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(horizontal_dist_convexity
(horiz_dist_convex_scaf 0
(horiz_dist_convex_scaf-1 nil 3467389274
("" (skeep)
(("" (expand "horiz_dist_scaf")
(("" (expand "sqv")
(("" (lemma "quad_convex")
(("" (inst - "sqv(v)" "2*(s*v)" "sqv(s) - sq(D)")
(("" (grind) nil nil)) nil))
nil))
nil))
nil))
nil)
((sq_nz_pos application-judgement "posreal" sq "reals/")
(real_minus_real_is_real application-judgement "real" reals nil)
(horiz_dist_scaf const-decl "real" horizontal_dist_convexity nil)
(quad_convex formula-decl nil convex_functions "reals/")
(quadratic const-decl "real" quadratic "reals/")
(convex? const-decl "bool" convex_functions "reals/")
(* const-decl "Vector" vectors_2D "vectors/")
(+ const-decl "Vector" vectors_2D "vectors/")
(posreal_times_posreal_is_posreal application-judgement "posreal"
real_types nil)
(real_plus_real_is_real application-judgement "real" reals nil)
(D formal-const-decl "posreal" horizontal_dist_convexity nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(> const-decl "bool" reals nil)
(sq const-decl "nonneg_real" sq "reals/")
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(* const-decl "real" vectors_2D "vectors/")
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(Vect2 type-eq-decl nil vectors_2D_def "vectors/")
(Vector type-eq-decl nil vectors_2D "vectors/")
(nnreal 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)
(real_times_real_is_real application-judgement "real" reals nil)
(sqv const-decl "nnreal" vectors_2D "vectors/"))
nil))
(horiz_dist_strictly_convex_scaf 0
(horiz_dist_strictly_convex_scaf-2 nil 3467394574
("" (skeep)
(("" (expand "horiz_dist_scaf")
(("" (expand "sqv")
(("" (lemma "quad_strictly_convex")
(("" (inst - "sqv(v)" "2*(s*v)" "sqv(s) - sq(D)")
(("1" (grind) nil nil)
("2" (lemma "vectors_2D.sqv_eq_0")
(("2" (inst - "v") (("2" (assert) nil nil)) nil)) nil))
nil))
nil))
nil))
nil))
nil)
((sq_nz_pos application-judgement "posreal" sq "reals/")
(real_minus_real_is_real application-judgement "real" reals nil)
(horiz_dist_scaf const-decl "real" horizontal_dist_convexity nil)
(quad_strictly_convex formula-decl nil convex_functions "reals/")
(sqv_eq_0 formula-decl nil vectors_2D "vectors/")
(/= const-decl "boolean" notequal nil)
(quadratic const-decl "real" quadratic "reals/")
(strictly_convex? const-decl "bool" convex_functions "reals/")
(* const-decl "Vector" vectors_2D "vectors/")
(+ const-decl "Vector" vectors_2D "vectors/")
(posreal_times_posreal_is_posreal application-judgement "posreal"
real_types nil)
(real_plus_real_is_real application-judgement "real" reals nil)
(D formal-const-decl "posreal" horizontal_dist_convexity nil)
(sq const-decl "nonneg_real" sq "reals/")
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(* const-decl "real" vectors_2D "vectors/")
(* 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)
(nonneg_real nonempty-type-eq-decl nil real_types 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)
(Vector type-eq-decl nil vectors_2D "vectors/")
(>= const-decl "bool" reals nil)
(nnreal type-eq-decl nil real_types nil)
(Vect2 type-eq-decl nil vectors_2D_def "vectors/")
(v skolem-const-decl "Vect2" horizontal_dist_convexity nil)
(real_times_real_is_real application-judgement "real" reals nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(sqv const-decl "nnreal" vectors_2D "vectors/"))
nil)
(horiz_dist_strictly_convex_scaf-1 nil 3467389208
("" (skeep)
(("" (expand "horiz_dist_scaf")
(("" (expand "sqv")
(("" (lemma "quad_strictly_convex")
((""
(inst - "sqv(vect2(v))" "2*(vect2(s)*vect2(v))"
"sqv(vect2(s)) - sq(D)")
(("1" (grind) nil nil)
("2" (lemma "vectors_2D.sqv_eq_0")
(("2" (inst - "vect2(v)") (("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil)
((sqv const-decl "nnreal" vectors_2D "vectors/")
(Vect2 type-eq-decl nil vectors_2D_def "vectors/")
(Vector type-eq-decl nil vectors_2D "vectors/")
(* const-decl "real" vectors_2D "vectors/")
(sq const-decl "nonneg_real" sq "reals/")
(+ const-decl "Vector" vectors_2D "vectors/")
(* const-decl "Vector" vectors_2D "vectors/")
(strictly_convex? const-decl "bool" convex_functions "reals/")
(quadratic const-decl "real" quadratic "reals/")
(sqv_eq_0 formula-decl nil vectors_2D "vectors/")
(quad_strictly_convex formula-decl nil convex_functions "reals/")
(sq_nz_pos application-judgement "posreal" sq "reals/"))
nil)))
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