)
(("1" (inst?)
(("1" (expand "intersection")
(("1"
(assert)
(("1"
(flatten)
(("1"
(assert)
(("1"
(expand "ball")
(("1"
(assert)
(("1"
(rewrite "dt_sym")
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (expand "intersection")
(("2" (assert) nil nil)) nil))
nil))
nil)
("2" (expand "ball")
(("2" (lemma "ds_eq_0")
(("2" (inst?) (("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((ball const-decl "set[T]" metric_spaces nil)) shostak))
(ball_cover_lem 0
(ball_cover_lem-1 nil 3459690736
("" (skosimp*)
(("" (expand "ball_cover")
(("" (expand "open_cover?")
(("" (split +)
(("1" (expand "subset?")
(("1" (skosimp*)
(("1" (assert)
(("1" (expand "Union")
(("1" (lemma "Hset_def")
(("1" (inst?)
(("1" (inst?)
(("1" (assert)
(("1" (inst - "x!1")
(("1" (skosimp*)
(("1"
(inst + "ball[S, ds](p!1)")
(("1"
(expand "ball_covering")
(("1"
(inst + "(p!1`1, p!1`2)")
(("1" (assert) nil nil)
("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (skosimp*)
(("2" (expand "ball_covering")
(("2" (skosimp*)
(("2" (replace -1)
(("2" (hide -)
(("2" (lemma "ball_open[S,ds]")
(("2" (inst?) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((ball_cover const-decl "set[set[S]]" uniform_continuity nil)
(Union const-decl "set" sets nil)
(T formal-nonempty-type-decl nil uniform_continuity nil)
(set type-eq-decl nil sets nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(S formal-nonempty-type-decl nil uniform_continuity nil)
(A!1 skolem-const-decl "set[S]" uniform_continuity nil)
(epsilon!1 skolem-const-decl "posreal" uniform_continuity nil)
(f!1 skolem-const-decl "[S -> T]" uniform_continuity nil)
(p!1 skolem-const-decl "[a: (A!1), r: posreal]" uniform_continuity
nil)
(nnreal type-eq-decl nil real_types nil)
(ds formal-const-decl "[S, S -> nnreal]" uniform_continuity nil)
(ball_covering const-decl "set[set[T]]" compactness nil)
(Hset const-decl "set[[S, posreal]]" uniform_continuity nil)
(ball const-decl "set[T]" metric_spaces nil)
(number nonempty-type-decl nil numbers nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(>= const-decl "bool" reals nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(> const-decl "bool" reals nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(Hset_def formula-decl nil uniform_continuity nil)
(member const-decl "bool" sets nil)
(Union_surjective name-judgement
"(surjective?[setofsets[T], set[T]])" sets_lemmas nil)
(subset? const-decl "bool" sets nil)
(ball_open formula-decl nil metric_spaces nil)
(open_cover? const-decl "bool" compactness nil))
shostak))
(compact_ball_all 0
(compact_ball_all-1 nil 3459694390
("" (skosimp*)
(("" (expand "restrict")
(("" (typepred "a!1")
(("" (expand "continuous?")
(("" (inst - "a!1")
(("" (expand "continuous_at?")
(("" (inst?)
(("" (skosimp*)
(("" (assert)
(("" (expand "ball")
(("" (expand "intersection")
(("" (assert)
(("" (inst + "delta!1")
(("" (skosimp*)
((""
(inst - "x!1")
((""
(assert)
(("" (rewrite "dt_sym") nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((set type-eq-decl nil sets nil)
(S formal-nonempty-type-decl nil uniform_continuity nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(>= const-decl "bool" reals nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(> const-decl "bool" reals nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(member const-decl "bool" sets nil)
(intersection const-decl "set" sets nil)
(A!1 skolem-const-decl "set[S]" uniform_continuity nil)
(x!1 skolem-const-decl "S" uniform_continuity nil)
(T formal-nonempty-type-decl nil uniform_continuity nil)
(dt_sym formula-decl nil uniform_continuity nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(ball const-decl "set[T]" metric_spaces nil)
(continuous_at? const-decl "bool" continuity_ms_def nil)
(continuous? const-decl "bool" continuity_ms_def nil))
shostak))
(rset_prep 0
(rset_prep-3 nil 3460197959
("" (skosimp*)
(("" (name "H" "Hset(A!1, epsilon!1, f!1)")
(("" (replace -1)
(("" (expand "ball_covering")
(("" (expand "open_cover?")
