Quelle clock_minmax.prf
Sprache: Lisp
(clock_minmax
(clock_min_witness 0
(clock_min_witness-1 nil 3389336991
("" (skosimp*)
(("" (expand "clock_min" )
(("" (typepred "min(image(t_at(T!1), participant!1))" )
(("" (hide -2)
(("" (rewrite "image" -)
(("" (expand "t_at" )
(("" (skosimp*)
(("" (inst?) (("" (assert ) nil nil )) nil )) nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
((clock_min const-decl "real" clock_minmax nil )
(nonempty_image application-judgement "(nonempty?[R])" clock_minmax
nil )
(nonempty_finite_image application-judgement
"non_empty_finite_set[real]" clock_minmax nil )
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil )
(boolean nonempty-type-decl nil booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(NOT const-decl "[bool -> bool]" 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 )
(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 )
(AND const-decl "[bool, bool -> bool]" booleans nil )
(<= const-decl "bool" reals 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 )
(>= 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 )
(rho formal-const-decl "nonneg_real" clock_minmax nil )
(rate const-decl "posreal" physical_clocks nil )
(- const-decl "[numfield, numfield -> numfield]" number_fields nil )
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil )
(good_clock nonempty-type-eq-decl nil physical_clocks nil )
(set type-eq-decl nil sets nil )
(image const-decl "set[R]" function_image nil )
(t_at const-decl "real" clock_minmax nil )
(is_finite const-decl "bool" finite_sets nil )
(finite_set type-eq-decl nil finite_sets nil )
(empty? const-decl "bool" sets nil )
(non_empty_finite_set type-eq-decl nil finite_sets nil )
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil )
(min const-decl
"{a: T | SS(a) AND (FORALL (x: T): SS(x) IMPLIES a <= x)}"
finite_sets_minmax "finite_sets/" ))
shostak))
(clock_max_witness 0
(clock_max_witness-1 nil 3389337114
("" (skosimp*)
(("" (expand "clock_max" )
(("" (typepred "max(image(t_at(T!1), participant!1))" )
(("" (hide -2)
(("" (rewrite "image" -)
(("" (expand "t_at" )
(("" (skosimp*)
(("" (inst?) (("" (assert ) nil nil )) nil )) nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
((clock_max const-decl "real" clock_minmax nil )
(nonempty_image application-judgement "(nonempty?[R])" clock_minmax
nil )
(nonempty_finite_image application-judgement
"non_empty_finite_set[real]" clock_minmax nil )
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil )
(boolean nonempty-type-decl nil booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(NOT const-decl "[bool -> bool]" 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 )
(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 )
(AND const-decl "[bool, bool -> bool]" booleans nil )
(<= const-decl "bool" reals 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 )
(>= 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 )
(rho formal-const-decl "nonneg_real" clock_minmax nil )
(rate const-decl "posreal" physical_clocks nil )
(- const-decl "[numfield, numfield -> numfield]" number_fields nil )
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil )
(good_clock nonempty-type-eq-decl nil physical_clocks nil )
(set type-eq-decl nil sets nil )
(image const-decl "set[R]" function_image nil )
(t_at const-decl "real" clock_minmax nil )
(is_finite const-decl "bool" finite_sets nil )
(finite_set type-eq-decl nil finite_sets nil )
(empty? const-decl "bool" sets nil )
(non_empty_finite_set type-eq-decl nil finite_sets nil )
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil )
(max const-decl
"{a: T | SS(a) AND (FORALL (x: T): SS(x) IMPLIES x <= a)}"
finite_sets_minmax "finite_sets/" ))
shostak))
(clock_min_is_min 0
(clock_min_is_min-1 nil 3389337201
("" (skosimp*)
(("" (expand "clock_min" )
(("" (typepred "min(image(t_at(T!1), participant!1))" )
(("" (hide -1)
(("" (inst?)
