(vs_only
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(vs_only_TCC1-2 nil 3465560929
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(("" (assert)
(("" (lemma "Delta_gt_0_nzv")
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nil))
nil)
((sq_nz_pos application-judgement "posreal" sq "reals/")
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"(strict_total_order?[real])" real_props nil)
(vect2 const-decl "Vect2" vect_3D_2D "vectors/")
(Vect3 type-eq-decl nil vectors_3D_def "vectors/")
(Vect2 type-eq-decl nil vectors_2D_def "vectors/")
(Delta_gt_0_nzv formula-decl nil horizontal 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)
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(posreal nonempty-type-eq-decl nil real_types nil)
(D formal-const-decl "posreal" vs_only nil))
nil)
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("" (skeep) (("" (assert) nil nil)) nil)
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("" (skeep)
(("" (lemma "Theta_D_neq_0")
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nil)
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"(strict_total_order?[real])" real_props nil)
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(zero const-decl "Vector" vectors_2D "vectors/")
(Sign type-eq-decl nil sign "reals/")
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(/= const-decl "boolean" notequal nil)
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(rational_pred const-decl "[real -> boolean]" rationals nil)
(Vector type-eq-decl nil vectors_2D "vectors/")
(nnreal type-eq-decl nil real_types nil)
(sqv const-decl "nnreal" vectors_2D "vectors/")
(Vect3 type-eq-decl nil vectors_3D_def "vectors/")
(Vect2 type-eq-decl nil vectors_2D_def "vectors/")
(vect2 const-decl "Vect2" vect_3D_2D "vectors/")
(s skolem-const-decl "Vect3" vs_only nil)
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"(strict_total_order?[real])" real_props nil)
(sq_nz_pos application-judgement "posreal" sq "reals/"))
nil)
(vs_only_TCC2-1 nil 3465683704 ("" (subtype-tcc) nil nil) nil nil))
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(Sign type-eq-decl nil sign "reals/")
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(* const-decl "real" vectors_2D "vectors/")
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(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
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(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
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(/= const-decl "boolean" notequal nil)
(real_times_real_is_real application-judgement "real" reals nil)
(real_minus_real_is_real application-judgement "real" reals nil)
(real_plus_real_is_real application-judgement "real" reals nil))
nil))
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nil))
nil))
nil)
((sign_neg_clos application-judgement "Sign" sign "reals/")
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(* const-decl "Vector" vectors_3D "vectors/")
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(>= const-decl "bool" reals nil)
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real_props nil)
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(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(+ const-decl "Vector" vectors_3D "vectors/")
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(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(H formal-const-decl "posreal" vs_only 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)
(vertical_sep_dir_at formula-decl nil vz_criteria nil))
nil)
(circle_vs_only_ge-1 nil 3451818153
("" (skeep)
(("" (expand "circle_criterion?")
(("" (flatten)
(("" (rewrite "vect2_add")
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nil))
nil))
nil))
nil)
((sign_neg_clos application-judgement "Sign" sign "reals/")
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(Vector type-eq-decl nil vectors_3D "vectors/")
(* const-decl "Vector" vectors_3D "vectors/")
(sq_nz_pos application-judgement "posreal" sq "reals/")
(vect2_scal formula-decl nil vect_3D_2D "vectors/"))
nil))
(vs_entry_meets_circle_criterion_TCC1 0
(vs_entry_meets_circle_criterion_TCC1-2 nil 3471099308
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(("" (rewrite "horizontal_conflict")
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nil)
((nzv2 application-judgement "Nz_vect2" definitions_3D nil)
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(Vector type-eq-decl nil vectors_2D "vectors/")
