|
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(("1" (div-by -3 "rate")
(("1" (expand "id") (("1" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (inst + "0")
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nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
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real_props nil)
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real_props nil)
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(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
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(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
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(real_times_real_is_real application-judgement "real" reals nil))
shostak))
(upper_Clocktime_exists 0
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("" (skosimp*)
(("" (lemma "axiom_of_archimedes")
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(("" (case "i!1 > 0")
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(("1" (expand "id") (("1" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (inst + "0")
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(("2" (assert)
(("2" (expand "id") (("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((axiom_of_archimedes formula-decl nil real_props nil)
(neg_times_lt formula-decl nil real_props nil)
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(times_div_cancel2 formula-decl nil extra_real_props nil)
(nonzero_real nonempty-type-eq-decl nil reals nil)
(real_div_nzreal_is_real application-judgement "real" reals nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(drift_left formula-decl nil physical_clocks nil)
(good_clock nonempty-type-eq-decl nil physical_clocks nil)
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(rate const-decl "posreal" physical_clocks nil)
(rho formal-const-decl "nonneg_real" inverse_clocks 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)
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(<= const-decl "bool" reals nil)
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(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(id const-decl "(bijective?[T, T])" identity nil)
(bijective? const-decl "bool" functions nil)
(bool nonempty-type-eq-decl nil booleans nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields 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)
(real_minus_real_is_real application-judgement "real" reals nil)
(real_times_real_is_real application-judgement "real" reals nil))
nil)
(upper_Clocktime_exists-1 nil 3276602031
("" (skosimp*)
(("" (lemma "axiom_of_archimedes")
(("" (inst - "id(t!1-c!1(0))*id(1+rho)")
(("" (skosimp*)
(("" (case "i!1 > 0")
(("1" (inst + "i!1")
(("1" (lemma "drift_left")
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(("1" (assert)
(("1" (div-by -3 "id(1 + rho)")
(("1" (expand "id") (("1" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (inst + "0")
(("2" (use "neg_times_lt")
(("2" (assert)
(("2" (expand "id") (("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((drift_left formula-decl nil physical_clocks nil)
(good_clock nonempty-type-eq-decl nil physical_clocks nil))
shostak))
(past_ticks_max_set 0
(past_ticks_max_set-2 nil 3399329805
("" (skosimp*)
(("" (split +)
(("1" (rewrite "nonempty_exists")
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(("1" (inst?)
(("1" (expand "past_ticks") (("1" (propax) nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
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(("2" (use "upper_Clocktime_exists")
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(("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("3" (use "sup_int_is_in_set")
(("3" (rewrite "sup_int_in_set") nil nil)) nil))
nil))
nil)
((lower_Clocktime_exists formula-decl nil inverse_clocks nil)
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nil)
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(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
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(set type-eq-decl nil sets nil)
(bool nonempty-type-eq-decl nil booleans nil)
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real_props nil)
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(sup_set type-eq-decl nil bounded_reals "reals/")
(sup_int_is_in_set application-judgement "(SS)" bounded_ints nil)
(sup_int_is_in_set judgement-tcc nil bounded_ints nil))
nil)
(past_ticks_max_set-1 nil 3399329765 ("" (judgement-tcc) nil nil) nil
nil))
(Clock_rewrite 0
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(("1" (expand "past_ticks")
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nil))
nil))
nil))
nil)
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(("2" (expand "upper_bound")
(("2" (inst?)
