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(> const-decl "bool" reals nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(Vector type-eq-decl nil vectors_2D nil)
(zero const-decl "Vector" vectors_2D nil)
(comp_zero_x formula-decl nil vectors_2D nil))
nil)
(angle_xx_TCC1-2 nil 3431180799
(";;; Proof angle_0x_TCC1-1 for formula angles_2D.angle_0x_TCC1"
(skeep)
((";;; Proof angle_0x_TCC1-1 for formula angles_2D.angle_0x_TCC1"
(rewrite "nzv_xy_neq_0") nil))
";;; developed with shostak decision procedures")
nil nil)
(angle_xx_TCC1-1 nil 3414486827
("" (skeep) (("" (rewrite "nzv_xy_neq_0") nil nil)) nil)
((nzv_xy_neq_0 formula-decl nil vectors_2D nil)
(Vector type-eq-decl nil vectors_2D nil))
nil))
(angle_xx 0
(angle_xx-1 nil 3414486832
("" (skeep)
(("" (rewrite "angle_Angle")
(("" (expand "Angle")
(("" (expand "atan2")
(("" (assert)
(("" (lemma "atan_tan")
(("" (inst - "pi/4")
(("" (rewrite "tan_pi4") (("" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((angle_Angle formula-decl nil angles_2D nil)
(real nonempty-type-from-decl nil reals nil)
(Vector type-eq-decl nil vectors_2D nil)
(boolean nonempty-type-decl nil booleans nil)
(/= const-decl "boolean" notequal nil)
(zero const-decl "Vector" vectors_2D nil)
(Nz_vect2 type-eq-decl nil vectors_2D nil)
(number nonempty-type-decl nil numbers 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)
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(>= const-decl "bool" reals nil)
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(> const-decl "bool" reals nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(atan2 const-decl "real" atan2 "trig/")
(atan_tan formula-decl nil trig_inverses "trig/")
(tan_pi4 formula-decl nil trig_values "trig/")
(AND const-decl "[bool, bool -> bool]" booleans nil)
(< const-decl "bool" reals nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(pi_lb const-decl "posreal" trig_basic "trig/")
(pi_ub const-decl "posreal" trig_basic "trig/")
(pi const-decl "{r: posreal | r > pi_lb AND r < pi_ub}" trig_basic
"trig/")
(real_abs_lt_pi2 nonempty-type-eq-decl nil atan "trig/")
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
real_types nil)
(posreal_div_posreal_is_posreal application-judgement "posreal"
real_types nil)
(minus_nzreal_is_nzreal application-judgement "nzreal" real_types
nil)
(Angle const-decl "Angle" angles_2D nil))
shostak))
(angle_n0_TCC1 0
(angle_n0_TCC1-2 nil 3431180821
("" (skeep)
(("" (decompose-equality -1) (("" (assert) nil nil)) nil)) nil)
((boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
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(= const-decl "[T, T -> boolean]" equalities 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)
(<= const-decl "bool" reals nil)
(nonpos_real nonempty-type-eq-decl nil real_types nil)
(< const-decl "bool" reals nil)
(negreal nonempty-type-eq-decl nil real_types nil)
(Vector type-eq-decl nil vectors_2D nil)
(zero const-decl "Vector" vectors_2D nil)
(comp_zero_x formula-decl nil vectors_2D nil))
nil)
(angle_n0_TCC1-1 nil 3414487843
("" (skeep) (("" (rewrite "nzv_xy_neq_0") nil nil)) nil)
((nzv_xy_neq_0 formula-decl nil vectors_2D nil)
(Vector type-eq-decl nil vectors_2D nil))
nil))
(angle_n0 0
(angle_n0-1 nil 3414487848
("" (skeep)
(("" (rewrite "angle_Angle")
(("" (expand "Angle")
(("" (expand "atan2") (("" (rewrite "atan_0") nil nil)) nil))
nil))
nil))
nil)
((angle_Angle formula-decl nil angles_2D nil)
(real nonempty-type-from-decl nil reals nil)
(Vector type-eq-decl nil vectors_2D nil)
