(derivatives_lam
(IMP_derivatives_TCC1 0
(IMP_derivatives_TCC1-1 nil 3301761309
("" (lemma "deriv_domain" ) (("" (propax) nil nil )) nil )
((deriv_domain formula-decl nil derivatives_lam nil )) shostak))
(IMP_derivatives_TCC2 0
(IMP_derivatives_TCC2-1 nil 3301761489
("" (lemma "not_one_element" ) (("" (propax) nil nil )) nil )
((not_one_element formula-decl nil derivatives_lam nil )) shostak))
(derivable_id_lam 0
(derivable_id_lam-1 nil 3304425174
("" (expand "derivable?" )
(("" (lemma "derivable_id" )
(("" (expand "I" )
(("" (skeep)
(("" (expand "derivable?" -1) (("" (inst?) nil nil )) nil ))
nil ))
nil ))
nil ))
nil )
((T formal-subtype-decl nil derivatives_lam nil )
(T_pred const-decl "[real -> boolean]" derivatives_lam 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 )
(derivable_id judgement-tcc nil derivatives nil )
(I const-decl "(bijective?[T, T])" identity nil )
(derivable? const-decl "bool" derivatives nil ))
shostak))
(derivable_const_lam 0
(derivable_const_lam-1 nil 3304425582
("" (skosimp*)
(("" (lemma "const_derivable_fun" )
(("" (inst?)
(("" (expand "const_fun" ) (("" (propax) nil nil )) nil )) nil ))
nil ))
nil )
((T formal-subtype-decl nil derivatives_lam nil )
(T_pred const-decl "[real -> boolean]" derivatives_lam 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 )
(const_derivable_fun formula-decl nil derivatives nil ))
shostak))
(derivable_add_lam 0
(derivable_add_lam-1 nil 3304429143
("" (skosimp :preds? t)
(("" (lemma "sum_derivable_fun" )
(("" (inst - "f!1" "g!1" )
(("" (expand "+ " ) (("" (propax) nil nil )) nil )) nil ))
nil ))
nil )
((sum_derivable_fun formula-decl nil derivatives nil )
(real_plus_real_is_real application-judgement "real" reals nil )
(+ const-decl "[T -> real]" real_fun_ops "reals/" )
(boolean nonempty-type-decl nil booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(NOT const-decl "[bool -> bool]" booleans 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 )
(real nonempty-type-from-decl nil reals nil )
(T_pred const-decl "[real -> boolean]" derivatives_lam nil )
(T formal-subtype-decl nil derivatives_lam nil )
(derivable? const-decl "bool" derivatives nil )
(deriv_fun type-eq-decl nil derivatives nil ))
nil ))
(derivable_mult_lam 0
(derivable_mult_lam-1 nil 3304429240
("" (skosimp*)
(("" (lemma "prod_derivable_fun" )
(("" (inst - "f!1" "g!1" )
(("" (expand "*" ) (("" (propax) nil nil )) nil )) nil ))
nil ))
nil )
((T formal-subtype-decl nil derivatives_lam nil )
(T_pred const-decl "[real -> boolean]" derivatives_lam 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 )
(prod_derivable_fun formula-decl nil derivatives nil )
(real_times_real_is_real application-judgement "real" reals nil )
(* const-decl "[T -> real]" real_fun_ops "reals/" )
(deriv_fun type-eq-decl nil derivatives nil )
(derivable? const-decl "bool" derivatives nil )
(bool nonempty-type-eq-decl nil booleans nil ))
shostak))
(derivable_pow_lam_TCC1 0
(derivable_pow_lam_TCC1-1 nil 3305042267 ("" (subtype-tcc) nil nil )
((/= const-decl "boolean" notequal nil )) shostak))
(derivable_pow_lam 0
(derivable_pow_lam-1 nil 3305042471
("" (skosimp*)
(("" (case-replace "n!1=0" )
(("1" (expand "^" )
(("1" (expand "expt" )
(("1" (rewrite "derivable_const_lam" ) nil nil )) nil ))
nil )
("2" (lemma "deriv_x_to_n" )
(("2" (inst - "n!1" "1" )
(("1" (assert )
(("1" (flatten)
(("1"
(case-replace
"(LAMBDA (t): t ^ n!1) = (LAMBDA (x: T): 1 * x ^ n!1)" )
(("1" (apply-extensionality 1 :hide? t) nil nil )) nil ))
nil ))
nil )
("2" (assert ) nil nil ))
nil ))
nil ))
nil ))
nil )
((number nonempty-type-decl nil numbers nil )
(boolean nonempty-type-decl nil booleans 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 )
(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 )
