|
(synch_constant_definitions
(P_bound 0
(P_bound-1 nil 3292973572
("" (auto-rewrite-defs)
(("" (typepred "pi_0") (("" (assert) nil nil)) nil)) nil)
((pi_0 formal-const-decl
"{pi: posreal | P_bound?(P, rho, alpha_l, alpha_u, pi)}"
synch_constant_definitions nil)
(alpha_u formal-const-decl "nnreal" synch_constant_definitions nil)
(alpha_l formal-const-decl "nnreal" synch_constant_definitions nil)
(rho formal-const-decl "nnreal" synch_constant_definitions nil)
(nnreal type-eq-decl nil real_types nil)
(P formal-const-decl "posnat" synch_constant_definitions nil)
(P_bound? const-decl "bool" synch_parameter_constraints nil)
(posnat nonempty-type-eq-decl nil integers nil)
(nonneg_int nonempty-type-eq-decl nil integers 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)
(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)
(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_ge_is_total_order name-judgement "(total_order?[real])"
real_props 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_times_real_is_real application-judgement "real" reals nil)
(posreal_plus_nnreal_is_posreal application-judgement "posreal"
real_types nil)
(real_plus_real_is_real application-judgement "real" reals nil)
(nonneg_real_max application-judgement
"{z: nonneg_real | z >= x AND z >= y}" real_defs nil)
(real_minus_real_is_real application-judgement "real" reals nil)
(posreal_div_posreal_is_posreal application-judgement "posreal"
real_types nil)
(posreal_times_posreal_is_posreal application-judgement "posreal"
real_types nil)
(nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(nnreal_plus_posreal_is_posreal application-judgement "posreal"
real_types nil)
(drift const-decl "nonneg_real" physical_clocks nil)
(rate const-decl "posreal" physical_clocks nil))
shostak))
(rho_bound 0
(rho_bound-1 nil 3292974283
("" (lemma "P_bound")
(("" (mult-by 1 "P")
(("" (invoke (then (case "%1 <= %2") (assert)) (! 1 l) (! -1 l))
(("" (hide-all-but 1)
(("" (expand* "drift" "rate" "id") (("" (field 1) nil nil))
nil))
nil))
nil))
nil))
nil)
((nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(both_sides_times_pos_ge1_imp formula-decl nil extra_real_props
nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(rho formal-const-decl "nnreal" synch_constant_definitions nil)
(nnreal type-eq-decl nil real_types nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(P formal-const-decl "posnat" synch_constant_definitions nil)
(posnat nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers 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_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)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(posreal_plus_nnreal_is_posreal application-judgement "posreal"
real_types 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)
(nonneg_real_max application-judgement
"{z: nonneg_real | z >= x AND z >= y}" real_defs nil)
(nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(< const-decl "bool" reals nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(posint_times_posint_is_posint application-judgement "posint"
integers nil)
(nnreal_plus_posreal_is_posreal application-judgement "posreal"
real_types nil)
(real_minus_real_is_real application-judgement "real" reals nil)
(real_plus_real_is_real application-judgement "real" reals nil)
(minus_odd_is_odd application-judgement "odd_int" integers nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(real_times_real_is_real application-judgement "real" reals nil)
(nzint_times_nzint_is_nzint application-judgement "nzint" integers
nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(both_sides_plus_le2 formula-decl nil real_props nil)
(both_sides_times_pos_le1 formula-decl nil real_props nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(bijective? const-decl "bool" functions nil)
(id const-decl "(bijective?[T, T])" identity nil)
(TRUE const-decl "bool" booleans nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/= const-decl "boolean" notequal nil)
(nnreal_div_posreal_is_nnreal application-judgement "nnreal"
real_types nil)
(= const-decl "[T, T -> boolean]" equalities 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)
(<= const-decl "bool" reals nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(rate const-decl "posreal" physical_clocks nil)
(P_bound? const-decl "bool" synch_parameter_constraints nil)
(alpha_l formal-const-decl "nnreal" synch_constant_definitions nil)
(alpha_u formal-const-decl "nnreal" synch_constant_definitions nil)
(pi_0 formal-const-decl
"{pi: posreal | P_bound?(P, rho, alpha_l, alpha_u, pi)}"
synch_constant_definitions nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(max const-decl "{p: real | p >= m AND p >= n}" real_defs nil)
