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nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
nil shostak))
(sin_cos 0
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("" (skosimp*)
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(("" (lemma "cos_neg" ("a" "a!1+pi/2"))
(("" (lemma "sin_neg" ("a" "a!1")) (("" (assert) nil nil))
nil))
nil))
nil))
nil)
((pi const-decl "{r: posreal | r > pi_lb AND r < pi_ub}" trig_basic
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nil)
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(cos_range application-judgement "trig_range" trig_basic nil)
(posreal_div_posreal_is_posreal application-judgement "posreal"
real_types nil)
(cos_neg formula-decl nil trig_basic nil)
(real_plus_real_is_real application-judgement "real" reals nil))
shostak))
(sin_shift 0
(sin_shift-1 nil 3265074854
("" (skosimp*)
(("" (lemma "sin_neg" ("a" "pi/2-a!1"))
(("" (lemma "sin_cos" ("a" "a!1-pi/2")) (("" (assert) nil nil))
nil))
nil))
nil)
((pi const-decl "{r: posreal | r > pi_lb AND r < pi_ub}" trig_basic
nil)
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nil)
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(real_plus_real_is_real application-judgement "real" reals nil)
(cos_range application-judgement "trig_range" trig_basic nil)
(minus_real_is_real application-judgement "real" reals nil)
(posreal_div_posreal_is_posreal application-judgement "posreal"
real_types nil)
(sin_range application-judgement "trig_range" trig_basic nil)
(sin_cos formula-decl nil trig_basic nil))
shostak))
(cos_shift 0
(cos_shift-1 nil 3265010327
("" (skosimp*)
(("" (lemma "sin_shift" ("a" "pi/2-a!1")) (("" (assert) nil nil))
nil))
nil)
((pi const-decl "{r: posreal | r > pi_lb AND r < pi_ub}" trig_basic
nil)
(pi_ub const-decl "posreal" trig_basic nil)
(< const-decl "bool" reals nil)
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(AND const-decl "[bool, bool -> bool]" booleans nil)
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(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
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(real_minus_real_is_real application-judgement "real" reals nil)
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(posreal_div_posreal_is_posreal application-judgement "posreal"
real_types nil)
(cos_range application-judgement "trig_range" trig_basic nil))
shostak))
(neg_cos 0
(neg_cos-1 nil 3265010987
("" (skosimp*)
(("" (rewrite "cos_sin")
(("" (rewrite "sin_cos") (("" (assert) nil nil)) nil)) nil))
nil)
((cos_sin formula-decl nil trig_basic nil)
(number nonempty-type-decl nil numbers nil)
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(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)
(cos_range application-judgement "trig_range" trig_basic nil)
(posreal_div_posreal_is_posreal application-judgement "posreal"
real_types nil)
(real_plus_real_is_real application-judgement "real" reals nil)
(sin_range application-judgement "trig_range" trig_basic nil)
(posreal_times_posreal_is_posreal application-judgement "posreal"
real_types nil)
(minus_real_is_real application-judgement "real" reals nil)
(pi const-decl "{r: posreal | r > pi_lb AND r < pi_ub}" trig_basic