(/= const-decl "boolean" notequal nil)
(zero const-decl "Vector" vectors_2D "vectors/")
(Nz_vect2 type-eq-decl nil vectors_2D "vectors/")
(Vect3 type-eq-decl nil vectors_3D_def "vectors/")
(Vect2 type-eq-decl nil vectors_2D_def "vectors/")
(vect2 const-decl "Vect2" vect_3D_2D "vectors/")
(Nzv2_vect3 type-eq-decl nil definitions_3D nil)
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(sqv const-decl "nnreal" vectors_2D "vectors/")
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(real_times_real_is_real application-judgement "real" reals nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(sq_nz_pos application-judgement "posreal" sq "reals/")
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(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil))
nil)
(vs_entry_meets_circle_criterion_TCC1-1 nil 3471099160
("" (subtype-tcc) nil nil) nil nil))
(vs_entry_meets_circle_criterion_TCC2 0
(vs_entry_meets_circle_criterion_TCC2-2 nil 3471099331
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(("" (lemma "Theta_D_entry_gt_0")
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(number_field_pred const-decl "[number -> boolean]" number_fields
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(real_times_real_is_real application-judgement "real" reals nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
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(sq const-decl "nonneg_real" sq "reals/")
(sqv const-decl "nnreal" vectors_2D "vectors/")
(nnreal type-eq-decl nil real_types nil)
(Nzv2_vect3 type-eq-decl nil definitions_3D nil)
(vect2 const-decl "Vect2" vect_3D_2D "vectors/")
(Vect2 type-eq-decl nil vectors_2D_def "vectors/")
(Vect3 type-eq-decl nil vectors_3D_def "vectors/")
(Nz_vect2 type-eq-decl nil vectors_2D "vectors/")
(zero const-decl "Vector" vectors_2D "vectors/")
(/= const-decl "boolean" notequal nil)
(Vector type-eq-decl nil vectors_2D "vectors/")
(nzv2 application-judgement "Nz_vect2" definitions_3D nil)
(ssv2 application-judgement "Ss_vect2[D]" vs_only nil))
nil)
(vs_entry_meets_circle_criterion_TCC2-1 nil 3471099160
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(vs_entry_meets_circle_criterion 0
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(boolean nonempty-type-decl nil booleans nil)
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real_props nil)
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"(strict_total_order?[real])" real_props nil)
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(circle_vs_only_ge formula-decl nil vs_only nil)
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(NOT const-decl "[bool -> bool]" booleans nil)
(IFF const-decl "[bool, bool -> bool]" booleans nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(sign const-decl "Sign" sign "reals/")
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(circle_criterion? const-decl "bool" circle_criterion nil)
(Vector type-eq-decl nil vectors_3D "vectors/")
(+ const-decl "Vector" vectors_3D "vectors/")
(* const-decl "Vector" vectors_3D "vectors/")
(<= const-decl "bool" reals nil)
(vect2_add formula-decl nil vect_3D_2D "vectors/")
(nzreal_times_nzreal_is_nzreal application-judgement "nzreal"
real_types nil)
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(horizontal_conflict_entry formula-decl nil horizontal nil)
(sign_abs formula-decl nil sign "reals/")
(nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(TRUE const-decl "bool" booleans nil)
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(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(both_sides_times_pos_ge1 formula-decl nil real_props nil)
(posreal_div_posreal_is_posreal application-judgement "posreal"
real_types nil)
(posreal_times_posreal_is_posreal application-judgement "posreal"
real_types nil)
(real_div_nzreal_is_real application-judgement "real" reals nil)
(times_div2 formula-decl nil real_props nil)
(times_div1 formula-decl nil real_props nil)
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(div_mult_pos_ge1 formula-decl nil real_props nil)
(div_mult_pos_ge2 formula-decl nil real_props nil)
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(sign_id formula-decl nil sign "reals/")
(sign_mult_pos formula-decl nil sign "reals/")
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(+ const-decl "Vector" vectors_2D "vectors/")
(* const-decl "Vector" vectors_2D "vectors/")
(nonzero_abs_is_pos application-judgement "{y: posreal | y >= x}"
real_defs nil)
(Theta_D_on_D formula-decl nil horizontal nil)