(boolean nonempty-type-decl nil booleans nil)
(/= const-decl "boolean" notequal nil)
(zero const-decl "Vector" vectors_2D nil)
(Nz_vect2 type-eq-decl nil vectors_2D nil)
(number nonempty-type-decl nil numbers 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)
(bool nonempty-type-eq-decl nil booleans nil)
(<= const-decl "bool" reals nil)
(nonpos_real nonempty-type-eq-decl nil real_types nil)
(< const-decl "bool" reals nil)
(negreal nonempty-type-eq-decl nil real_types nil)
(atan2 const-decl "real" atan2 "trig/")
(atan_0 formula-decl nil atan "trig/")
(Angle const-decl "Angle" angles_2D nil))
shostak))
(angle_0n_TCC1 0
(angle_0n_TCC1-2 nil 3431180834
("" (skeep)
(("" (decompose-equality -1) (("" (assert) nil nil)) nil)) nil)
((boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(number nonempty-type-decl nil numbers nil)
(= const-decl "[T, T -> boolean]" equalities 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)
(<= const-decl "bool" reals nil)
(nonpos_real nonempty-type-eq-decl nil real_types nil)
(< const-decl "bool" reals nil)
(negreal nonempty-type-eq-decl nil real_types nil)
(Vector type-eq-decl nil vectors_2D nil)
(zero const-decl "Vector" vectors_2D nil)
(comp_zero_y formula-decl nil vectors_2D nil)
(comp_zero_x formula-decl nil vectors_2D nil))
nil)
(angle_0n_TCC1-1 nil 3414487843
("" (skeep) (("" (rewrite "nzv_xy_neq_0") nil nil)) nil)
((nzv_xy_neq_0 formula-decl nil vectors_2D nil)
(Vector type-eq-decl nil vectors_2D nil))
nil))
(angle_0n 0
(angle_0n-1 nil 3414487912
("" (skeep)
(("" (rewrite "angle_Angle")
(("" (expand "Angle")
(("" (expand "atan2") (("" (propax) nil nil)) nil)) nil))
nil))
nil)
((angle_Angle formula-decl nil angles_2D nil)
(real nonempty-type-from-decl nil reals nil)
(Vector type-eq-decl nil vectors_2D nil)
(boolean nonempty-type-decl nil booleans nil)
(/= const-decl "boolean" notequal nil)
(zero const-decl "Vector" vectors_2D nil)
(Nz_vect2 type-eq-decl nil vectors_2D nil)
(number nonempty-type-decl nil numbers 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)
(bool nonempty-type-eq-decl nil booleans nil)
(<= const-decl "bool" reals nil)
(nonpos_real nonempty-type-eq-decl nil real_types nil)
(< const-decl "bool" reals nil)
(negreal nonempty-type-eq-decl nil real_types nil)
(posreal_times_posreal_is_posreal application-judgement "posreal"
real_types nil)
(atan2 const-decl "real" atan2 "trig/")
(Angle const-decl "Angle" angles_2D nil))
nil))
(angle_nx_TCC1 0
(angle_nx_TCC1-2 nil 3431180840
("" (skeep)
(("" (decompose-equality -1) (("" (assert) nil nil)) nil)) nil)
((minus_nzreal_is_nzreal application-judgement "nzreal" real_types
nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(number nonempty-type-decl nil numbers nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(- const-decl "[numfield -> numfield]" 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)
(>= 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)
(Vector type-eq-decl nil vectors_2D nil)
(zero const-decl "Vector" vectors_2D nil)
(comp_zero_x formula-decl nil vectors_2D nil))
nil)
(angle_nx_TCC1-1 nil 3414488036
("" (skeep) (("" (rewrite "nzv_xy_neq_0") nil nil)) nil)
((nzv_xy_neq_0 formula-decl nil vectors_2D nil)
(Vector type-eq-decl nil vectors_2D nil))
nil))
(angle_nx 0
(angle_nx-1 nil 3414488044
("" (skeep)
(("" (rewrite "angle_Angle")
(("" (expand "Angle")
(("" (expand "atan2")
(("" (lemma "atan_neg")
(("" (inst - "1")
--> --------------------
--> maximum size reached
--> --------------------
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