|
(trigx
(sin_nz_TCC1 0
(sin_nz_TCC1-1 nil 3394178341
("" (rewrite "sin_pi2") (("" (assert) nil nil)) nil)
((sin_pi2 formula-decl nil trig_basic "trig_fnd/")
(pi_bound name-judgement "{r: posreal | pi_lb < r AND r < pi_ub}"
atan_approx "trig_fnd/"))
nil))
(cos_nz_TCC1 0
(cos_nz_TCC1-1 nil 3394178341
("" (rewrite "cos_0") (("" (assert) nil nil)) nil)
((cos_0 formula-decl nil trig_basic "trig_fnd/")) nil))
(cauchy_sin_nz_TCC1 0
(cauchy_sin_nz_TCC1-1 nil 3394178341
("" (expand "cauchy_sin_nz?")
(("" (lemma "lemma_div2n" ("x" "pi" "cx" "cauchy_pi" "n" "1"))
(("" (rewrite "pi_lemma")
(("" (expand "div2n")
(("" (rewrite "expt_x1")
(("" (inst + "pi / 2")
(("" (rewrite "sin_pi2") (("" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil)
((pi const-decl "posreal" atan "trig_fnd/")
(posreal nonempty-type-eq-decl nil real_types nil)
(> const-decl "bool" reals nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(cauchy_pi const-decl "cauchy_real" atanx nil)
(cauchy_real nonempty-type-eq-decl nil cauchy nil)
(cauchy_real? const-decl "bool" cauchy nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans 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)
(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)
(lemma_div2n formula-decl nil shift nil)
(div2n const-decl "real" shift nil)
(sin_range application-judgement "trig_range" sincos_def
"trig_fnd/")
(posreal_div_posreal_is_posreal application-judgement "posreal"
real_types nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(sin_nz nonempty-type-eq-decl nil trigx nil)
(sin const-decl "real" sincos_def "trig_fnd/")
(/= const-decl "boolean" notequal nil)
(sin_pi2 formula-decl nil trig_basic "trig_fnd/")
(posint_exp application-judgement "posint" exponentiation nil)
(pi_bound name-judgement "{r: posreal | pi_lb < r AND r < pi_ub}"
atan_approx "trig_fnd/")
(expt_x1 formula-decl nil exponentiation nil)
(pi_lemma formula-decl nil atanx nil)
(cauchy_sin_nz? const-decl "bool" trigx nil))
nil))
(cauchy_cos_nz_TCC1 0
(cauchy_cos_nz_TCC1-1 nil 3394178341
("" (expand "cauchy_cos_nz?")
(("" (inst + "0")
(("1" (expand "cauchy_prop")
(("1" (skosimp)
(("1" (assert)
(("1" (expand "cauchy_zero") (("1" (propax) nil nil)) nil))
nil))
nil))
nil)
("2" (rewrite "cos_0") (("2" (assert) nil nil)) nil))
nil))
nil)
((cos_range application-judgement "trig_range" sincos_def
"trig_fnd/")
(cos const-decl "real" sincos_def "trig_fnd/")
(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)
(/= const-decl "boolean" notequal nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(cos_nz nonempty-type-eq-decl nil trigx nil)
(cauchy_zero const-decl "cauchy_nnreal" cauchy nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(int_times_int_is_int application-judgement "int" integers nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(cauchy_prop const-decl "bool" cauchy nil)
(posint_exp application-judgement "posint" exponentiation nil)
(cos_0 formula-decl nil trig_basic "trig_fnd/")
(cauchy_cos_nz? const-decl "bool" trigx nil))
nil))
(subtype_TCC1 0
(subtype_TCC1-1 nil 3394178341
("" (skosimp)
(("" (typepred "x!1")
(("" (expand "cauchy_sin_nz?")
(("" (skosimp)
(("" (expand "cauchy_real?") (("" (inst + "nsx!1") nil nil))
nil))
nil))
nil))
nil))
nil)
((cauchy_sin_nz nonempty-type-eq-decl nil trigx nil)
(cauchy_sin_nz? const-decl "bool" trigx nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals 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)
(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)
(number nonempty-type-decl nil numbers nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(sin_nz nonempty-type-eq-decl nil trigx nil)
(sin const-decl "real" sincos_def "trig_fnd/")
(/= const-decl "boolean" notequal nil)
(cauchy_real? const-decl "bool" cauchy nil))
nil))
(subtype_TCC2 0
(subtype_TCC2-1 nil 3394178341
("" (skosimp)
(("" (typepred "x!1")
(("" (expand "cauchy_cos_nz?")