(("2" (expand "past_ticks") (("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
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real_props nil)
(int nonempty-type-eq-decl nil integers nil)
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(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)
(boolean nonempty-type-decl nil booleans nil)
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(good_clock nonempty-type-eq-decl nil physical_clocks nil)
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(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(rate const-decl "posreal" physical_clocks nil)
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inverse_clocks nil))
nil))
(Clock_lower 0
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(("" (use "sup_int_in_set")
(("" (expand* "in_set" "past_ticks") nil nil)) nil))
nil))
nil)
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inverse_clocks nil)
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nil)
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(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
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(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
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(good_clock nonempty-type-eq-decl nil physical_clocks nil)
(past_ticks const-decl "boolean" inverse_clocks nil)
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shostak))
(Clock_upper 0
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nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((max const-decl "T" bounded_reals "reals/")
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real_props nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(upper_bound const-decl "bool" bound_defs "reals/")
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(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
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(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
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(least_upper_bound const-decl "bool" bound_defs "reals/")
(int nonempty-type-eq-decl nil integers nil)
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(rational_pred const-decl "[real -> boolean]" rationals nil)
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(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)
(sup_int_is_in_set application-judgement "(SS)" bounded_ints nil)
(past_ticks_max_set application-judgement "max_set[int]"
inverse_clocks nil))
shostak))
(Clock_nondecreasing 0
(Clock_nondecreasing-1 nil 3276295641
("" (skosimp*)
(("" (lemma "clock_nondecreasing")
(("" (inst - "1+ C(c!1)(t2!1)" "C(c!1)(t1!1)" "c!1")
(("" (assert)
(("" (use "Clock_lower")
(("" (use "Clock_upper") (("" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
((rho formal-const-decl "nonneg_real" inverse_clocks nil)
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(number_field_pred const-decl "[number -> boolean]" number_fields
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(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(Clock_upper formula-decl nil inverse_clocks nil)
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(int_minus_int_is_int application-judgement "int" integers nil)
(odd_minus_odd_is_even application-judgement "even_int" integers
nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(Clock_lower formula-decl nil inverse_clocks nil)
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(good_clock nonempty-type-eq-decl nil physical_clocks nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
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(> const-decl "bool" reals nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
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(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
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nil))
(alt_clock_edge 0
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nil)
("2" (inst?) (("2" (assert) nil nil)) nil))
nil))
nil))
nil)
((clock_edge? const-decl "bool" physical_clocks nil)
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(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)
(bool nonempty-type-eq-decl nil booleans 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" inverse_clocks 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))
shostak))
(conversion_left 0
(conversion_left-1 nil 3399313032
("" (skosimp*)
(("" (lemma "clock_increasing")
(("" (inst - "T!1" "C(c!1)(t!1)" "c!1")
(("" (use "Clock_lower") (("" (assert) nil nil)) nil)) nil))
nil))
nil)
((rho formal-const-decl "nonneg_real" inverse_clocks 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)
(clock_increasing formula-decl nil physical_clocks nil)
(Clock_lower formula-decl nil inverse_clocks nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(C const-decl "int" inverse_clocks 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)
(posreal 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))
nil))
(conversion_left_alt 0
(conversion_left_alt-1 nil 3400097352
("" (skosimp*)
(("" (prop)
(("1" (lemma "clock_nondecreasing")
(("1" (inst - "C(c!1)(t!1) + 1" "T!1 + 1" "c!1")
(("1" (use "Clock_upper") (("1" (assert) nil nil)) nil))
nil))
nil)
("2" (lemma "clock_nondecreasing")
(("2" (inst - "T!1 + 1" "C(c!1)(t!1)" "c!1")
(("2" (use "Clock_lower") (("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil)
((int_plus_int_is_int application-judgement "int" integers 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)
(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)
(posreal nonempty-type-eq-decl nil real_types 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)
(C const-decl "int" inverse_clocks nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(odd_minus_odd_is_even application-judgement "even_int" integers
nil)
(real_minus_real_is_real application-judgement "real" reals nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(Clock_upper formula-decl nil inverse_clocks nil)
(clock_nondecreasing formula-decl nil physical_clocks 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)
(rho formal-const-decl "nonneg_real" inverse_clocks nil)
(Clock_lower formula-decl nil inverse_clocks nil))
nil))
(conversion_right 0
(conversion_right-1 nil 3399313037
("" (skosimp*)
(("" (prop)
(("1" (lemma "clock_nondecreasing")
(("1" (inst - "T!1" "C(c!1)(t!1)" "c!1")
(("1" (use "Clock_lower") (("1" (assert) nil nil)) nil))
nil))
nil)
("2" (lemma "clock_nondecreasing")
(("2" (inst - "C(c!1)(t!1) + 1" "T!1" "c!1")
(("2" (use "Clock_upper") (("2" (assert) nil nil)) nil))
nil))
nil))
nil))
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)
(posreal nonempty-type-eq-decl nil real_types 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)
(C const-decl "int" inverse_clocks nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(Clock_lower formula-decl nil inverse_clocks nil)
(clock_nondecreasing formula-decl nil physical_clocks 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)
(rho formal-const-decl "nonneg_real" inverse_clocks nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(odd_minus_odd_is_even application-judgement "even_int" integers
nil)
(real_minus_real_is_real application-judgement "real" reals nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(Clock_upper formula-decl nil inverse_clocks nil))
nil))
(obs_bound 0
(obs_bound-2 nil 3399314973
("" (expand "obs?")