nil)
(pi_ub const-decl "posreal" trig_basic nil)
(< const-decl "bool" reals nil)
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(AND const-decl "[bool, bool -> bool]" booleans nil)
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(nonneg_real nonempty-type-eq-decl nil real_types nil)
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(/ 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)
(sin_cos formula-decl nil trig_basic nil))
shostak))
(neg_sin 0
(neg_sin-1 nil 3265071739
("" (skosimp*)
(("" (rewrite "sin_cos")
(("" (rewrite "cos_sin") (("" (assert) nil nil)) nil)) nil))
nil)
((sin_cos formula-decl nil trig_basic nil)
(number nonempty-type-decl nil numbers nil)
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nil)
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(posreal_div_posreal_is_posreal application-judgement "posreal"
real_types nil)
(real_plus_real_is_real application-judgement "real" reals nil)
(cos_range application-judgement "trig_range" trig_basic nil)
(minus_real_is_real application-judgement "real" reals nil)
(posreal_times_posreal_is_posreal application-judgement "posreal"
real_types nil)
(pi const-decl "{r: posreal | r > pi_lb AND r < pi_ub}" trig_basic
nil)
(pi_ub const-decl "posreal" trig_basic nil)
(< const-decl "bool" reals nil)
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(/ 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)
(cos_sin formula-decl nil trig_basic nil))
shostak))
(sin_pi 0
(sin_pi-2 nil 3279387666
("" (case "pi=pi/2 + pi/2")
(("1" (replace -1 :hide? t)
(("1" (lemma "sin_minus")
(("1" (inst -1 "pi/2" "-pi/2")
(("1" (case "pi / 2 - -pi / 2 = pi / 2 + pi / 2")
(("1" (replace -1 :hide? t)
(("1" (replace -1 :hide? t)
(("1" (case "(pi / 2 + pi / 2) / 2 = pi/2")
(("1" (replace -1 :hide? t)
(("1" (case "-(pi / 2 + pi / 2)/2 = -(pi/2)")
(("1" (replace -1 :hide? t)
(("1" (rewrite "sin_neg")
(("1" (rewrite "cos_neg")
(("1" (rewrite "sin_pi2")
(("1"
(rewrite "cos_pi2")
(("1" (ground) nil)))))))))))
("2" (ground) nil)))))
("2" (ground) nil)))))))
("2" (ground) nil)))))))))
("2" (ground) nil))
nil)
nil nil)
(sin_pi-1 nil 3265006547
("" (expand "sin")
(("" (lemma "div_cancel1" ("x" "1/2" "n0z" "pi"))
(("" (replace -1 1)
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(("" (split -1)
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nil))
nil))
nil))
nil))
nil))
nil)
("2" (assert) nil nil) ("3" (assert) nil nil))
nil))
nil))
nil))
nil))
nil)
nil shostak))
(cos_pi 0
(cos_pi-2 nil 3279154503
("" (expand "cos")
(("" (lemma "div_cancel1" ("x" "1/2" "n0z" "pi"))
(("" (replace -1)
(("" (lemma "floor_val" ("i" "1" "j" "2" "k" "0"))
(("" (split -1)
(("1" (replace -1)
(("1" (simplify 1)
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nil))
nil)
("2" (assert) nil nil) ("3" (assert) nil nil))
nil))
nil))
nil))
nil))
nil)
nil nil)
(cos_pi-1 nil 3265008251
("" (expand "pi")
(("" (expand "cos")
(("" (lemma "div_cancel1" ("x" "1/2" "n0z" "pi"))
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nil))
nil)
("2" (assert) nil nil) ("3" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
nil shostak))
(tan_pi_TCC1 0
(tan_pi_TCC1-1 nil 3264999490
("" (expand "Tan?")
