(vect_trig_3D
(cos_range 0
(cos_range-1 nil 3403546047
("" (skosimp*)
(("" (expand "cos")
(("" (lemma "dot_norm")
(("" (inst?)
(("" (prop)
(("1" (cross-mult 1) (("1" (assert) nil nil)) nil)
("2" (cross-mult 1) (("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
((nz_norm_gt_0 application-judgement "posreal" vectors_3D nil)
(posreal_times_posreal_is_posreal application-judgement "posreal"
real_types nil)
(cos const-decl "real" vect_trig_3D nil)
(minus_real_is_real application-judgement "real" reals nil)
(real nonempty-type-from-decl nil reals nil)
(Vector type-eq-decl nil vectors_3D nil)
(boolean nonempty-type-decl nil booleans nil)
(/= const-decl "boolean" notequal nil)
(zero const-decl "Vector" vectors_3D nil)
(Nz_vector type-eq-decl nil vectors_3D nil)
(real_div_nzreal_is_real application-judgement "real" reals nil)
(div_mult_pos_le1 formula-decl nil real_props nil)
(minus_odd_is_odd application-judgement "odd_int" integers nil)
(div_mult_pos_le2 formula-decl nil real_props nil)
(* const-decl "real" vectors_3D nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(norm const-decl "nnreal" vectors_3D 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)
(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)
(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)
(nzreal_times_nzreal_is_nzreal application-judgement "nzreal"
real_types nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(minus_nzreal_is_nzreal application-judgement "nzreal" real_types
nil)
(dot_norm formula-decl nil vectors_3D nil))
nil))
(cos_symm 0
(cos_symm-1 nil 3427044409
("" (skeep)
(("" (expand "cos")
(("" (lemma "dot_comm")
(("" (inst?) (("" (assert) nil nil)) nil)) nil))
nil))
nil)
((cos const-decl "real" vect_trig_3D nil)
(real nonempty-type-from-decl nil reals nil)
(Vector type-eq-decl nil vectors_3D nil)
(boolean nonempty-type-decl nil booleans nil)
(/= const-decl "boolean" notequal nil)
(zero const-decl "Vector" vectors_3D nil)
(Nz_vector type-eq-decl nil vectors_3D nil)
(real_div_nzreal_is_real application-judgement "real" reals nil)
(posreal_times_posreal_is_posreal application-judgement "posreal"
real_types nil)
(nz_norm_gt_0 application-judgement "posreal" vectors_3D nil)
(dot_comm formula-decl nil vectors_3D nil))
shostak)))
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