(("" (skosimp*)
(("" (rewrite "conversion_right" :dir rl)
(("" (rewrite "conversion_left_alt" :dir rl)
(("" (rewrite "abs_max")
(("" (rewrite "max_le") (("" (assert) nil nil)) nil)) nil))
nil))
nil))
nil))
nil)
((int_minus_int_is_int application-judgement "int" integers nil)
(conversion_left_alt formula-decl nil inverse_clocks nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(max_le formula-decl nil minmax_ineq nil)
(minus_int_is_int application-judgement "int" integers nil)
(int_max application-judgement "{k: int | i <= k AND j <= k}"
real_defs nil)
(rat_max application-judgement "{s: rat | s >= q AND s >= r}"
real_defs nil)
(abs_max formula-decl nil abs_props nil)
(C const-decl "int" inverse_clocks nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(good_clock nonempty-type-eq-decl nil physical_clocks nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(rate const-decl "posreal" physical_clocks nil)
(rho formal-const-decl "nonneg_real" inverse_clocks 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 "[numfield, nznum -> numfield]" number_fields nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/= const-decl "boolean" notequal nil)
(<= const-decl "bool" reals nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields 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)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(conversion_right formula-decl nil inverse_clocks nil)
(obs? const-decl "bool" inverse_clocks nil))
nil)
(obs_bound-1 nil 3366976655
("" (skosimp*)
(("" (expand "abs")
(("" (lift-if)
(("" (expand "obs?")
(("" (prop)
(("1" (lemma "clock_nondecreasing")
(("1" (inst - "C(c!1)(t!1) + 1" "T!1 - X!1" "c!1")
(("1" (assert)
(("1" (lemma "Clock_upper")
(("1" (inst - "c!1" "t!1") (("1" (assert) nil nil))
nil))
nil))
nil))
nil))
nil)
("2" (lemma "clock_nondecreasing")
(("2" (inst - "T!1 + X!1" "C(c!1)(t!1)" "c!1")
(("2" (assert)
(("2" (lemma "Clock_lower")
(("2" (inst - "c!1" "t!1") (("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((clock_nondecreasing formula-decl nil physical_clocks nil)
(good_clock nonempty-type-eq-decl nil physical_clocks nil)
(rate const-decl "posreal" physical_clocks nil))
nil))
(precision_conversion_sym 0
(precision_conversion_sym-1 nil 3366739250
("" (skosimp*)
(("" (use "skew_bound")
(("" (assert)
(("" (rewrite "obs_bound")
(("" (use "Clock_lower")
(("" (use "Clock_upper") (("" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
((skew_bound formula-decl nil physical_clocks 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)
(rho formal-const-decl "nonneg_real" inverse_clocks nil)
(nnreal type-eq-decl nil real_types nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(C const-decl "int" inverse_clocks 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)
(posreal 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)
(nonneg_ceiling_is_nat application-judgement "nat" floor_ceil nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(obs_bound formula-decl nil inverse_clocks nil)
(Clock_upper formula-decl nil inverse_clocks nil)
(odd_minus_odd_is_even application-judgement "even_int" integers
nil)
(Clock_lower formula-decl nil inverse_clocks nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(int_abs_is_nonneg application-judgement "{j: nonneg_int | j >= i}"
real_defs nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(posreal_plus_nnreal_is_posreal application-judgement "posreal"
real_types nil)
(nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(real_minus_real_is_real application-judgement "real" reals nil))
nil))
(precision_conversion 0
(precision_conversion-1 nil 3366740126
("" (skosimp*)
(("" (use "precision_conversion_sym")
(("" (prop)
(("" (rewrite "abs_diff_commutes" +)
(("" (rewrite "abs_diff_commutes")
(("" (use "precision_conversion_sym")
(("" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
((precision_conversion_sym formula-decl nil inverse_clocks 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" inverse_clocks 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 "[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)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil 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)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(int_abs_is_nonneg application-judgement "{j: nonneg_int | j >= i}"
real_defs nil)