(bool nonempty-type-eq-decl nil booleans nil )
(>= const-decl "bool" reals nil )
(nat nonempty-type-eq-decl nil naturalnumbers nil )
(expt def-decl "real" exponentiation nil )
(derivable_const_lam formula-decl nil derivatives_lam nil )
(^ const-decl "real" exponentiation nil )
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil )
(> const-decl "bool" reals nil )
(n!1 skolem-const-decl "nat" derivatives_lam nil )
(posnat nonempty-type-eq-decl nil integers nil )
(nonneg_int nonempty-type-eq-decl nil integers nil )
(numfield nonempty-type-eq-decl nil number_fields nil )
(OR const-decl "[bool, bool -> bool]" booleans nil )
(/= const-decl "boolean" notequal nil )
(* const-decl "[numfield, numfield -> numfield]" number_fields nil )
(real_times_real_is_real application-judgement "real" reals nil )
(T formal-subtype-decl nil derivatives_lam nil )
(T_pred const-decl "[real -> boolean]" derivatives_lam nil )
(deriv_x_to_n formula-decl nil derivatives nil ))
shostak))
(derivable_scal1_lam 0
(derivable_scal1_lam-2 nil 3304699767
("" (skosimp :preds? t)
(("" (lemma "scal_derivable_fun" )
(("" (inst - "a!1" "f!1" )
(("" (expand "*" ) (("" (propax) nil nil )) nil )) nil ))
nil ))
nil )
((scal_derivable_fun formula-decl nil derivatives nil )
(real_times_real_is_real application-judgement "real" reals nil )
(* const-decl "[T -> real]" real_fun_ops "reals/" )
(boolean nonempty-type-decl nil booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(NOT const-decl "[bool -> bool]" booleans 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 )
(real nonempty-type-from-decl nil reals nil )
(T_pred const-decl "[real -> boolean]" derivatives_lam nil )
(T formal-subtype-decl nil derivatives_lam nil )
(derivable? const-decl "bool" derivatives nil )
(deriv_fun type-eq-decl nil derivatives nil ))
nil ))
(derivable_scal2_lam 0
(derivable_scal2_lam-2 nil 3472317982
("" (skosimp :preds? t)
(("" (lemma "scal_derivable_fun" )
(("" (inst - "a!1" "f!1" )
(("" (expand "*" )
((""
(case-replace
"(LAMBDA (x: T): a!1 * f!1(x)) = (LAMBDA (t): f!1(t) * a!1)" )
(("" (apply-extensionality 1 :hide? t) nil nil )) nil ))
nil ))
nil ))
nil ))
nil )
((scal_derivable_fun formula-decl nil derivatives nil )
(real_times_real_is_real application-judgement "real" reals nil )
(* const-decl "[T -> real]" real_fun_ops "reals/" )
(numfield nonempty-type-eq-decl nil number_fields nil )
(= const-decl "[T, T -> boolean]" equalities nil )
(* const-decl "[numfield, numfield -> numfield]" number_fields nil )
(boolean nonempty-type-decl nil booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(NOT const-decl "[bool -> bool]" booleans 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 )
(real nonempty-type-from-decl nil reals nil )
(T_pred const-decl "[real -> boolean]" derivatives_lam nil )
(T formal-subtype-decl nil derivatives_lam nil )
(derivable? const-decl "bool" derivatives nil )
(deriv_fun type-eq-decl nil derivatives nil ))
nil )
(derivable_scal2_lam-1 nil 3304431294
("" (skosimp :preds? t)
(("" (lemma "derivable_scal1_lam" )
(("" (inst -1 "a!1" "f!1" ) (("" (assert ) nil nil )) nil )) nil ))
nil )
((derivable? const-decl "bool" derivatives nil )
(deriv_fun type-eq-decl nil derivatives nil ))
shostak))
(derivable_neg_lam 0
(derivable_neg_lam-2 nil 3442593099
("" (skosimp*)
(("" (lemma "neg_derivable_fun" )
(("" (inst - "g!1" )
(("" (expand "-" ) (("" (propax) nil nil )) nil )) nil ))
nil ))
nil )
((T formal-subtype-decl nil derivatives_lam nil )
(T_pred const-decl "[real -> boolean]" derivatives_lam 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 )
(neg_derivable_fun formula-decl nil derivatives nil )
(minus_real_is_real application-judgement "real" reals nil )
(- const-decl "[T -> real]" real_fun_ops "reals/" )