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(vect2_scal formula-decl nil vect_3D_2D "vectors/")
(vs_at_H formula-decl nil vertical nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
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(vs_at const-decl "real" vertical nil)
(tentry skolem-const-decl "real" vs_only nil)
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(Sign type-eq-decl nil sign "reals/")
(- const-decl "[numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(nzint nonempty-type-eq-decl nil integers nil)
(int nonempty-type-eq-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)
(Delta const-decl "real" horizontal nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(Ss_vect2 type-eq-decl nil horizontal nil)
(Ss2_vect3 type-eq-decl nil space_3D nil)
(H formal-const-decl "posreal" vs_only nil)
(sq const-decl "nonneg_real" sq "reals/")
(sqv const-decl "nnreal" vectors_2D "vectors/")
(nnreal type-eq-decl nil real_types nil)
(Nzv2_vect3 type-eq-decl nil definitions_3D nil)
(vect2 const-decl "Vect2" vect_3D_2D "vectors/")
(Vect2 type-eq-decl nil vectors_2D_def "vectors/")
(Vect3 type-eq-decl nil vectors_3D_def "vectors/")
(Nz_vect2 type-eq-decl nil vectors_2D "vectors/")
(zero const-decl "Vector" vectors_2D "vectors/")
(/= const-decl "boolean" notequal nil)
(Vector type-eq-decl nil vectors_2D "vectors/")
(nzv2 application-judgement "Nz_vect2" definitions_3D nil))
nil))
(vs_exit_meets_circle_criterion_TCC1 0
(vs_exit_meets_circle_criterion_TCC1-2 nil 3471099258
("" (skeep)
(("" (rewrite "horizontal_conflict")
(("" (flatten) (("" (assert) nil nil)) nil)) nil))
nil)
((nzv2 application-judgement "Nz_vect2" definitions_3D nil)
(horizontal_conflict formula-decl nil horizontal nil)
(Vector type-eq-decl nil vectors_2D "vectors/")
(/= const-decl "boolean" notequal nil)
(zero const-decl "Vector" vectors_2D "vectors/")
(Nz_vect2 type-eq-decl nil vectors_2D "vectors/")
(Vect3 type-eq-decl nil vectors_3D_def "vectors/")
(Vect2 type-eq-decl nil vectors_2D_def "vectors/")
(vect2 const-decl "Vect2" vect_3D_2D "vectors/")
(Nzv2_vect3 type-eq-decl nil definitions_3D 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)
(bool nonempty-type-eq-decl nil booleans 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)
(D formal-const-decl "posreal" vs_only nil)
(minus_odd_is_odd application-judgement "odd_int" integers nil)
(real_times_real_is_real application-judgement "real" reals nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(sq_nz_pos application-judgement "posreal" sq "reals/")
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil))
nil)
(vs_exit_meets_circle_criterion_TCC1-1 nil 3471099186
("" (subtype-tcc) nil nil) nil nil))
(vs_exit_meets_circle_criterion_TCC2 0
(vs_exit_meets_circle_criterion_TCC2-2 nil 3471099282
("" (skeep)
(("" (rewrite "horizontal_conflict")
(("" (flatten)
(("" (lemma "Theta_D_exit_gt_0")
(("" (inst?) (("" (assert) nil nil)) nil)) nil))
nil))
nil))
nil)
((nzv2 application-judgement "Nz_vect2" definitions_3D nil)
(horizontal_conflict formula-decl nil horizontal nil)
(Vector type-eq-decl nil vectors_2D "vectors/")
(/= const-decl "boolean" notequal nil)
(zero const-decl "Vector" vectors_2D "vectors/")
(Nz_vect2 type-eq-decl nil vectors_2D "vectors/")
(Vect3 type-eq-decl nil vectors_3D_def "vectors/")
(Vect2 type-eq-decl nil vectors_2D_def "vectors/")
(vect2 const-decl "Vect2" vect_3D_2D "vectors/")
(Nzv2_vect3 type-eq-decl nil definitions_3D 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)
(bool nonempty-type-eq-decl nil booleans 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)
(D formal-const-decl "posreal" vs_only nil)
(minus_odd_is_odd application-judgement "odd_int" integers nil)
(real_times_real_is_real application-judgement "real" reals nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(sq_nz_pos application-judgement "posreal" sq "reals/")
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(Theta_D_exit_gt_0 formula-decl nil horizontal nil))
nil)
(vs_exit_meets_circle_criterion_TCC2-1 nil 3471099186
("" (subtype-tcc) nil nil) nil nil))
(vs_exit_meets_circle_criterion 0
(vs_exit_meets_circle_criterion-1 nil 3471099186
("" (skeep)
(("" (lemma "horizontal_conflict")
(("" (inst?)
(("" (assert)
(("" (flatten)
(("" (lemma "Theta_D_exit_gt_0")
(("" (inst?)
(("" (assert)
(("" (replaces -1)
((""
(name-replace "texit" "Theta_D(s, vgs, Exit)"
:hide? nil)
(("" (expand "circle_criterion?")
(("" (lemma "vs_at_H")
(("" (inst?)
