(timing_window
(timing_conforms_def 0
(timing_conforms_def-1 nil 3310129453
("" (skosimp*)
(("" (rewrite "abs_max" )
(("" (rewrite "max_le" )
(("" (expand "timing_conforms?" )
(("" (prop)
(("1" (lemma "clock_increasing" )
(("1"
(inst - "Timestamp(c!1, ev!1)"
"T!1 - Delta_max(skew!1)" "c!1" )
(("1" (assert ) nil nil )) nil ))
nil )
("2" (lemma "clock_increasing" )
(("2"
(inst - "Delta_max(skew!1) + T!1"
"Timestamp(c!1, ev!1)" "c!1" )
(("2" (assert ) nil nil )) nil ))
nil )
("3" (rewrite "clock_nondecreasing" ) nil nil )
("4" (rewrite "clock_nondecreasing" ) nil nil ))
nil ))
nil ))
nil ))
nil ))
nil )
((abs_max formula-decl nil abs_props 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 )
(numfield nonempty-type-eq-decl nil number_fields nil )
(- const-decl "[numfield, numfield -> numfield]" number_fields 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 )
(/= 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" timing_window 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 )
(integer nonempty-type-from-decl nil integers nil )
(min_latency formal-const-decl "nonneg_real" timing_window nil )
(var_latency formal-const-decl "nonneg_real" timing_window nil )
(Timestamp const-decl "integer" timing_imprecision nil )
(rat_max application-judgement "{s: rat | s >= q AND s >= r}"
real_defs nil )
(int_max application-judgement "{k: int | i <= k AND j <= k}"
real_defs nil )
(minus_int_is_int application-judgement "int" integers nil )
(timing_conforms? const-decl "bool" timing_window nil )
(clock_nondecreasing formula-decl nil physical_clocks nil )
(clock_increasing formula-decl nil physical_clocks nil )
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil )
(int_plus_int_is_int application-judgement "int" integers nil )
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil )
(max_le formula-decl nil minmax_ineq nil )
(- const-decl "[numfield -> numfield]" number_fields nil )
(nat nonempty-type-eq-decl nil naturalnumbers nil )
(Delta_max const-decl "nat" timing_window nil )
(int_minus_int_is_int application-judgement "int" integers nil ))
shostak))
(good_range_always_conforms 0
(good_range_always_conforms-2 nil 3351527353
("" (skosimp*)
(("" (rewrite "timing_conforms_def" )
(("" (expand "Delta_max" )
(("" (rewrite "le_floor_r" )
(("" (factor 1 r)
(("" (div-by 1 "rate" )
(("" (use "link_abs_bound" )
(("" (assert )
(("" (use "abs_drift_lb" )
(("" (lemma "triangle" )
((""
(invoke (inst - "%1" "%2" ) (! -3 l 1)
(! -5 l 1))
(("" (assert ) nil nil )) nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
((int_minus_int_is_int application-judgement "int" integers nil )
(timing_conforms_def formula-decl nil timing_window 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 )
(integer nonempty-type-from-decl nil 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" timing_window 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 )
(int_abs_is_nonneg application-judgement "{j: nonneg_int | j >= i}"
real_defs nil )
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil )
(Timestamp const-decl "integer" timing_imprecision nil )
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil )
(- const-decl "[numfield -> numfield]" number_fields nil )
(max_error const-decl "posreal" timing_imprecision nil )
(var_latency formal-const-decl "nonneg_real" timing_window nil )
(min_latency formal-const-decl "nonneg_real" timing_window nil )
(* const-decl "[numfield, numfield -> numfield]" number_fields nil )
(le_floor_r formula-decl nil floor_ceiling_ineq nil )
(posreal_plus_nnreal_is_posreal application-judgement "posreal"
real_types nil )
(both_sides_div_pos_le1 formula-decl nil real_props nil )
(times_div_cancel1 formula-decl nil extra_real_props nil )
(nonzero_real nonempty-type-eq-decl nil reals nil )
(nnreal_div_posreal_is_nnreal application-judgement "nnreal"
real_types nil )
(triangle formula-decl nil real_props nil )
(nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
real_types nil )
(real_plus_real_is_real application-judgement "real" reals nil )
(abs_drift_lb formula-decl nil physical_clocks nil )
(int_plus_int_is_int application-judgement "int" integers nil )
(minus_odd_is_odd application-judgement "odd_int" integers nil )
(link_abs_bound formula-decl nil timing_imprecision nil )
(= const-decl "[T, T -> boolean]" equalities nil )
(Delta_max const-decl "nat" timing_window nil )
(nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
real_types nil )
(posreal_times_posreal_is_posreal application-judgement "posreal"
real_types nil )
(real_minus_real_is_real application-judgement "real" reals nil ))
nil )
(good_range_always_conforms-1 nil 3351512334
("" (skosimp*)
(("" (forward-chain "good_range_is_good_event" )
(("" (rewrite "timing_conforms_def" )
(("" (lemma "good_event_lem" )
(("" (assert )
(("" (inst - "T!1" "c1!1" "c2!1" "ev!1" "skew!1" )
(("" (assert ) nil nil )) nil ))
nil ))
nil ))
nil ))
nil ))
nil )
((rate const-decl "posreal" physical_clocks nil )
(good_clock nonempty-type-eq-decl nil physical_clocks nil ))
nil ))
(good_range_inner_window 0
(good_range_inner_window-1 nil 3373808691
("" (expand "inner_window?" )
(("" (skosimp*)
(("" (forward-chain "good_range_always_conforms" ) nil nil )) nil ))
nil )
((real_minus_real_is_real application-judgement "real" reals 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" timing_window 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 )
(int nonempty-type-eq-decl nil integers nil )
(integer nonempty-type-from-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 )
(good_range_always_conforms formula-decl nil timing_window nil )
(inner_window? const-decl "bool" timing_window nil ))
shostak)))
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