(deriv_fun type-eq-decl nil derivatives nil )
(derivable? const-decl "bool" derivatives nil )
(bool nonempty-type-eq-decl nil booleans nil ))
nil )
(derivable_neg_lam-1 nil 3304429291
("" (skosimp :preds? t)
(("" (expand "derivable?" )
(("" (lemma "derivable_opp" )
(("" (inst -1 "g!1" )
(("" (expand "-" ) (("" (propax) nil nil )) nil )) nil ))
nil ))
nil ))
nil )
((deriv_fun type-eq-decl nil derivatives nil )) shostak))
(derivable_sub_lam 0
(derivable_sub_lam-1 nil 3304429323
("" (skosimp :preds? t)
(("" (lemma "diff_derivable_fun" )
(("" (inst - "f!1" "g!1" )
(("" (expand "-" ) (("" (propax) nil nil )) nil )) nil ))
nil ))
nil )
((diff_derivable_fun formula-decl nil derivatives nil )
(real_minus_real_is_real application-judgement "real" reals nil )
(- const-decl "[T -> real]" real_fun_ops "reals/" )
(boolean nonempty-type-decl nil booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(NOT const-decl "[bool -> bool]" booleans 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 )
(real nonempty-type-from-decl nil reals nil )
(T_pred const-decl "[real -> boolean]" derivatives_lam nil )
(T formal-subtype-decl nil derivatives_lam nil )
(derivable? const-decl "bool" derivatives nil )
(deriv_fun type-eq-decl nil derivatives nil ))
shostak))
(derivable_sq_lam 0
(derivable_sq_lam-1 nil 3304429366
("" (expand "sq" )
(("" (rewrite "derivable_mult_lam" )
(("" (rewrite "derivable_id_lam" ) nil nil )) nil ))
nil )
((derivable_mult_lam formula-decl nil derivatives_lam 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 )
(T_pred const-decl "[real -> boolean]" derivatives_lam nil )
(T formal-subtype-decl nil derivatives_lam nil )
(bool nonempty-type-eq-decl nil booleans nil )
(derivable? const-decl "bool" derivatives nil )
(deriv_fun type-eq-decl nil derivatives nil )
(derivable_id_lam formula-decl nil derivatives_lam nil )
(sq const-decl "nonneg_real" sq "reals/" )
(real_times_real_is_real application-judgement "real" reals nil ))
shostak))
(derivable_div_lam 0
(derivable_div_lam-1 nil 3304431982
("" (skosimp :preds? t)
(("" (lemma "div_derivable_fun" )
(("" (inst - "f!1" "k!1" )
(("" (expand "/" ) (("" (propax) nil nil )) nil )) nil ))
nil ))
nil )
((div_derivable_fun formula-decl nil derivatives nil )
(real_div_nzreal_is_real application-judgement "real" reals nil )
(/ const-decl "[T -> real]" real_fun_ops "reals/" )
(boolean nonempty-type-decl nil booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(NOT const-decl "[bool -> bool]" booleans 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 )
(real nonempty-type-from-decl nil reals nil )
(T_pred const-decl "[real -> boolean]" derivatives_lam nil )
(T formal-subtype-decl nil derivatives_lam nil )
(derivable? const-decl "bool" derivatives nil )
(deriv_fun type-eq-decl nil derivatives nil )
(/= const-decl "boolean" notequal nil )
(nzreal nonempty-type-eq-decl nil reals nil )
(nz_deriv_fun type-eq-decl nil derivatives nil ))
shostak))
(derivable_scald1_lam 0
(derivable_scald1_lam-1 nil 3304432031
("" (skosimp :preds? t)
(("" (lemma "derivable_div" )
(("" (inst -1 "LAMBDA(t):a!1" "k!1" )
(("1" (expand "/" ) (("1" (propax) nil nil )) nil )
("2" (lemma "derivable_const" )
(("2" (expand "const_fun" ) (("2" (inst?) nil nil )) nil ))
nil ))
nil ))
nil ))
nil )
((derivable_div judgement-tcc nil derivatives nil )
(derivable_const judgement-tcc nil derivatives nil )
(const_fun const-decl "[T -> real]" real_fun_ops "reals/" )
(/ const-decl "[T -> real]" real_fun_ops "reals/" )
(deriv_fun type-eq-decl nil derivatives nil )
(a!1 skolem-const-decl "real" derivatives_lam nil )
(boolean nonempty-type-decl nil booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(NOT const-decl "[bool -> bool]" booleans 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 )