(("" (split +)
(("1" (expand "subset?")
(("1" (skosimp*)
(("1" (assert)
(("1" (expand "Union")
(("1" (expand "continuous?")
(("1" (inst - "x!1")
(("1" (expand "continuous_at?")
(("1" (inst - "epsilon!1/2")
(("1"
(skosimp*)
(("1"
(assert)
(("1"
(expand "Hset")
(("1"
(inst
+
"ball[S, ds](x!1, delta!1/2)")
(("1"
(expand "ball")
(("1"
(lemma "ds_eq_0")
(("1"
(inst?)
(("1" (assert) nil nil))
nil))
nil))
nil)
("2"
(inst + "(x!1, delta!1/2)")
(("2"
(replace -2 + :dir rl)
(("2"
(assert)
(("2"
(skosimp*)
(("2"
(inst -4 "x!2")
(("1"
(assert)
(("1"
(expand
"intersection")
(("1"
(assert)
(("1"
(flatten)
(("1"
(expand
"ball")
(("1"
(assert)
(("1"
(rewrite
"dt_sym")
(("1"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(expand
"intersection")
(("2"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (skosimp*)
(("2" (lemma "ball_open[S,ds]")
(("2" (inst?) (("2" (assert) nil nil)) nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((Hset const-decl "set[[S, posreal]]" uniform_continuity nil)
(T formal-nonempty-type-decl nil uniform_continuity nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(set type-eq-decl nil sets nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(> const-decl "bool" reals nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(S formal-nonempty-type-decl nil uniform_continuity nil)
(ball_covering const-decl "set[set[T]]" compactness nil)
(Union const-decl "set" sets nil)
(posreal_div_posreal_is_posreal application-judgement "posreal"
real_types nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/= const-decl "boolean" notequal nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(H skolem-const-decl "set[[S, posreal]]" uniform_continuity nil)
(nnreal type-eq-decl nil real_types nil)
(ds formal-const-decl "[S, S -> nnreal]" uniform_continuity nil)
(ball const-decl "set[T]" metric_spaces nil)
(x!1 skolem-const-decl "S" uniform_continuity nil)
(delta!1 skolem-const-decl "posreal" uniform_continuity nil)
(ds_eq_0 formula-decl nil uniform_continuity nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(posreal_times_posreal_is_posreal application-judgement "posreal"
real_types nil)
(dt_sym formula-decl nil uniform_continuity nil)
(intersection const-decl "set" sets nil)
(x!2 skolem-const-decl "S" uniform_continuity nil)
(A!1 skolem-const-decl "set[S]" uniform_continuity nil)
(continuous_at? const-decl "bool" continuity_ms_def nil)
(continuous? const-decl "bool" continuity_ms_def nil)
(member const-decl "bool" sets nil)
(Union_surjective name-judgement
"(surjective?[setofsets[T], set[T]])" sets_lemmas nil)
(subset? const-decl "bool" sets nil)
(ball_open formula-decl nil metric_spaces nil)
(open_cover? const-decl "bool" compactness nil))
nil)
(rset_prep-2 nil 3460197883
(";;; Proof rset_prep-1 for formula unif_cont.rset_prep" (skosimp*)
((";;; Proof rset_prep-1 for formula unif_cont.rset_prep"
(name "H" "Hset(A!1, epsilon!1, f!1)")
((";;; Proof rset_prep-1 for formula unif_cont.rset_prep"
(replace -1)
((";;; Proof rset_prep-1 for formula unif_cont.rset_prep"
(expand "ball_covering")
((";;; Proof rset_prep-1 for formula unif_cont.rset_prep"
(expand "open_cover?")
((";;; Proof rset_prep-1 for formula unif_cont.rset_prep"
(split +)
(("1" (expand "subset?")
(("1" (skosimp*)
(("1" (assert)
(("1" (expand "Union")
(("1" (expand "continuous?")
(("1" (inst - "x!1")
(("1" (expand "continuous_at?")
(("1" (inst - "epsilon!1/2")
(("1"
(skosimp*)
(("1"
(assert)
(("1"
(expand "restrict")
(("1"
(expand "Hset")
(("1"
(inst
+
"ball[S, ds](x!1, delta!1/2)")
(("1"
(expand "ball")
(("1"
(lemma "ds_eq_0")
(("1"
(inst?)