(drift const-decl "nonneg_real" physical_clocks nil)
(P_bound formula-decl nil synch_constant_definitions nil))
shostak))
(ADJ_ineq 0
(ADJ_ineq-1 nil 3381419890
("" (swap-rel +)
(("" (expand "ADJ") (("" (rewrite "floor_monotone") nil nil)) nil))
nil)
((nonneg_real_max application-judgement
"{z: nonneg_real | z >= x AND z >= y}" real_defs nil)
(nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(floor_monotone formula-decl nil floor_ceiling_ineq nil)
(max const-decl "{p: real | p >= m AND p >= n}" real_defs nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
(nnreal_plus_posreal_is_posreal application-judgement "posreal"
real_types nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(rate const-decl "posreal" physical_clocks nil)
(pi_0 formal-const-decl
"{pi: posreal | P_bound?(P, rho, alpha_l, alpha_u, pi)}"
synch_constant_definitions nil)
(alpha_u formal-const-decl "nnreal" synch_constant_definitions nil)
(alpha_l formal-const-decl "nnreal" synch_constant_definitions nil)
(P_bound? const-decl "bool" synch_parameter_constraints nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(P formal-const-decl "posnat" synch_constant_definitions nil)
(posnat nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(drift const-decl "nonneg_real" physical_clocks nil)
(rho formal-const-decl "nnreal" synch_constant_definitions nil)
(nnreal type-eq-decl nil real_types nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(floor const-decl "{i | i <= x & x < i + 1}" floor_ceil nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(< const-decl "bool" reals nil) (<= const-decl "bool" reals nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(integer nonempty-type-from-decl nil integers nil)
(ADJ const-decl "nat" synch_constant_definitions nil)
(nat nonempty-type-eq-decl nil naturalnumbers 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)
(>= const-decl "bool" reals 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)
(IFF const-decl "[bool, bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(posreal_times_posreal_is_posreal application-judgement "posreal"
real_types nil)
(nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
real_types nil))
nil))
(ADJ_ineq_l 0
(ADJ_ineq_l-1 nil 3381419661
("" (swap-rel +)
(("" (expand "ADJ")
(("" (rewrite "floor_monotone")
(("" (hide 2) (("" (cancel-by 1 "rate") nil nil)) nil)) nil))
nil))
nil)
((nonneg_real_max application-judgement
"{z: nonneg_real | z >= x AND z >= y}" real_defs nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(posreal_div_posreal_is_posreal application-judgement "posreal"
real_types nil)
(both_sides_times_pos_le1 formula-decl nil real_props nil)
(/= const-decl "boolean" notequal nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(bijective? const-decl "bool" functions nil)
(id const-decl "(bijective?[T, T])" identity nil)
(TRUE const-decl "bool" booleans nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(floor_monotone formula-decl nil floor_ceiling_ineq nil)
(max const-decl "{p: real | p >= m AND p >= n}" real_defs nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
(nnreal_plus_posreal_is_posreal application-judgement "posreal"
real_types nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(rate const-decl "posreal" physical_clocks nil)
(pi_0 formal-const-decl
"{pi: posreal | P_bound?(P, rho, alpha_l, alpha_u, pi)}"
synch_constant_definitions nil)
(alpha_u formal-const-decl "nnreal" synch_constant_definitions nil)
(P_bound? const-decl "bool" synch_parameter_constraints nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(alpha_l formal-const-decl "nnreal" synch_constant_definitions nil)
(P formal-const-decl "posnat" synch_constant_definitions nil)
(posnat nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(drift const-decl "nonneg_real" physical_clocks nil)
(rho formal-const-decl "nnreal" synch_constant_definitions nil)
(nnreal type-eq-decl nil real_types nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(floor const-decl "{i | i <= x & x < i + 1}" floor_ceil nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(< const-decl "bool" reals nil) (<= const-decl "bool" reals nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(integer nonempty-type-from-decl nil integers nil)
(ADJ const-decl "nat" synch_constant_definitions nil)
(nat nonempty-type-eq-decl nil naturalnumbers 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)
(>= const-decl "bool" reals 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)
(IFF const-decl "[bool, bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(posreal_times_posreal_is_posreal application-judgement "posreal"