(real nonempty-type-from-decl nil reals nil )
(T_pred const-decl "[real -> boolean]" derivatives_lam nil )
(T formal-subtype-decl nil derivatives_lam nil )
(derivable? const-decl "bool" derivatives nil )
(/= const-decl "boolean" notequal nil )
(nzreal nonempty-type-eq-decl nil reals nil )
(nz_deriv_fun type-eq-decl nil derivatives nil ))
shostak))
(derivable_scald2_lam 0
(derivable_scald2_lam-1 nil 3304432497
("" (skosimp)
(("" (lemma "derivable_scal1_lam" )
(("" (inst -1 "1/b!1" "f!1" ) (("" (assert ) nil nil )) nil )) nil ))
nil )
((derivable_scal1_lam formula-decl nil derivatives_lam nil )
(real_div_nzreal_is_real application-judgement "real" reals nil )
(real_times_real_is_real application-judgement "real" reals nil )
(deriv_fun type-eq-decl nil derivatives nil )
(derivable? const-decl "bool" derivatives nil )
(bool nonempty-type-eq-decl nil booleans nil )
(T formal-subtype-decl nil derivatives_lam nil )
(T_pred const-decl "[real -> boolean]" derivatives_lam nil )
(nzreal nonempty-type-eq-decl nil reals nil )
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil )
(nznum nonempty-type-eq-decl nil number_fields nil )
(/= const-decl "boolean" notequal nil )
(numfield nonempty-type-eq-decl nil number_fields 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 )
(nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
real_types nil ))
shostak))
(deriv_id_lam_TCC1 0
(deriv_id_lam_TCC1-1 nil 3304424118
("" (rewrite "derivable_id_lam" ) nil nil )
((derivable_id_lam formula-decl nil derivatives_lam nil )) shostak))
(deriv_id_lam 0
(deriv_id_lam-1 nil 3304429116
("" (expand "D" )
(("" (lemma "deriv_id_fun" )
(("" (expand "I" )
(("" (expand "const_fun" ) (("" (propax) nil nil )) nil )) nil ))
nil ))
nil )
((deriv_id_fun formula-decl nil derivatives 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 )
(T_pred const-decl "[real -> boolean]" derivatives_lam nil )
(T formal-subtype-decl nil derivatives_lam nil ))
shostak))
(deriv_const_lam_TCC1 0
(deriv_const_lam_TCC1-1 nil 3304424144
("" (skosimp) (("" (rewrite "derivable_const_lam" ) nil nil )) nil )
((derivable_const_lam formula-decl nil derivatives_lam 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 ))
shostak))
(deriv_const_lam 0
(deriv_const_lam-1 nil 3304430079
("" (skosimp)
(("" (expand "D" )
(("" (lemma "deriv_const_fun" )
(("" (inst -1 "a!1" )
(("" (expand "const_fun" ) (("" (propax) nil nil )) nil )) nil ))
nil ))
nil ))
nil )
((T formal-subtype-decl nil derivatives_lam nil )
(T_pred const-decl "[real -> boolean]" derivatives_lam 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 )
(deriv_const_fun formula-decl nil derivatives nil ))
shostak))
(deriv_add_lam_TCC1 0
(deriv_add_lam_TCC1-1 nil 3304424494
("" (skosimp) (("" (rewrite "derivable_add_lam" ) nil nil )) nil )
((derivable_add_lam formula-decl nil derivatives_lam 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 )
(T_pred const-decl "[real -> boolean]" derivatives_lam nil )
(T formal-subtype-decl nil derivatives_lam nil )
(bool nonempty-type-eq-decl nil booleans nil )
(derivable? const-decl "bool" derivatives nil )
(deriv_fun type-eq-decl nil derivatives nil ))
shostak))
(deriv_add_lam 0
(deriv_add_lam-1 nil 3304430121
("" (skosimp :preds? t)
(("" (expand * "derivable?" "D" )
(("" (lemma "deriv_sum_fun" )
(("" (inst -1 "f!1" "g!1" )
(("" (expand "+" ) (("" (propax) nil nil )) nil )) nil ))
nil ))
nil ))
nil )
((+ const-decl "[T -> real]" real_fun_ops "reals/" )
(deriv_sum_fun formula-decl nil derivatives nil )
(boolean nonempty-type-decl nil booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(NOT const-decl "[bool -> bool]" booleans 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 )
(real nonempty-type-from-decl nil reals nil )