(("" (skosimp)
(("" (expand "cauchy_real?") (("" (inst + "ncx!1") nil nil))
nil))
nil))
nil))
nil))
nil)
((cauchy_cos_nz nonempty-type-eq-decl nil trigx nil)
(cauchy_cos_nz? const-decl "bool" trigx nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals 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)
(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)
(number nonempty-type-decl nil numbers nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(cos_nz nonempty-type-eq-decl nil trigx nil)
(cos const-decl "real" sincos_def "trig_fnd/")
(/= const-decl "boolean" notequal nil)
(cauchy_real? const-decl "bool" cauchy nil))
nil))
(cauchy_sec_TCC1 0
(cauchy_sec_TCC1-1 nil 3394179601
("" (skosimp)
(("" (typepred "cncx!1")
(("" (expand "cauchy_cos_nz?")
(("" (skosimp)
(("" (typepred "ncx!1")
(("" (expand "cauchy_nzreal?")
(("" (inst + "cos(ncx!1)")
(("" (lemma "cos_lemma" ("x" "ncx!1" "cx" "cncx!1"))
(("" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((cauchy_cos_nz nonempty-type-eq-decl nil trigx nil)
(cauchy_cos_nz? const-decl "bool" trigx nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals 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)
(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)
(number nonempty-type-decl nil numbers nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(cauchy_nzreal? const-decl "bool" cauchy nil)
(cos_lemma formula-decl nil sincosx nil)
(cauchy_real? const-decl "bool" cauchy nil)
(cauchy_real nonempty-type-eq-decl nil cauchy nil)
(nzreal nonempty-type-eq-decl nil reals nil)
(cos_range application-judgement "trig_range" sincos_def
"trig_fnd/")
(cos_nz nonempty-type-eq-decl nil trigx nil)
(cos const-decl "real" sincos_def "trig_fnd/")
(/= const-decl "boolean" notequal nil))
nil))
(cauchy_cosec_TCC1 0
(cauchy_cosec_TCC1-1 nil 3394179601
("" (skosimp)
(("" (typepred "cnsx!1")
(("" (expand "cauchy_sin_nz?")
(("" (skosimp)
(("" (typepred "nsx!1")
(("" (expand "cauchy_nzreal?")
(("" (lemma "sin_lemma" ("x" "nsx!1" "cx" "cnsx!1"))
(("" (inst + "sin(nsx!1)") (("" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((cauchy_sin_nz nonempty-type-eq-decl nil trigx nil)
(cauchy_sin_nz? const-decl "bool" trigx nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals 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)
(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)
(number nonempty-type-decl nil numbers nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(cauchy_nzreal? const-decl "bool" cauchy nil)
(sin_range application-judgement "trig_range" sincos_def
"trig_fnd/")
(nzreal nonempty-type-eq-decl nil reals nil)
(sin_lemma formula-decl nil sincosx nil)
(cauchy_real? const-decl "bool" cauchy nil)
(cauchy_real nonempty-type-eq-decl nil cauchy nil)
(sin_nz nonempty-type-eq-decl nil trigx nil)
(sin const-decl "real" sincos_def "trig_fnd/")
(/= const-decl "boolean" notequal nil))
nil))
(sec_TCC1 0
(sec_TCC1-1 nil 3394179601
("" (skosimp) (("" (typepred "ncx!1") (("" (assert) nil nil)) nil))
nil)
((cos_nz nonempty-type-eq-decl nil trigx nil)
(cos const-decl "real" sincos_def "trig_fnd/")
(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)
(/= const-decl "boolean" notequal nil)
(number nonempty-type-decl nil numbers nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(cos_range application-judgement "trig_range" sincos_def
"trig_fnd/"))
nil))
(cosec_TCC1 0
(cosec_TCC1-1 nil 3394179601
("" (skosimp) (("" (typepred "nsx!1") (("" (assert) nil nil)) nil))