real_types nil)
(nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
real_types nil))
nil))
(ADJ_ineq_h 0
(ADJ_ineq_h-1 nil 3381419694
("" (swap-rel +)
(("" (expand "ADJ")
(("" (rewrite "floor_monotone")
(("" (hide 2) (("" (cancel-by 1 "rate") nil nil)) nil)) nil))
nil))
nil)
((nonneg_real_max application-judgement
"{z: nonneg_real | z >= x AND z >= y}" real_defs nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(posreal_div_posreal_is_posreal application-judgement "posreal"
real_types nil)
(both_sides_times_pos_le1 formula-decl nil real_props nil)
(/= const-decl "boolean" notequal nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(bijective? const-decl "bool" functions nil)
(id const-decl "(bijective?[T, T])" identity nil)
(TRUE const-decl "bool" booleans nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(floor_monotone formula-decl nil floor_ceiling_ineq nil)
(max const-decl "{p: real | p >= m AND p >= n}" real_defs nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
(nnreal_plus_posreal_is_posreal application-judgement "posreal"
real_types nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(rate const-decl "posreal" physical_clocks nil)
(pi_0 formal-const-decl
"{pi: posreal | P_bound?(P, rho, alpha_l, alpha_u, pi)}"
synch_constant_definitions nil)
(alpha_l formal-const-decl "nnreal" synch_constant_definitions nil)
(P_bound? const-decl "bool" synch_parameter_constraints nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(alpha_u formal-const-decl "nnreal" synch_constant_definitions nil)
(P formal-const-decl "posnat" synch_constant_definitions nil)
(posnat nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(drift const-decl "nonneg_real" physical_clocks nil)
(rho formal-const-decl "nnreal" synch_constant_definitions nil)
(nnreal type-eq-decl nil real_types nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(floor const-decl "{i | i <= x & x < i + 1}" floor_ceil nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(< const-decl "bool" reals nil) (<= const-decl "bool" reals nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(integer nonempty-type-from-decl nil integers nil)
(ADJ const-decl "nat" synch_constant_definitions nil)
(nat nonempty-type-eq-decl nil naturalnumbers 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)
(>= const-decl "bool" reals 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)
(IFF const-decl "[bool, bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(posreal_times_posreal_is_posreal application-judgement "posreal"
real_types nil)
(nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
real_types nil))
nil))
(ADJ_bound 0
(ADJ_bound-1 nil 3292973792
("" (lemma "P_bound")
(("" (expand* "ADJ" "id") (("" (assert) nil nil)) nil)) nil)
((nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(nonneg_real_max application-judgement
"{z: nonneg_real | z >= x AND z >= y}" real_defs nil)
(ADJ const-decl "nat" synch_constant_definitions 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)
(posreal_plus_nnreal_is_posreal application-judgement "posreal"
real_types nil)
(nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
(nnreal_plus_posreal_is_posreal application-judgement "posreal"
real_types nil)
(P_bound formula-decl nil synch_constant_definitions nil))
shostak))
(P_min_TCC1 0
(P_min_TCC1-1 nil 3292975885
("" (use "ADJ_bound") (("" (assert) nil nil)) nil)
((int_minus_int_is_int application-judgement "int" integers nil)
(real_ge_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)
(ADJ_bound formula-decl nil synch_constant_definitions nil))
shostak))
(p_min_bound 0
(p_min_bound-1 nil 3292982433
("" (lemma "P_bound") (("" (assert) (("" (assert) nil nil)) nil))
nil)
((nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(nonneg_real_max application-judgement
"{z: nonneg_real | z >= x AND z >= y}" real_defs nil)
(posreal_plus_nnreal_is_posreal application-judgement "posreal"
real_types 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)
(nnreal_plus_posreal_is_posreal application-judgement "posreal"
real_types nil)
(P_bound formula-decl nil synch_constant_definitions nil))
shostak))
(p_lower_TCC1 0
(p_lower_TCC1-1 nil 3292982874
("" (invoke (then (case "%1") (assert)) (! 1 2))
(("" (hide 2)
(("" (move-terms 1 l 2)
(("" (cross-mult)
(("" (lemma "p_min_bound")
(("" (assert)
(("" (expand "max")
(("" (lift-if)
(("" (prop)
(("1" (div-by (-2 1) "rate")
(("1" (assert) nil nil)) nil)
("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(div_mult_pos_gt1 formula-decl nil extra_real_props nil)
(nonneg_real_max application-judgement
"{z: nonneg_real | z >= x AND z >= y}" real_defs nil)