(T_pred const-decl "[real -> boolean]" derivatives_lam nil )
(T formal-subtype-decl nil derivatives_lam nil )
(derivable? const-decl "bool" derivatives nil )
(deriv_fun type-eq-decl nil derivatives nil ))
shostak))
(deriv_mult_lam_TCC1 0
(deriv_mult_lam_TCC1-1 nil 3304424503
("" (skosimp) (("" (rewrite "derivable_mult_lam" ) nil nil )) nil )
((derivable_mult_lam formula-decl nil derivatives_lam 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 )
(T_pred const-decl "[real -> boolean]" derivatives_lam nil )
(T formal-subtype-decl nil derivatives_lam nil )
(bool nonempty-type-eq-decl nil booleans nil )
(derivable? const-decl "bool" derivatives nil )
(deriv_fun type-eq-decl nil derivatives nil ))
shostak))
(deriv_mult_lam 0
(deriv_mult_lam-1 nil 3304430162
("" (skosimp :preds? t)
(("" (expand * "derivable?" "D" )
(("" (lemma "deriv_prod_fun" )
(("" (inst -1 "f!1" "g!1" )
(("" (expand "*" )
(("" (expand "+" ) (("" (propax) nil nil )) nil )) nil ))
nil ))
nil ))
nil ))
nil )
((+ const-decl "[T -> real]" real_fun_ops "reals/" )
(* const-decl "[T -> real]" real_fun_ops "reals/" )
(deriv_prod_fun formula-decl nil derivatives nil )
(boolean nonempty-type-decl nil booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(NOT const-decl "[bool -> bool]" booleans 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 )
(real nonempty-type-from-decl nil reals nil )
(T_pred const-decl "[real -> boolean]" derivatives_lam nil )
(T formal-subtype-decl nil derivatives_lam nil )
(derivable? const-decl "bool" derivatives nil )
(deriv_fun type-eq-decl nil derivatives nil ))
shostak))
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shostak))
(deriv_pow_lam_TCC3 0
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nil ))
nil ))
nil ))
nil )
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shostak))
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nil ))
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(("" (lemma "deriv_scal_fun" )
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nil ))
nil )
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nil ))
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nil ))
(deriv_scal2_lam 0
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("" (skosimp :preds? t)
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nil )
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(T formal-subtype-decl nil derivatives_lam nil )
(derivable? const-decl "bool" derivatives nil )
(deriv_fun type-eq-decl nil derivatives nil ))
shostak))
(deriv_neg_lam_TCC1 0
(deriv_neg_lam_TCC1-1 nil 3304424526
("" (skosimp) (("" (rewrite "derivable_neg_lam" ) nil nil )) nil )
((derivable_neg_lam formula-decl nil derivatives_lam nil )
(number nonempty-type-decl nil numbers nil )
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(derivable? const-decl "bool" derivatives nil )
(deriv_fun type-eq-decl nil derivatives nil ))
shostak))
(deriv_neg_lam 0
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("" (skosimp :preds? t)
(("" (expand * "derivable?" "D" )
(("" (lemma "deriv_neg_fun" )
(("" (inst -1 "g!1" )
(("" (expand "-" ) (("" (propax) nil nil )) nil )) nil ))
nil ))
nil ))
nil )
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nil )
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(T_pred const-decl "[real -> boolean]" derivatives_lam nil )
(T formal-subtype-decl nil derivatives_lam nil )
(derivable? const-decl "bool" derivatives nil )
(deriv_fun type-eq-decl nil derivatives nil ))
nil )
(deriv_neg_lam-1 nil 3304430224
("" (skosimp :preds? t)
(("" (expand * "derivable?" "D" )
(("" (lemma "deriv_opp_fun" )
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(("" (expand "-" ) (("" (propax) nil nil )) nil )) nil ))
nil ))
nil ))
nil )
