(cauchy
(cauchy_real_TCC1 0
(cauchy_real_TCC1-1 nil 3250063205
("" (expand "cauchy_real?")
(("" (inst 1 "0") (("" (grind) nil nil)) nil)) 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)
(posnat_expt application-judgement "posnat" exponentiation nil)
(cauchy_prop const-decl "bool" cauchy nil)
(^ const-decl "real" exponentiation nil)
(cauchy_real? const-decl "bool" cauchy nil))
nil))
(cauchy_nzreal_TCC1 0
(cauchy_nzreal_TCC1-1 nil 3250063205
("" (expand "cauchy_nzreal?")
(("" (inst 1 "1") (("" (grind) nil nil)) nil)) 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)
(/= const-decl "boolean" notequal nil)
(nzreal nonempty-type-eq-decl nil reals nil)
(posint_exp application-judgement "posint" exponentiation nil)
(posnat_expt application-judgement "posnat" exponentiation nil)
(cauchy_prop const-decl "bool" cauchy nil)
(^ const-decl "real" exponentiation nil)
(cauchy_nzreal? const-decl "bool" cauchy nil))
nil))
(cauchy_nnreal_TCC1 0
(cauchy_nnreal_TCC1-1 nil 3250063205
("" (expand "cauchy_nnreal?")
(("" (inst 1 "1") (("" (grind) nil nil)) nil)) 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)
(nnreal type-eq-decl nil real_types nil)
(posint_exp application-judgement "posint" exponentiation nil)
(posnat_expt application-judgement "posnat" exponentiation nil)
(cauchy_prop const-decl "bool" cauchy nil)
(^ const-decl "real" exponentiation nil)
(cauchy_nnreal? const-decl "bool" cauchy nil))
nil))
(cauchy_npreal_TCC1 0
(cauchy_npreal_TCC1-1 nil 3250063205
("" (expand "cauchy_npreal?")
(("" (inst + "0") (("" (grind) nil nil)) nil)) 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)
(npreal type-eq-decl nil real_types nil)
(posnat_expt application-judgement "posnat" exponentiation nil)
(cauchy_prop const-decl "bool" cauchy nil)
(^ const-decl "real" exponentiation nil)
(cauchy_npreal? const-decl "bool" cauchy nil))
nil))
(cauchy_posreal_TCC1 0
(cauchy_posreal_TCC1-1 nil 3250063205
("" (expand "cauchy_posreal?")
(("" (inst + "1")
(("" (expand "cauchy_prop") (("" (propax) nil nil)) nil)) nil))
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)
(cauchy_prop const-decl "bool" cauchy nil)
(posint_exp application-judgement "posint" exponentiation nil)
(cauchy_posreal? const-decl "bool" cauchy nil))
nil))
(cauchy_negreal_TCC1 0
(cauchy_negreal_TCC1-1 nil 3250063205
("" (expand "cauchy_negreal?")
(("" (inst + "-1") (("" (grind) nil nil)) nil)) nil)
((minus_odd_is_odd application-judgement "odd_int" integers 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)
(nonpos_real nonempty-type-eq-decl nil real_types nil)
(< const-decl "bool" reals nil)
(negreal nonempty-type-eq-decl nil real_types nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(minus_nzint_is_nzint application-judgement "nzint" integers nil)
(posnat_expt application-judgement "posnat" exponentiation nil)
(cauchy_prop const-decl "bool" cauchy nil)
(^ const-decl "real" exponentiation nil)
(cauchy_negreal? const-decl "bool" cauchy nil)
(posint_exp application-judgement "posint" exponentiation nil))
nil))
(cauchy_smallreal_TCC1 0
(cauchy_smallreal_TCC1-1 nil 3250063205
("" (expand "cauchy_smallreal?")