(("1" (assert) nil)))))))
("2"
(inst + "(x!1, delta!1)")
(("2"
(replace -2 + :dir rl)
(("2"
(assert)
(("2"
(skosimp*)
(("2"
(inst -4 "x!2")
(("1"
(assert)
(("1"
(expand
"intersection")
(("1"
(assert)
(("1"
(flatten)
(("1"
(expand
"ball")
(("1"
(assert)
(("1"
(postpone)
nil)))))))))))))
("2"
(postpone)
nil)))))))))))))))))))))))))))))))))))))
("2" (skosimp*)
(("2" (lemma "ball_open")
(("2" (inst?) (("2" (assert) nil))))))))))))))))))
";;; developed with shostak decision procedures")
nil nil)
(rset_prep-1 nil 3460196706
("" (skosimp*)
(("" (name "H" "Hset(A!1, epsilon!1, f!1)")
(("" (replace -1)
(("" (expand "ball_covering")
(("" (expand "open_cover?")
(("" (split +)
(("1" (expand "subset?")
(("1" (skosimp*)
(("1" (assert)
(("1" (expand "Union")
(("1" (expand "continuous?")
(("1" (inst - "x!1")
(("1" (expand "continuous_at?")
(("1" (inst - "epsilon!1/2")
(("1"
(skosimp*)
(("1"
(assert)
(("1"
(expand "restrict")
(("1"
(expand "Hset")
(("1"
(inst
+
"ball[S, ds](x!1, delta!1)")
(("1"
(expand "ball")
(("1"
(lemma "ds_eq_0")
(("1"
(inst?)
(("1" (assert) nil nil))
nil))
nil))
nil)
("2"
(inst + "(x!1, delta!1)")
(("2"
(replace -2 + :dir rl)
(("2"
(assert)
(("2"
(skosimp*)
(("2"
(inst -4 "x!2")
(("1"
(assert)
(("1"
(expand
"intersection")
(("1"
(assert)
(("1"
(flatten)
(("1"
(expand
"ball")
(("1"
(assert)
(("1"
(postpone)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(postpone)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (skosimp*)
(("2" (lemma "ball_open")
(("2" (inst?) (("2" (assert) nil nil)) nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
nil shostak))
(rset_TCC1 0
(rset_TCC1-1 nil 3460130465
("" (skosimp*)
(("" (rewrite "rset_prep") (("" (postpone) nil nil)) nil)) nil)
((rset_prep formula-decl nil uniform_continuity nil)
(S formal-nonempty-type-decl nil uniform_continuity nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(set type-eq-decl nil sets nil)
(number nonempty-type-decl nil numbers nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(>= const-decl "bool" reals nil)
(nnreal type-eq-decl nil real_types nil)
(ds formal-const-decl "[S, S -> nnreal]" uniform_continuity nil)
(compact? const-decl "bool" compactness nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(> const-decl "bool" reals nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(T formal-nonempty-type-decl nil uniform_continuity nil)
(dt formal-const-decl "[T, T -> nnreal]" uniform_continuity nil)
(continuous? const-decl "bool" continuity_ms_def nil)
(continuous_funs type-eq-decl nil uniform_continuity nil))
nil))
(rset_lem_TCC1 0
(rset_lem_TCC1-1 nil 3460127743
("" (skosimp*) (("" (rewrite "rset_prep") nil nil)) nil)
((rset_prep formula-decl nil uniform_continuity nil)
(S formal-nonempty-type-decl nil uniform_continuity nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(set type-eq-decl nil sets nil)
(number nonempty-type-decl nil numbers nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(>= const-decl "bool" reals nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(> const-decl "bool" reals nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(T formal-nonempty-type-decl nil uniform_continuity nil))
nil))
(rset_lem 0
(rset_lem-1 nil 3460127746
("" (skosimp*)
(("" (assert) (("" (expand "rset") (("" (propax) nil nil)) nil))
nil))
nil)
((rset const-decl "set[posreal]" uniform_continuity nil)) shostak))
(rset_finite 0
(rset_finite-1 nil 3460198192
("" (skosimp*)
(("" (expand "rset")
(("" (lemma "is_finite_exists_N")
(("" (inst?)