((deriv_fun type-eq-decl nil derivatives nil )) shostak))
(deriv_sub_lam_TCC1 0
(deriv_sub_lam_TCC1-1 nil 3304424618
("" (skosimp) (("" (rewrite "derivable_sub_lam" ) nil nil )) nil )
((derivable_sub_lam formula-decl nil derivatives_lam nil )
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(deriv_fun type-eq-decl nil derivatives nil ))
shostak))
(deriv_sub_lam 0
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("" (skosimp :preds? t)
(("" (expand * "derivable?" "D" )
(("" (lemma "deriv_diff_fun" )
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(("" (expand "-" ) (("" (propax) nil nil )) nil )) nil ))
nil ))
nil ))
nil )
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(T formal-subtype-decl nil derivatives_lam nil )
(derivable? const-decl "bool" derivatives nil )
(deriv_fun type-eq-decl nil derivatives nil ))
shostak))
(deriv_sq_lam_TCC1 0
(deriv_sq_lam_TCC1-1 nil 3304424624
("" (rewrite "derivable_sq_lam" ) nil nil )
((derivable_sq_lam formula-decl nil derivatives_lam nil )) shostak))
(deriv_sq_lam 0
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("" (expand "sq" )
(("" (rewrite "deriv_mult_lam" )
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("2" (rewrite "derivable_id_lam" ) nil nil ))
nil ))
nil )
((deriv_mult_lam formula-decl nil derivatives_lam 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 )
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(real_plus_real_is_real application-judgement "real" reals nil )
(deriv_id_lam formula-decl nil derivatives_lam nil )
(derivable_id_lam formula-decl nil derivatives_lam nil )
(sq const-decl "nonneg_real" sq "reals/" ))
shostak))
(deriv_div_lam_TCC1 0
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nil )
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nil )
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shostak))
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nil ))
nil ))
nil ))
nil )
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nil ))
nil ))
nil ))
nil )
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shostak))
(deriv_scald1_lam_TCC1 0
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("" (skosimp :preds? t)
(("" (rewrite "derivable_scald1_lam" ) nil nil )) nil )
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shostak))
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nil )
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nil ))
nil ))
nil ))
nil )
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shostak))
(deriv_scald2_lam_TCC1 0
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("" (skosimp) (("" (rewrite "derivable_scald2_lam" ) nil nil )) nil )
((derivable_scald2_lam formula-decl nil derivatives_lam nil )
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(number_field_pred const-decl "[number -> boolean]" number_fields
nil )
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(derivable? const-decl "bool" derivatives nil )
(deriv_fun type-eq-decl nil derivatives nil ))
shostak))
(deriv_scald2_lam 0
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("" (skosimp)
(("" (lemma "deriv_scal1_lam" )
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nil )
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(T_pred const-decl "[real -> boolean]" derivatives_lam nil )
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(/ const-decl "[numfield, nznum -> numfield]" number_fields nil )
(nznum nonempty-type-eq-decl nil number_fields nil )
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(number_field_pred const-decl "[number -> boolean]" number_fields
nil )
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(nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
real_types nil ))
shostak)))
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