((""
(case-replace
"(s+texit*vgs)`z = s`z+texit*vgs`z")
(("1"
(hide -1)
(("1"
(replace -7 :dir rl)
(("1"
(replaces -1)
(("1"
(rewrite "vect2_add")
(("1"
(rewrite "vect2_scal")
(("1"
(lemma "Theta_D_on_D")
(("1"
(inst?)
(("1"
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(("1"
(case
"abs(eps*H) >= H")
(("1"
(assert)
(("1"
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(("1"
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(("1"
(inst?)
(("1"
(assert)
(("1"
(lemma
"horizontal_conflict")
(("1"
(inst?)
(("1"
(assert)
(("1"
(lemma
"Delta_eq")
(("1"
(inst?)
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(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(replaces -8)
(("2"
(expand
"vs_at")
(("2"
(cancel-by
1
"H")
(("2"
(hide-all-but
(-7 2))
(("2"
(typepred
"eps")
(("2"
(cross-mult
1)
(("2"
(grind)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(hide-all-but 1)
(("2"
(typepred "eps")
(("2"
(grind)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(hide-all-but 1)
(("2" (expand* "+" "*") nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((D formal-const-decl "posreal" vs_only 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 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)
(horizontal_conflict formula-decl nil horizontal nil)
(minus_odd_is_odd application-judgement "odd_int" integers nil)
(sq_nz_pos application-judgement "posreal" sq "reals/")
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_times_real_is_real application-judgement "real" reals nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(Theta_D_exit_gt_0 formula-decl nil horizontal nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(Delta const-decl "real" horizontal 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)
(nzint nonempty-type-eq-decl nil integers nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(Sign type-eq-decl nil sign "reals/")
(Theta_D const-decl "real" horizontal nil)
(vs_at_H formula-decl nil vertical nil)
(H formal-const-decl "posreal" vs_only nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(* const-decl "Vector" vectors_3D "vectors/")
(+ const-decl "Vector" vectors_3D "vectors/")
(Vector type-eq-decl nil vectors_3D "vectors/")
(real_plus_real_is_real application-judgement "real" reals nil)
(vect2_add formula-decl nil vect_3D_2D "vectors/")
(Theta_D_on_D formula-decl nil horizontal nil)
(minus_nzreal_is_nzreal application-judgement "nzreal" real_types
nil)
(nonzero_abs_is_pos application-judgement "{y: posreal | y >= x}"
real_defs nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(real_div_nzreal_is_real application-judgement "real" reals nil)
(TRUE const-decl "bool" booleans nil)
(id const-decl "(bijective?[T, T])" identity nil)
(bijective? const-decl "bool" functions nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(both_sides_times_pos_ge1 formula-decl nil real_props nil)
(posreal_div_posreal_is_posreal application-judgement "posreal"
real_types nil)
(nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(nnreal_div_posreal_is_nnreal application-judgement "nnreal"
real_types nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(nzint_times_nzint_is_nzint application-judgement "nzint" integers
nil)
(zero_div formula-decl nil extra_tegies nil)
(div_mult_pos_ge1 formula-decl nil real_props nil)
(vs_at const-decl "real" vertical nil)
(real_minus_real_is_real application-judgement "real" reals nil)
(not_horizontal_conflict_exit formula-decl nil horizontal nil)
(* const-decl "Vector" vectors_2D "vectors/")
(+ const-decl "Vector" vectors_2D "vectors/")
(Delta_eq formula-decl nil horizontal nil)
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(vect2_scal formula-decl nil vect_3D_2D "vectors/")
(nzreal_times_nzreal_is_nzreal application-judgement "nzreal"
real_types nil)
(nzreal nonempty-type-eq-decl nil reals nil)
(circle_criterion? const-decl "bool" circle_criterion nil)
(Vector type-eq-decl nil vectors_2D "vectors/")
(/= const-decl "boolean" notequal nil)
(zero const-decl "Vector" vectors_2D "vectors/")
(Nz_vect2 type-eq-decl nil vectors_2D "vectors/")
(Vect3 type-eq-decl nil vectors_3D_def "vectors/")
(Vect2 type-eq-decl nil vectors_2D_def "vectors/")
(vect2 const-decl "Vect2" vect_3D_2D "vectors/")
(Nzv2_vect3 type-eq-decl nil definitions_3D nil)
(nzv2 application-judgement "Nz_vect2" definitions_3D nil))
nil)))
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