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(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(posreal_times_posreal_is_posreal application-judgement "posreal"
real_types nil)
(posreal_min application-judgement
"{z: posreal | z <= x AND z <= y}" real_defs nil)
(min const-decl "{p: real | p <= m AND p <= n}" real_defs nil)
(<= const-decl "bool" reals nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(posreal_plus_nnreal_is_posreal application-judgement "posreal"
real_types nil)
(nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(triangle formula-decl nil real_props nil)
(nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(real_plus_real_is_real application-judgement "real" reals nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(- const-decl "Vector" vectors_2D "vectors/")
(dot_sub_left formula-decl nil vectors_2D "vectors/")
(norm_add_le formula-decl nil vectors_2D "vectors/")
(sub_cancel formula-decl nil vectors_2D "vectors/")
(add_neg_sub formula-decl nil vectors_2D "vectors/")
(norm_neg formula-decl nil vectors_2D "vectors/")
(- const-decl "Vector" vectors_2D "vectors/")
(nonzero_real nonempty-type-eq-decl nil reals nil)
(times_div2 formula-decl nil real_props nil)
(nnreal_div_posreal_is_nnreal application-judgement "nnreal"
real_types nil)
(div_mult_pos_lt1 formula-decl nil real_props nil)
(div_mult_pos_lt2 formula-decl nil real_props nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(X skolem-const-decl "Vect2" vect_vect_2D_continuity nil)
(both_sides_times_pos_lt1 formula-decl nil real_props nil)
(both_sides_times_pos_le1_imp formula-decl nil extra_real_props
nil)
(< const-decl "bool" reals nil)
(dot_sub_right formula-decl nil vectors_2D "vectors/")
(schwarz formula-decl nil vectors_2D "vectors/")
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(* const-decl "real" vectors_2D "vectors/")
(dot_vvv const-decl "real" vect_vect_2D_continuity nil)
(nnreal_plus_posreal_is_posreal application-judgement "posreal"
real_types nil)
(posreal_div_posreal_is_posreal application-judgement "posreal"
real_types 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)
(number_field nonempty-type-from-decl nil number_fields nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(real_pred const-decl "[number_field -> boolean]" 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)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(nnreal type-eq-decl nil real_types nil)
(norm const-decl "nnreal" vectors_2D "vectors/"))
nil)
(dot_vvv_cont-1 nil 3515488825 ("" (postpone) nil nil) nil shostak))
(prod_vvr_cont 0
(prod_vvr_cont-1 nil 3515496006
("" (skeep)
(("" (name "fffv" "LAMBDA (s,nzv): (# x:= ffrc(s,nzv), y:= 0 #)")
(("" (name "gggv" "LAMBDA (s,nzv): (# x:= ggrc(s,nzv), y:= 0 #)")
(("" (lemma "dot_vvv_cont")
(("" (inst - "fffv" "gggv")
(("1" (hide -2 -3)
(("1" (expand "dot_vvv")
(("1" (expand "prod_vvr")
(("1" (expand "gggv")
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(("2" (expand "continuous_vvv?")
(("2" (typepred "ggrc")
(("2" (expand "continuous_vvr?")
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(("1"
(rewrite -1)
(("1"
(expand "gggv" +)
(("1"
(expand "-" +)
(("1"
(rewrite "sq_0")
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(grind)
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("3" (hide-all-but 1)
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"FORALL (vvww:Vect2): sqv(vvww) = sq(vvww`x) + sq(vvww`y)")
(("1"
(rewrite -1)
(("1"
(expand "fffv" +)
(("1"
(expand "-" +)
(("1"
(rewrite "sq_0")
(("1"
(assert)
(("1"
(case
"FORALL (aaa:real): sqrt(sq(aaa)) = abs(aaa)")
(("1"
(rewrite -1 1)
nil
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(hide-all-but 1)
(("2"
(skeep)
(("2"
(case "aaa>=0")
(("1"
(grind)
nil
nil)
("2"
(lemma
"sqrt_sq")
--> --------------------
--> maximum size reached
--> --------------------
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