(test_contnil 3431788742"" (expand "metric?" )"" (expand "metric_zero?" )"" (expand "metric_symmetric?" )"" (expand "metric_triangle?" ) (("" (grind) nil nil )) nil ))nil ))nil ))nil )"real" reals nil )"bool" metric_def nil )"bool" metric_def nil )"odd_int" integers nil )"{n: nonneg_real | n >= m AND n >= -m}" real_defsnil )"real" reals nil )"(strict_total_order?[real])" real_props nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil numbers nil )NOT const-decl "[bool -> bool]" booleans nil )nil booleans nil )nil booleans nil )"bool" metric_def nil )"bool" metric_def nil ))nil ))nil 3431795137"" (expand "restrict" )"" (expand "metric?" )"" (expand "metric_zero?" )"" (expand "metric_symmetric?" )"" (expand "metric_triangle?" ) (("" (grind) nil nil )) nil ))nil ))nil ))nil ))nil )"bool" metric_def nil )"bool" metric_def nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil numbers nil )"boolean" notequal nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )nil reals nil )"real" reals nil )"(strict_total_order?[real])" real_props nil )"{n: nonneg_real | n >= m AND n >= -m}" real_defsnil )"odd_int" integers nil )"bool" metric_def nil )"bool" metric_def nil )"R" restrict nil )"real" reals nil ))nil ))nil 3431788749"" (expand "metric_continuous?" )"" (skosimp)"" (expand "metric_continuous_at?" )"" (skosimp)"" (expand "member" )"" (expand "ball" )"" (expand "restrict" )"" case "forall (x,y:nzreal): 1 / x - 1 / y = (y-x)/(x*y)" )"1" case "FORALL (x, y: nzreal,delta:posreal): abs(x-y) (abs(x)/2)"1" "min(abs(x!1)/3,epsilon!1*(abs(x!1)*abs(x!1)/2))" )"1" (skosimp)"1" (inst -2 "x!1" "x!2" )"1" (replace -2)"1" (rewrite "abs_div" )"1" rewrite "abs_mult" )"1" rewrite "div_mult_pos_lt1" 1)"1" "x!1" "x!2" "min(abs(x!1) / 3, epsilon!1 * (abs(x!1) * abs(x!1) / 2))" )"1" assert )"1" "1" "both_sides_times_pos_lt1" "pz" "epsilon!1 * abs(x!1)" "x" "abs(x!1) / 2" "y" "abs(x!2)" ))"1" assert )"1" "1" (grind) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (hide-all-but 1) (("2" (grind) nil nil ))nil ))nil )"2" (hide 2) (("2" (grind) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"real" reals nil )"set[T]" metric_space_def nil )"[numfield, numfield -> numfield]" number_fields nil )"[numfield, nznum -> numfield]" number_fields nil )nil number_fields nil )"[numfield, numfield -> numfield]" number_fields nil )nil number_fields nil )"[T, T -> boolean]" equalities nil )nil reals nil )"boolean" notequal nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )"nzreal" nil )"real" reals nil )NOT const-decl "[bool -> bool]" booleans nil )"(total_order?[real])" nil )"{z: posreal | z <= x AND z <= y}" real_defs nil )"posreal" nil )"{y: posreal | y >= x}" nil )min const-decl "{p: real | p <= m AND p <= n}" real_defs nil )"bool" reals nil )nil reals nil )nil real_props nil )"nnreal" nil )nil real_props nil )"(strict_total_order?[real])" real_props nil )nil real_props nil )"odd_int" integers nil )"real" reals nil )"nzreal" real_typesnil )"(strict_total_order?[real])" real_props nil )nil real_props nil )"{n: nonneg_real | n >= m AND n >= -m}" real_defsnil )"[numfield -> numfield]" number_fields nil )"bool" reals nil )AND const-decl "[bool, bool -> bool]" booleans nil )"[bool, bool -> bool]" booleans nil )nil real_types nil )"bool" reals nil )nil real_types nil )"bool" reals nil )nil booleans nil )"posreal" nil )"R" restrict nil )"bool" sets nil )"nzreal" nil )"bool" metric_continuity nil )"bool" metric_continuity nil ))quality 96%
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