nil)
((sin_nz nonempty-type-eq-decl nil trigx nil)
(sin const-decl "real" sincos_def "trig_fnd/")
(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)
(/= const-decl "boolean" notequal nil)
(number nonempty-type-decl nil numbers nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(sin_range application-judgement "trig_range" sincos_def
"trig_fnd/"))
nil))
(sec_lemma 0
(sec_lemma-1 nil 3394180068
("" (skosimp)
(("" (expand "sec")
(("" (expand "cauchy_sec")
(("" (lemma "cos_lemma" ("x" "ncx!1" "cx" "cncx!1"))
(("" (assert)
((""
(lemma "inv_lemma"
("nzx" "cos(ncx!1)" "nzcx" "cauchy_cos(cncx!1)"))
(("" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
((sec const-decl "nzreal" trigx nil)
(cos_nz nonempty-type-eq-decl nil trigx nil)
(cos const-decl "real" sincos_def "trig_fnd/")
(/= const-decl "boolean" notequal nil)
(cauchy_cos_nz nonempty-type-eq-decl nil trigx nil)
(cauchy_cos_nz? const-decl "bool" trigx nil)
(cauchy_real nonempty-type-eq-decl nil cauchy nil)
(cauchy_real? const-decl "bool" cauchy nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans 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)
(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)
(cos_lemma formula-decl nil sincosx nil)
(nzreal nonempty-type-eq-decl nil reals nil)
(cauchy_cos const-decl "cauchy_real" sincosx nil)
(cauchy_nzreal nonempty-type-eq-decl nil cauchy nil)
(cauchy_nzreal? const-decl "bool" cauchy nil)
(inv_lemma formula-decl nil inv nil)
(nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
real_types nil)
(cos_range application-judgement "trig_range" sincos_def
"trig_fnd/")
(cauchy_sec const-decl "cauchy_nzreal" trigx nil))
shostak))
(cosec_lemma 0
(cosec_lemma-1 nil 3394180131
("" (skosimp)
(("" (expand "cosec")
(("" (expand "cauchy_cosec")
(("" (lemma "sin_lemma" ("x" "nsx!1" "cx" "cnsx!1"))
(("" (assert)
((""
(lemma "inv_lemma"
("nzx" "sin(nsx!1)" "nzcx" "cauchy_sin(cnsx!1)"))
(("" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
((cosec const-decl "nzreal" trigx nil)
(sin_nz nonempty-type-eq-decl nil trigx nil)
(sin const-decl "real" sincos_def "trig_fnd/")
(/= const-decl "boolean" notequal nil)
(cauchy_sin_nz nonempty-type-eq-decl nil trigx nil)
(cauchy_sin_nz? const-decl "bool" trigx nil)
(cauchy_real nonempty-type-eq-decl nil cauchy nil)
(cauchy_real? const-decl "bool" cauchy nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans 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)
(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)
(sin_lemma formula-decl nil sincosx nil)
(nzreal nonempty-type-eq-decl nil reals nil)
(cauchy_sin const-decl "cauchy_real" sincosx nil)
(cauchy_nzreal nonempty-type-eq-decl nil cauchy nil)
(cauchy_nzreal? const-decl "bool" cauchy nil)
(inv_lemma formula-decl nil inv nil)
(nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
real_types nil)
(sin_range application-judgement "trig_range" sincos_def
"trig_fnd/")
(cauchy_cosec const-decl "cauchy_nzreal" trigx nil))
shostak))
(tan_lemma_TCC1 0
(tan_lemma_TCC1-1 nil 3394179601
("" (skosimp)
(("" (typepred "ncx!1")
(("" (expand "Tan?") (("" (propax) nil nil)) nil)) nil))
nil)
((cos_nz nonempty-type-eq-decl nil trigx nil)
(cos const-decl "real" sincos_def "trig_fnd/")
(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)
(/= const-decl "boolean" notequal nil)
(number nonempty-type-decl nil numbers nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(Tan? const-decl "bool" sincos_def "trig_fnd/"))