(("" (rewrite "cos_pi") (("" (assert) nil nil)) nil)) nil)
((cos_pi formula-decl nil trig_basic nil)
(minus_odd_is_odd application-judgement "odd_int" integers nil)
(Tan? const-decl "bool" trig_basic nil))
shostak))
(tan_pi 0
(tan_pi-1 nil 3265006469
("" (expand "tan")
(("" (rewrite "sin_pi")
(("" (rewrite "cos_pi") (("" (assert) nil nil)) nil)) nil))
nil)
((sin_pi formula-decl nil trig_basic nil)
(sin_range application-judgement "trig_range" trig_basic nil)
(cos_range application-judgement "trig_range" trig_basic nil)
(rat_div_nzrat_is_rat application-judgement "rat" rationals nil)
(minus_odd_is_odd application-judgement "odd_int" integers nil)
(cos_pi formula-decl nil trig_basic nil)
(tan const-decl "real" trig_basic nil))
shostak))
(sin_3pi2 0
(sin_3pi2-1 nil 3265010743
("" (lemma "neg_sin" ("a" "pi/2"))
(("" (rewrite "sin_pi2") (("" (assert) nil nil)) nil)) nil)
((sin_pi2 formula-decl nil trig_basic nil)
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real_types nil)
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real_types nil)
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real_types nil)
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nil)
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(< const-decl "bool" reals nil)
(pi_ub const-decl "posreal" trig_basic nil)
(pi const-decl "{r: posreal | r > pi_lb AND r < pi_ub}" trig_basic
nil))
shostak))
(cos_3pi2 0
(cos_3pi2-1 nil 3265010800
("" (lemma "neg_cos" ("a" "pi/2"))
(("" (rewrite "cos_pi2") (("" (assert) nil nil)) nil)) nil)
((cos_pi2 formula-decl nil trig_basic nil)
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real_types nil)
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real_types nil)
(posreal_div_posreal_is_posreal application-judgement "posreal"
real_types nil)
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nil)
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(< const-decl "bool" reals nil)
(pi_ub const-decl "posreal" trig_basic nil)
(pi const-decl "{r: posreal | r > pi_lb AND r < pi_ub}" trig_basic
nil))
shostak))
(sin_2pi 0
(sin_2pi-2 nil 3279154535
("" (expand "sin")
(("" (rewrite "div_simp")
(("" (rewrite "floor_int")
(("" (assert) (("" (rewrite "sin_phase_0") nil nil)) nil))
nil))
nil))
nil)
nil nil)
(sin_2pi-1 nil 3265010441
("" (expand "pi")
(("" (expand "sin")
(("" (rewrite "div_simp")
(("" (rewrite "floor_int")
(("" (assert) (("" (rewrite "sin_phase_0") nil nil)) nil))
nil))
nil))
nil))
nil)
nil shostak))
(cos_2pi 0
(cos_2pi-2 nil 3279154560
("" (expand "cos")
(("" (rewrite "div_simp")
(("" (rewrite "floor_int")
(("" (assert) (("" (rewrite "cos_phase_0") nil nil)) nil))
nil))
nil))
nil)
nil nil)
(cos_2pi-1 nil 3265010493
("" (expand "cos")
(("" (expand "pi")
(("" (rewrite "div_simp")
(("" (rewrite "floor_int")
(("" (assert) (("" (rewrite "cos_phase_0") nil nil)) nil))
nil))
nil))
nil))
nil)
nil shostak))
(tan_2pi_TCC1 0
(tan_2pi_TCC1-1 nil 3264999491
("" (expand "Tan?")
(("" (rewrite "cos_2pi") (("" (assert) nil nil)) nil)) nil)
((cos_2pi formula-decl nil trig_basic nil)
(Tan? const-decl "bool" trig_basic nil))
shostak))
(tan_2pi 0
(tan_2pi-1 nil 3265006491
("" (expand "tan")
(("" (rewrite "sin_2pi")
(("" (rewrite "cos_2pi") (("" (assert) nil nil)) nil)) nil))
nil)
((sin_2pi formula-decl nil trig_basic nil)
(sin_range application-judgement "trig_range" trig_basic nil)
(cos_range application-judgement "trig_range" trig_basic nil)
(cos_2pi formula-decl nil trig_basic nil)
(tan const-decl "real" trig_basic nil))
shostak))
(sin_plus 0
(sin_plus-1 nil 3265083493
("" (skosimp*)
(("" (expand "sin")
(("" (expand "cos")
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(("" (name "FLB" "floor(b!1 / (2 * pi))")
(("" (replace -1)