(("" (assert )
(("" (rewrite "image" )
(("" (expand "t_at" ) (("" (inst?) nil nil )) nil )) nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
((clock_min const-decl "real" clock_minmax nil )
(nonempty_image application-judgement "(nonempty?[R])" clock_minmax
nil )
(nonempty_finite_image application-judgement
"non_empty_finite_set[real]" clock_minmax nil )
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil )
(boolean nonempty-type-decl nil booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(NOT const-decl "[bool -> bool]" 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 )
(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 )
(AND const-decl "[bool, bool -> bool]" booleans nil )
(<= const-decl "bool" reals 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 )
(>= 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 )
(rho formal-const-decl "nonneg_real" clock_minmax nil )
(rate const-decl "posreal" physical_clocks nil )
(- const-decl "[numfield, numfield -> numfield]" number_fields nil )
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil )
(good_clock nonempty-type-eq-decl nil physical_clocks nil )
(set type-eq-decl nil sets nil )
(image const-decl "set[R]" function_image nil )
(t_at const-decl "real" clock_minmax nil )
(is_finite const-decl "bool" finite_sets nil )
(finite_set type-eq-decl nil finite_sets nil )
(empty? const-decl "bool" sets nil )
(non_empty_finite_set type-eq-decl nil finite_sets nil )
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil )
(min const-decl
"{a: T | SS(a) AND (FORALL (x: T): SS(x) IMPLIES a <= x)}"
finite_sets_minmax "finite_sets/" ))
shostak))
(clock_max_is_max 0
(clock_max_is_max-1 nil 3389337260
("" (skosimp*)
(("" (expand "clock_max" )
(("" (invoke (typepred "%1" ) (! 1 r))
(("" (hide -1)
(("" (inst?)
(("" (assert )
(("" (hide 2)
(("" (expand * "image" "t_at" ) (("" (inst?) nil nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
((clock_max const-decl "real" clock_minmax nil )
(max const-decl
"{a: T | SS(a) AND (FORALL (x: T): SS(x) IMPLIES x <= a)}"
finite_sets_minmax "finite_sets/" )
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil )
(non_empty_finite_set type-eq-decl nil finite_sets nil )
(empty? const-decl "bool" sets nil )
(finite_set type-eq-decl nil finite_sets nil )
(is_finite const-decl "bool" finite_sets nil )
(t_at const-decl "real" clock_minmax nil )
(image const-decl "set[R]" function_image nil )
(set type-eq-decl nil sets nil )
(good_clock nonempty-type-eq-decl nil physical_clocks nil )
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil )
(- const-decl "[numfield, numfield -> numfield]" number_fields nil )
(rate const-decl "posreal" physical_clocks nil )
(rho formal-const-decl "nonneg_real" clock_minmax 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 )
(/ 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 )
(<= const-decl "bool" reals nil )
(AND const-decl "[bool, bool -> bool]" booleans 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 )
(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 )
(number nonempty-type-decl nil numbers nil )
(NOT const-decl "[bool -> bool]" booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(boolean nonempty-type-decl nil booleans nil )
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil )
(nonempty_finite_image application-judgement
"non_empty_finite_set[real]" clock_minmax nil )
(nonempty_image application-judgement "(nonempty?[R])" clock_minmax
nil ))
shostak))
(clock_min_clock 0
(clock_min_clock-1 nil 3389336989
("" (skosimp*)
(("" (prop)
(("1" (use "clock_min_witness" )
(("1" (skosimp*)
(("1" (replace -2 :hide? t)
(("1" (use "clock_min_is_min" )
(("1" (typepred "c!1" )
(("1" (inst - "T!1" )
(("1" (flatten) (("1" (assert ) nil nil )) nil )) nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2" (lemma "clock_min_witness" )
(("2" (inst - "T!1" _)
(("2" (inst?)