(posreal_plus_nnreal_is_posreal application-judgement "posreal"
real_types 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)
(nnreal_plus_posreal_is_posreal application-judgement "posreal"
real_types nil)
(both_sides_div_pos_lt1 formula-decl nil real_props nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(alpha_u formal-const-decl "nnreal" synch_constant_definitions nil)
(P_bound? const-decl "bool" synch_parameter_constraints nil)
(pi_0 formal-const-decl
"{pi: posreal | P_bound?(P, rho, alpha_l, alpha_u, pi)}"
synch_constant_definitions nil)
(both_sides_div_pos_gt1 formula-decl nil real_props nil)
(times_div_cancel2 formula-decl nil extra_real_props nil)
(nonzero_real nonempty-type-eq-decl nil reals nil)
(max const-decl "{p: real | p >= m AND p >= n}" real_defs nil)
(p_min_bound formula-decl nil synch_constant_definitions nil)
(nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(IFF const-decl "[bool, bool -> bool]" booleans nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(posreal_div_posreal_is_posreal application-judgement "posreal"
real_types nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(alpha_l formal-const-decl "nnreal" synch_constant_definitions nil)
(rate const-decl "posreal" physical_clocks nil)
(rho formal-const-decl "nnreal" synch_constant_definitions nil)
(nnreal type-eq-decl nil real_types nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(P formal-const-decl "posnat" synch_constant_definitions nil)
(posnat nonempty-type-eq-decl nil integers nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(>= const-decl "bool" reals 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)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/= const-decl "boolean" notequal nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields 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)
(real_minus_real_is_real application-judgement "real" reals nil))
shostak))
(p_min_TCC1 0
(p_min_TCC1-1 nil 3292983076
("" (invoke (then (case "%1") (assert)) (! 1 2))
(("" (hide 2)
(("" (isolate 1 l 1)
(("" (cross-mult)
(("" (lemma "p_min_bound")
(("" (expand "id")
(("" (assert)
(("" (expand "max")
(("" (lift-if)
(("" (assert)
(("" (prop)
(("" (div-by (-2 1) "rate")
(("" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((posreal_times_posreal_is_posreal application-judgement "posreal"
real_types nil)
(nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(div_mult_pos_gt1 formula-decl nil extra_real_props nil)
(nonneg_real_max application-judgement
"{z: nonneg_real | z >= x AND z >= y}" real_defs nil)
(posreal_plus_nnreal_is_posreal application-judgement "posreal"
real_types nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(both_sides_div_pos_gt1 formula-decl nil real_props nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(both_sides_div_pos_lt1 formula-decl nil real_props nil)
(max const-decl "{p: real | p >= m AND p >= n}" real_defs nil)
(p_min_bound formula-decl nil synch_constant_definitions nil)
(nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(nnreal_plus_posreal_is_posreal application-judgement "posreal"
real_types nil)
(IFF const-decl "[bool, bool -> bool]" booleans nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(posreal_div_posreal_is_posreal application-judgement "posreal"
real_types nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(pi_0 formal-const-decl
"{pi: posreal | P_bound?(P, rho, alpha_l, alpha_u, pi)}"
synch_constant_definitions nil)
(alpha_u formal-const-decl "nnreal" synch_constant_definitions nil)
(P_bound? const-decl "bool" synch_parameter_constraints nil)
(alpha_l formal-const-decl "nnreal" synch_constant_definitions nil)
(rate const-decl "posreal" physical_clocks nil)
(rho formal-const-decl "nnreal" synch_constant_definitions nil)
(nnreal type-eq-decl nil real_types nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(P formal-const-decl "posnat" synch_constant_definitions nil)
(posnat nonempty-type-eq-decl nil integers nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(>= const-decl "bool" reals 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)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/= const-decl "boolean" notequal nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields 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)
(real_minus_real_is_real application-judgement "real" reals nil))
shostak))
(p_min_lower 0
(p_min_lower-1 nil 3399247956
("" (expand "p_min")
(("" (expand "p_lower") (("" (propax) nil nil)) nil)) nil)
((p_lower const-decl "posreal" synch_constant_definitions nil)
(p_min const-decl "posreal" synch_constant_definitions nil))
shostak))
(p_max_upper 0
(p_max_upper-1 nil 3399247972