(("1" (hide 2)
(("1" (skosimp*)
(("1" (lemma "rset_prep")
(("1" (inst?) (("1" (assert) nil nil)) nil)) nil))
nil))
nil)
("2" (hide 2) (("2" (skosimp*) nil nil)) nil)
("3" (hide 2)
(("3" (lemma "rset_prep")
(("3" (inst?) (("3" (assert) nil nil)) nil)) nil))
nil))
nil))
nil))
nil))
nil)
((rset const-decl "set[posreal]" uniform_continuity nil)
(A!1 skolem-const-decl "set[S]" uniform_continuity nil)
(compact? const-decl "bool" compactness nil)
(ds formal-const-decl "[S, S -> nnreal]" uniform_continuity nil)
(nnreal type-eq-decl nil real_types nil)
(set type-eq-decl nil sets nil)
(S formal-nonempty-type-decl nil uniform_continuity nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(int nonempty-type-eq-decl nil integers nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(open_cover? const-decl "bool" compactness nil)
(ball_covering const-decl "set[set[T]]" compactness nil)
(Htype type-eq-decl nil compactness nil)
(below type-eq-decl nil nat_types nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(< const-decl "bool" reals nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(idxCover const-decl "{pair: [N: nat, seq: [below[N] -> (H)]] |
open_cover?(ball_covering({h: [T, posreal]
|
H(h)
AND
(EXISTS
(n: below[pair`1]):
h = pair`2(n))}),
S)}" compactness nil)
(T formal-nonempty-type-decl nil uniform_continuity nil)
(Hset const-decl "set[[S, posreal]]" uniform_continuity nil)
(f!1 skolem-const-decl "[S -> T]" uniform_continuity nil)
(epsilon!1 skolem-const-decl "posreal" uniform_continuity nil)
(rset_prep formula-decl nil uniform_continuity nil)
(is_finite_exists_N formula-decl nil finite_sets_aux nil)
(number nonempty-type-decl nil numbers nil)
(boolean nonempty-type-decl nil booleans nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(>= const-decl "bool" reals nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(> const-decl "bool" reals nil)
(posreal nonempty-type-eq-decl nil real_types nil))
shostak))
(rset_not_empty 0
(rset_not_empty-1 nil 3460198699
("" (skosimp*)
(("" (expand "empty?")
(("" (skosimp*)
(("" (assert)
(("" (lemma "idxCover_def[S,ds]")
(("" (inst?)
(("" (expand "rset")
(("" (inst - "Hset(A!1, epsilon!1, f!1)")
(("" (assert)
(("" (expand "ball_cover")
(("" (assert)
(("" (skosimp*)
((""
(inst -7
"idxCover(A!1, Hset(A!1, epsilon!1, f!1))`2(n!1)`2")
(("" (inst + "n!1") nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((empty? const-decl "bool" sets nil)
(member const-decl "bool" sets nil) (set type-eq-decl nil sets nil)
(Hset const-decl "set[[S, posreal]]" uniform_continuity nil)
(T formal-nonempty-type-decl nil uniform_continuity nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(> const-decl "bool" reals nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(ball_cover const-decl "set[set[S]]" uniform_continuity nil)
(idxCover const-decl "{pair: [N: nat, seq: [below[N] -> (H)]] |
open_cover?(ball_covering({h: [T, posreal]
|
H(h)
AND
(EXISTS
(n: below[pair`1]):
h = pair`2(n))}),
S)}" compactness nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(< const-decl "bool" reals nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(below type-eq-decl nil nat_types nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(Htype type-eq-decl nil compactness nil)
(ball_covering const-decl "set[set[T]]" compactness nil)
(open_cover? const-decl "bool" compactness nil)
(compact? const-decl "bool" compactness nil)
(rset const-decl "set[posreal]" uniform_continuity nil)
(idxCover_def formula-decl nil compactness nil)
(S formal-nonempty-type-decl nil uniform_continuity nil)
(number nonempty-type-decl nil numbers nil)
(boolean nonempty-type-decl nil booleans nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(>= const-decl "bool" reals nil)
(nnreal type-eq-decl nil real_types nil)
(ds formal-const-decl "[S, S -> nnreal]" uniform_continuity nil))
shostak))
(Heine 0
(Heine-7 nil 3460196563
("" (skosimp*)
(("" (expand "uniformly_continuous?")
(("" (skosimp*)
(("" (lemma "ball_cover_lem")
(("" (inst?)