(("2" (skosimp*)
(("2" (replace -2 :hide? t)
(("2" (use "clock_min_is_min" )
(("2" (typepred "c!1" )
(("2" (inst - "T!1" )
(("2" (flatten) (("2" (assert ) nil nil )) nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
((clock_min_is_min formula-decl nil clock_minmax nil )
(real_minus_real_is_real application-judgement "real" reals nil )
(posreal_div_posreal_is_posreal application-judgement "posreal"
real_types nil )
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil )
(int_minus_int_is_int application-judgement "int" integers nil )
(minus_odd_is_odd application-judgement "odd_int" integers nil )
(int_plus_int_is_int application-judgement "int" integers 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 )
(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 )
(numfield nonempty-type-eq-decl nil number_fields nil )
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil )
(bool nonempty-type-eq-decl nil booleans nil )
(AND const-decl "[bool, bool -> bool]" booleans nil )
(<= const-decl "bool" reals nil )
(/= const-decl "boolean" notequal nil )
(nznum nonempty-type-eq-decl nil number_fields nil )
(/ const-decl "[numfield, nznum -> numfield]" number_fields 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 )
(rho formal-const-decl "nonneg_real" clock_minmax nil )
(rate const-decl "posreal" physical_clocks nil )
(- const-decl "[numfield, numfield -> numfield]" number_fields nil )
(good_clock nonempty-type-eq-decl nil physical_clocks nil )
(set type-eq-decl nil sets nil )
(is_finite const-decl "bool" finite_sets nil )
(finite_set type-eq-decl nil finite_sets nil )
(NOT const-decl "[bool -> bool]" booleans nil )
(empty? const-decl "bool" sets nil )
(non_empty_finite_set type-eq-decl nil finite_sets nil )
(clock_min_witness formula-decl nil clock_minmax nil ))
nil ))
(clock_max_clock 0
(clock_max_clock-1 nil 3389336989
("" (skosimp*)
(("" (prop)
(("1" (lemma "clock_max_witness" )
(("1" (inst - "T!1" _)
(("1" (inst?)
(("1" (skosimp*)
(("1" (replace -2 :hide? t)
(("1" (lemma "clock_max_is_max" )
(("1" (inst - "1 + T!1" _ _)
(("1" (inst?)
(("1" (typepred "c!1" )
(("1" (inst - "T!1" )
(("1" (flatten) (("1" (assert ) nil nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2" (use "clock_max_witness" )
(("2" (skosimp*)
(("2" (replace -2 :hide? t)
(("2" (lemma "clock_max_is_max" )
(("2" (inst - "T!1" _ _)
(("2" (inst?)
(("2" (typepred "c!1" )
(("2" (inst - "T!1" )
(("2" (flatten) (("2" (assert ) nil nil )) nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
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 )
(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 )
(clock_max_is_max formula-decl nil clock_minmax nil )
(real_minus_real_is_real application-judgement "real" reals nil )
(posreal_div_posreal_is_posreal application-judgement "posreal"
real_types nil )
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil )
(int_plus_int_is_int application-judgement "int" integers nil )
(non_empty_finite_set type-eq-decl nil finite_sets nil )
(empty? const-decl "bool" sets nil )
(NOT const-decl "[bool -> bool]" booleans nil )
(finite_set type-eq-decl nil finite_sets nil )
(is_finite const-decl "bool" finite_sets nil )
(set type-eq-decl nil sets nil )
(good_clock nonempty-type-eq-decl nil physical_clocks nil )
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil )
(- const-decl "[numfield, numfield -> numfield]" number_fields nil )
(rate const-decl "posreal" physical_clocks nil )
(rho formal-const-decl "nonneg_real" clock_minmax 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 )
(/ 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 )
(<= const-decl "bool" reals nil )
(AND const-decl "[bool, bool -> bool]" booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(clock_max_witness formula-decl nil clock_minmax nil )
(int_minus_int_is_int application-judgement "int" integers nil )
(minus_odd_is_odd application-judgement "odd_int" integers nil ))
nil )))
quality 100%
¤ Dauer der Verarbeitung: 0.3 Sekunden
(vorverarbeitet)
¤
*© Formatika GbR, Deutschland
2026-03-28