(C const-decl "int" inverse_clocks nil)
(abs_diff_commutes formula-decl nil abs_props nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(nonneg_ceiling_is_nat application-judgement "nat" floor_ceil nil)
(posreal_plus_nnreal_is_posreal application-judgement "posreal"
real_types nil)
(nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(real_minus_real_is_real application-judgement "real" reals nil))
nil))
(lower_accuracy_conversion 0
(lower_accuracy_conversion-2 nil 3399215061
("" (skosimp*)
(("" (rewrite "conversion_right" :dir rl)
(("" (lemma "upper_offset")
(("" (inst - "T!1" "1 + C(c!1)(t!1)" "X!1" "c!1")
(("" (assert)
(("" (use "Clock_upper")
(("" (cross-mult) (("" (assert) nil nil)) nil)) nil))
nil))
nil))
nil))
nil))
nil)
((int_minus_int_is_int application-judgement "int" integers nil)
(conversion_right formula-decl nil inverse_clocks 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)
(>= const-decl "bool" reals nil)
(nat nonempty-type-eq-decl nil naturalnumbers 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)
(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" inverse_clocks 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)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(C const-decl "int" inverse_clocks nil)
(Clock_upper formula-decl nil inverse_clocks nil)
(odd_minus_odd_is_even application-judgement "even_int" integers
nil)
(minus_odd_is_odd application-judgement "odd_int" integers nil)
(drift const-decl "nonneg_real" physical_clocks nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(div_mult_pos_le1 formula-decl nil real_props nil)
(div_mult_pos_lt1 formula-decl nil real_props nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_div_nzreal_is_real application-judgement "real" reals nil)
(real_minus_real_is_real application-judgement "real" reals nil)
(nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(real_times_real_is_real application-judgement "real" reals nil)
(real_plus_real_is_real application-judgement "real" reals nil)
(upper_offset formula-decl nil physical_clocks nil))
nil))
(upper_accuracy_conversion 0
(upper_accuracy_conversion-2 nil 3399217261
("" (skosimp*)
(("" (rewrite "conversion_right" :dir rl)
(("" (lemma "lower_offset")
(("" (inst - "T!1" "C(c!1)(t!1)" "X!1" "c!1")
(("" (assert)
(("" (use "Clock_lower")
(("" (mult-by -1 "rate") (("" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil)
((int_minus_int_is_int application-judgement "int" integers nil)
(conversion_right formula-decl nil inverse_clocks 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)
(>= const-decl "bool" reals nil)
(nat nonempty-type-eq-decl nil naturalnumbers 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)
(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" inverse_clocks 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)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(C const-decl "int" inverse_clocks nil)
(Clock_lower formula-decl nil inverse_clocks nil)
(both_sides_times_pos_le1_imp formula-decl nil extra_real_props
nil)
(real_times_real_is_real application-judgement "real" reals nil)
(real_plus_real_is_real application-judgement "real" reals nil)
(real_minus_real_is_real application-judgement "real" reals nil)
(nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(lower_offset formula-decl nil physical_clocks nil))
nil)
(upper_accuracy_conversion-1 nil 3399216258
(";;; Proof for formula inverse_clocks.lower_offset_conversion_alt"
(skosimp*)
((";;; Proof for formula inverse_clocks.lower_offset_conversion_alt"
(rewrite "min_le")
((";;; Proof for formula inverse_clocks.lower_offset_conversion_alt"
(flatten)
((";;; Proof for formula inverse_clocks.lower_offset_conversion_alt"
(case "gamma!1 >= 0")
(("1" (hide 1)
(("1" (lemma "drift_right")
(("1" (inst - "C(c!1)(t!1)" "T!1" "c!1")
(("1" (prop)
(("1" (use "Clock_lower")
(("1" (mult-by 1 "rate") (("1" (assert) nil)))))
("2" (lemma "Clock_nondecreasing")
(("2" (inst - "c!1" "t!1" "c!1(T!1)")
(("2" (assert)
(("2" (rewrite "Clock_rewrite")
nil)))))))))))))))
("2" (hide 3)
(("2" (lemma "drift_left")
(("2" (inst - "T!1" "C(c!1)(t!1)" "c!1")
(("2" (prop)
(("1" (use "Clock_lower")
(("1" (div-by 2 "rate") (("1" (assert) nil)))))
("2" (mult-by 2 "rate")
(("2" (assert) nil))))))))))))))))))
"")
nil nil)))
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