(("" (inst - "epsilon!1/2")
(("" (assert)
(("" (case "empty?(A!1)")
(("1" (propax) nil nil)
("2" (hide 1)
(("2" (inst + "min(rset(A!1, epsilon!1 / 2, f!1))")
(("1" (skosimp*)
(("1" (lemma "idxCover_def[S,ds]")
(("1"
(inst - "Hset(A!1, epsilon!1 / 2, f!1)"
"A!1" "x!1")
(("1" (assert)
(("1"
(split -1)
(("1"
(skosimp*)
(("1"
(name
"seq"
"idxCover(A!1, Hset(A!1, epsilon!1 / 2, f!1))")
(("1"
(replace -1)
(("1"
(name
"H"
"Hset(A!1, epsilon!1 / 2, f!1)")
(("1"
(replace -1)
(("1"
(expand "ball_covering")
(("1"
(skosimp*)
(("1"
(hide -4)
(("1"
(name
"ak"
"seq`2(n!1)`1")
(("1"
(name
"rk"
"seq`2(n!1)`2")
(("1"
(replace -1)
(("1"
(replace -2)
(("1"
(case
"dt(f!1(x!1), f!1(ak)) < epsilon!1/2")
(("1"
(case
"dt(f!1(ak), f!1(p!1)) < epsilon!1 / 2")
(("1"
(assert)
(("1"
(lemma
"dt_triangle")
(("1"
(inst
-
"f!1(x!1)"
"f!1(ak)"
"f!1(p!1)")
(("1"
(assert)
nil
nil))
nil))
nil))
nil)
("2"
(hide 2)
(("2"
(case
"ball(ak,2*rk)(p!1)")
(("1"
(typepred
"seq`2(n!1)")
(("1"
(expand
"Hset")
(("1"
(flatten)
(("1"
(replace
-6)
(("1"
(inst
-
"p!1")
(("1"
(expand
"intersection")
(("1"
(assert)
(("1"
(rewrite
"dt_sym")
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(hide
2)
(("2"
(expand
"ball")
(("2"
(lemma
"ds_triangle")
(("2"
(inst
-
"ak"
"x!1"
"p!1")
(("2"
(assert)
(("2"
(case
"min(rset(A!1, epsilon!1 / 2, f!1)) <= rk")
(("1"
(assert)
nil
nil)
("2"
(hide
-1
2)
(("2"
(typepred
"min(rset(A!1, epsilon!1 / 2, f!1))")
(("2"
(inst
-4
"rk")
(("2"
(assert)
(("2"
(hide
2)
(("2"
(hide
-9
-10
-11
-12
-13)
(("2"
(expand
"rset"
1)
(("2"
(inst
+
"n!1")
(("2"
(lemma
"idxCover_def[S,ds]")
(("2"
(inst?)
(("2"
(inst
-
"ak")
(("2"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(hide 2)
(("2"
(typepred
"seq`2(n!1)")
(("2"
(expand
"Hset")
(("2"
(assert)
(("2"
(flatten)
(("2"
(replace
-4)
(("2"
(inst
-2
"x!1")
(("2"
(expand
"intersection")
(("2"
(assert)
(("2"
(expand
"ball")
(("2"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(expand "ball_cover")
(("2" (propax) nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (lemma "rset_finite")
(("2" (inst?)
(("2" (assert)
(("2" (lemma "rset_not_empty")
(("2"
(inst?)
(("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((uniformly_continuous? const-decl "bool" uniform_continuity nil)
(ball_cover_lem formula-decl nil uniform_continuity nil)
(posreal_div_posreal_is_posreal application-judgement "posreal"
real_types nil)
(number nonempty-type-decl nil numbers nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(>= const-decl "bool" reals nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(> const-decl "bool" reals nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(/= const-decl "boolean" notequal nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(empty? const-decl "bool" sets nil)
(reflexive_restrict application-judgement "(reflexive?[S])"
restrict_order_props nil)
--> --------------------
--> maximum size reached
--> --------------------
¤ Dauer der Verarbeitung: 0.135 Sekunden
(vorverarbeitet)
¤
|
Haftungshinweis
Die Informationen auf dieser Webseite wurden
nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit,
noch Qualität der bereit gestellten Informationen zugesichert.
Bemerkung:
Die farbliche Syntaxdarstellung ist noch experimentell.
|