nil))
(tan_lemma 0
(tan_lemma-1 nil 3394180209
("" (skosimp)
(("" (expand "tan")
(("" (expand "cauchy_tan")
(("" (lemma "sin_lemma" ("x" "ncx!1" "cx" "cncx!1"))
(("" (lemma "cos_lemma" ("x" "ncx!1" "cx" "cncx!1"))
(("" (assert)
((""
(lemma "div_lemma"
("x" "sin(ncx!1)" "cx" "cauchy_sin(cncx!1)" "nzy"
"cos(ncx!1)" "nzcy" "cauchy_cos(cncx!1)"))
(("" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil)
((tan const-decl "real" sincos_def "trig_fnd/")
(cos_nz nonempty-type-eq-decl nil trigx nil)
(cos const-decl "real" sincos_def "trig_fnd/")
(/= const-decl "boolean" notequal nil)
(cauchy_cos_nz nonempty-type-eq-decl nil trigx nil)
(cauchy_cos_nz? const-decl "bool" trigx nil)
(cauchy_real nonempty-type-eq-decl nil cauchy nil)
(cauchy_real? const-decl "bool" cauchy nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans 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)
(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)
(sin_lemma formula-decl nil sincosx nil)
(cos_range application-judgement "trig_range" sincos_def
"trig_fnd/")
(sin_range application-judgement "trig_range" sincos_def
"trig_fnd/")
(real_div_nzreal_is_real application-judgement "real" reals nil)
(div_lemma formula-decl nil div nil)
(cauchy_sin const-decl "cauchy_real" sincosx nil)
(cauchy_nzreal? const-decl "bool" cauchy nil)
(cauchy_nzreal nonempty-type-eq-decl nil cauchy nil)
(cauchy_cos const-decl "cauchy_real" sincosx nil)
(nonzero_real nonempty-type-eq-decl nil reals nil)
(sin const-decl "real" sincos_def "trig_fnd/")
(cos_lemma formula-decl nil sincosx nil)
(cauchy_tan const-decl "cauchy_real" trigx nil))
shostak))
(cot_lemma 0
(cot_lemma-1 nil 3394180301
("" (skosimp)
(("" (lemma "sin_lemma" ("x" "nsx!1" "cx" "cnsx!1"))
(("" (lemma "cos_lemma" ("x" "nsx!1" "cx" "cnsx!1"))
(("" (assert)
((""
(lemma "div_lemma"
("nzy" "sin(nsx!1)" "nzcy" "cauchy_sin(cnsx!1)" "x"
"cos(nsx!1)" "cx" "cauchy_cos(cnsx!1)"))
(("1" (expand "cot")
(("1" (expand "cauchy_cot") (("1" (assert) nil nil))
nil))
nil)
("2" (expand "cauchy_nzreal?")
(("2" (inst + "sin(nsx!1)") nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
((sin_nz nonempty-type-eq-decl nil trigx nil)
(sin const-decl "real" sincos_def "trig_fnd/")
(/= const-decl "boolean" notequal nil)
(cauchy_sin_nz nonempty-type-eq-decl nil trigx nil)
(cauchy_sin_nz? const-decl "bool" trigx nil)
(cauchy_real nonempty-type-eq-decl nil cauchy nil)
(cauchy_real? const-decl "bool" cauchy nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans 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)
(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)
(sin_lemma formula-decl nil sincosx nil)
(nzreal nonempty-type-eq-decl nil reals nil)
(cot const-decl "real" trigx nil)
(real_div_nzreal_is_real application-judgement "real" reals nil)
(cos_range application-judgement "trig_range" sincos_def
"trig_fnd/")
(cauchy_cot const-decl "cauchy_real" trigx nil)
(sin_range application-judgement "trig_range" sincos_def
"trig_fnd/")
(div_lemma formula-decl nil div nil)
(cauchy_cos const-decl "cauchy_real" sincosx nil)
(cauchy_nzreal? const-decl "bool" cauchy nil)
(cauchy_nzreal nonempty-type-eq-decl nil cauchy nil)
(cauchy_sin const-decl "cauchy_real" sincosx nil)
(nonzero_real nonempty-type-eq-decl nil reals nil)
(cos const-decl "real" sincos_def "trig_fnd/")
(cos_lemma formula-decl nil sincosx nil))
shostak)))
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