(("" (replace -2)
((""
(lemma "floor_plus"
("x" "a!1/(2*pi)" "y" "b!1/(2*pi)"))
(("" (replace -2)
(("" (replace -3)
((""
(lemma "sin_phase_sum"
("x" "a!1 - 2 * (FLA * pi)" "y"
"b!1 - 2 * (FLB * pi)"))
(("1" (replace -1 1)
(("1" (hide -1)
(("1"
(case "a!1 - 2 * (FLA * pi) + (b!1 - 2 * (FLB * pi)) < 2 * pi")
(("1"
(assert)
(("1"
(case
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(("1" (assert) nil nil)
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(hide -2 2)
(("2"
(lemma
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("x"
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(("2"
(flatten)
(("2"
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(("2"
(replace -4)
(("2"
(replace -5)
(("2"
(lemma
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("x"
"floor(a!1 / (2 * pi) + b!1 / (2 * pi) - FLA - FLB)"
"y"
"a!1 / (2 * pi) + b!1 / (2 * pi) - FLA - FLB"
"pz"
"2*pi"))
(("2"
(lemma
"both_sides_times_pos_lt1"
("y"
"1+floor(a!1 / (2 * pi) + b!1 / (2 * pi) - FLA - FLB)"
"x"
"a!1 / (2 * pi) + b!1 / (2 * pi) - FLA - FLB"
"pz"
"2*pi"))
(("2"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
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(case
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(("1" (assert) nil nil)
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(hide 3)
(("2"
(case
"floor(fractional(a!1 / (2 * pi)) + fractional(b!1 / (2 * pi))) = 1")
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(hide 2)
(("2"
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(("2"
(replace -2)
(("2"
(replace -3)
(("2"
(hide -1)
(("2"
(lemma
"floor_def"
("x"
"a!1 / (2 * pi) + b!1 / (2 * pi) - FLA - FLB"))
(("2"
(lemma
"both_sides_times_pos_lt1"
("y"
"1+floor(a!1 / (2 * pi) + b!1 / (2 * pi) - FLA - FLB)"
"x"
"a!1 / (2 * pi) + b!1 / (2 * pi) - FLA - FLB"
"pz"
"2*pi"))
(("2"
(lemma
"both_sides_times_pos_lt1"
("x"
"floor(a!1 / (2 * pi) + b!1 / (2 * pi) - FLA - FLB)"
"y"
"a!1 / (2 * pi) + b!1 / (2 * pi) - FLA - FLB"
"pz"
"2*pi"))
(("2"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (hide 2)
(("2" (lemma "floor_def" ("x" "b!1/(2*pi)"))
(("2" (rewrite "div_mult_pos_lt1" -1)
(("2"
(rewrite "div_mult_pos_le2" -1)
(("2"
(flatten)
(("2"
(replace -4)
(("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
("3" (hide-all-but 1)
(("3" (expand "FLA")
(("3"
(lemma "floor_def" ("x" "a!1/(2*pi)"))
(("3"
(rewrite "div_mult_pos_lt1" -1)
(("3"
(rewrite "div_mult_pos_le2" -1)
(("3"
(flatten)
(("3" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
nil shostak))
(sin_minus 0
(sin_minus-1 nil 3265007645
("" (skosimp*)
(("" (lemma "sin_plus" ("a" "a!1" "b" "-b!1"))
(("" (rewrite "sin_neg")
(("" (rewrite "cos_neg") (("" (assert) nil nil)) nil)) nil))
nil))
nil)
((- const-decl "[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)
(sin_plus formula-decl nil trig_basic nil)
(minus_real_is_real application-judgement "real" reals nil)
(cos_neg formula-decl nil trig_basic nil)
(real_plus_real_is_real application-judgement "real" reals nil)
(real_minus_real_is_real application-judgement "real" reals nil)
(sin_range application-judgement "trig_range" trig_basic nil)
(real_times_real_is_real application-judgement "real" reals nil)
(cos_range application-judgement "trig_range" trig_basic nil)
(sin_neg formula-decl nil trig_basic nil))
shostak))
(cos_plus 0
(cos_plus-1 nil 3265071786
("" (skosimp*)
(("" (rewrite "cos_sin")
(("" (rewrite "cos_sin")
(("" (lemma "sin_cos" ("a" "a!1"))
(("" (lemma "sin_plus" ("a" "pi/2+a!1" "b" "b!1"))
(("" (assert) nil nil)) nil))
--> --------------------
--> maximum size reached
--> --------------------
¤ Dauer der Verarbeitung: 0.55 Sekunden
(vorverarbeitet)
¤
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