("" (expand "p_max")
(("" (expand "p_upper") (("" (propax) nil nil)) nil)) nil)
((p_upper const-decl "posreal" synch_constant_definitions nil)
(p_max const-decl "posreal" synch_constant_definitions nil))
shostak))
(drift_P_bound 0
(drift_P_bound-1 nil 3293977788
("" (expand "p_min")
(("" (lemma "P_bound")
(("" (isolate 1 r 1)
(("" (cross-mult)
((""
(invoke (then (case "%1 <= %2") (assert)) (! 1 l) (! -1 l))
(("" (hide-all-but 1)
(("" (assert)
(("" (expand "max")
(("" (lift-if)
(("" (assert)
(("" (expand "id")
(("" (prop)
(("" (assert)
(("" (isolate 1 l 2)
((""
(assert)
(("" (cancel) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((P_bound formula-decl nil synch_constant_definitions nil)
(posreal_times_posreal_is_posreal application-judgement "posreal"
real_types nil)
(div_mult_pos_lt2 formula-decl nil real_props nil)
(posreal_plus_nnreal_is_posreal application-judgement "posreal"
real_types nil)
(nonneg_real_max application-judgement
"{z: nonneg_real | z >= x AND z >= y}" real_defs nil)
(both_sides_times_pos_le1 formula-decl nil real_props nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(<= const-decl "bool" reals nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(max const-decl "{p: real | p >= m AND p >= n}" real_defs nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(pi_0 formal-const-decl
"{pi: posreal | P_bound?(P, rho, alpha_l, alpha_u, pi)}"
synch_constant_definitions nil)
(alpha_u formal-const-decl "nnreal" synch_constant_definitions nil)
(P_bound? const-decl "bool" synch_parameter_constraints nil)
(alpha_l formal-const-decl "nnreal" synch_constant_definitions nil)
(rate const-decl "posreal" physical_clocks nil)
(posreal 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 "[numfield, numfield -> numfield]" number_fields nil)
(P formal-const-decl "posnat" synch_constant_definitions nil)
(posnat nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers 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)
(drift const-decl "nonneg_real" physical_clocks nil)
(rho formal-const-decl "nnreal" synch_constant_definitions nil)
(nnreal type-eq-decl nil real_types nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(>= const-decl "bool" reals nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(< const-decl "bool" reals 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)
(IFF const-decl "[bool, bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(posreal_div_posreal_is_posreal application-judgement "posreal"
real_types nil)
(nnreal_plus_posreal_is_posreal application-judgement "posreal"
real_types nil)
(real_minus_real_is_real application-judgement "real" reals nil)
(nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(p_min const-decl "posreal" synch_constant_definitions nil))
nil))
(Pi_TCC1 0
(Pi_TCC1-1 nil 3293064140
("" (rewrite "gt_ceiling_l")
(("" (expand "id") (("" (assert) nil nil)) nil)) nil)
((real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(nnreal_plus_posreal_is_posreal application-judgement "posreal"
real_types nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(integer nonempty-type-from-decl nil integers nil)
(P_max const-decl "posnat" synch_constant_definitions nil)
(drift const-decl "nonneg_real" physical_clocks nil)
(pi_0 formal-const-decl
"{pi: posreal | P_bound?(P, rho, alpha_l, alpha_u, pi)}"
synch_constant_definitions nil)
(P formal-const-decl "posnat" synch_constant_definitions nil)
(P_bound? const-decl "bool" synch_parameter_constraints nil)
(posnat nonempty-type-eq-decl nil integers nil)
(nonneg_int nonempty-type-eq-decl nil integers 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)
(alpha_u formal-const-decl "nnreal" synch_constant_definitions nil)
(alpha_l formal-const-decl "nnreal" synch_constant_definitions nil)
(max const-decl "{p: real | p >= m AND p >= n}" real_defs nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(rate const-decl "posreal" physical_clocks nil)
(rho formal-const-decl "nnreal" synch_constant_definitions nil)
(nnreal type-eq-decl nil real_types 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)
(* 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)
(gt_ceiling_l formula-decl nil floor_ceiling_ineq nil)
(posreal_plus_nnreal_is_posreal application-judgement "posreal"
real_types nil)
(nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(nonneg_real_max application-judgement
"{z: nonneg_real | z >= x AND z >= y}" real_defs nil)
(nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(posreal_times_posreal_is_posreal application-judgement "posreal"
real_types nil))
shostak)))
¤ Dauer der Verarbeitung: 0.18 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.
|