(("" (inst + "0")
(("" (expand "cauchy_prop") (("" (propax) nil nil)) nil)) nil))
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)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(< const-decl "bool" reals nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(smallreal nonempty-type-eq-decl nil prelude_aux nil)
(cauchy_prop const-decl "bool" cauchy nil)
(posint_exp application-judgement "posint" exponentiation nil)
(cauchy_smallreal? const-decl "bool" cauchy nil))
nil))
(subtype_TCC1 0
(subtype_TCC1-1 nil 3250063205
("" (skosimp*)
(("" (typepred "x!1")
(("" (expand "cauchy_nzreal?")
(("" (expand "cauchy_real?")
(("" (skosimp) (("" (inst 1 "x!2") nil nil)) nil)) nil))
nil))
nil))
nil)
((cauchy_nzreal nonempty-type-eq-decl nil cauchy nil)
(cauchy_nzreal? const-decl "bool" cauchy 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_real? const-decl "bool" cauchy nil)
(nzreal nonempty-type-eq-decl nil reals nil)
(/= const-decl "boolean" notequal nil))
shostak))
(subtype_TCC2 0
(subtype_TCC2-1 nil 3250063205
("" (skosimp*)
(("" (typepred "x!1")
(("" (expand "cauchy_nnreal?")
(("" (expand "cauchy_real?")
(("" (skosimp*) (("" (inst 1 "x!2") nil nil)) nil)) nil))
nil))
nil))
nil)
((cauchy_nnreal nonempty-type-eq-decl nil cauchy nil)
(cauchy_nnreal? const-decl "bool" cauchy 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_real? const-decl "bool" cauchy nil)
(nnreal type-eq-decl nil real_types nil))
shostak))
(subtype_TCC3 0
(subtype_TCC3-1 nil 3250063205
("" (skosimp*)
(("" (typepred "x!1")
(("" (expand "cauchy_real?")
(("" (expand "cauchy_npreal?")
(("" (skosimp*) (("" (inst 1 "x!2") nil nil)) nil)) nil))
nil))
nil))
nil)
((cauchy_npreal nonempty-type-eq-decl nil cauchy nil)
(cauchy_npreal? const-decl "bool" cauchy 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)
(npreal type-eq-decl nil real_types nil)
(<= const-decl "bool" reals nil)
(cauchy_real? const-decl "bool" cauchy nil))
shostak))
(subtype_TCC4 0
(subtype_TCC4-1 nil 3250063205
("" (skosimp*)
(("" (typepred "x!1")
(("" (expand "cauchy_nnreal?")
(("" (expand "cauchy_posreal?")
(("" (skosimp*) (("" (inst 1 "x!2") nil nil)) nil)) nil))
nil))
nil))
nil)
((cauchy_posreal nonempty-type-eq-decl nil cauchy nil)
(cauchy_posreal? const-decl "bool" cauchy 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)
(posreal nonempty-type-eq-decl nil real_types nil)
(> const-decl "bool" reals nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(nnreal type-eq-decl nil real_types nil)
(cauchy_nnreal? const-decl "bool" cauchy nil))
shostak))
(subtype_TCC5 0
(subtype_TCC5-1 nil 3250063206
("" (skosimp*)
(("" (typepred "x!1")
(("" (expand "cauchy_nzreal?")
(("" (expand "cauchy_posreal?")
(("" (skosimp*) (("" (inst 1 "x!2") nil nil)) nil)) nil))
nil))
nil))
nil)
((cauchy_posreal nonempty-type-eq-decl nil cauchy nil)
(cauchy_posreal? const-decl "bool" cauchy 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)
(posreal nonempty-type-eq-decl nil real_types nil)
(> const-decl "bool" reals nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(nzreal nonempty-type-eq-decl nil reals nil)
(/= const-decl "boolean" notequal nil)
(cauchy_nzreal? const-decl "bool" cauchy nil))
shostak))
(subtype_TCC6 0
(subtype_TCC6-1 nil 3250063206
("" (skosimp*)
(("" (typepred "x!1")
(("" (expand "cauchy_nzreal?")
(("" (expand "cauchy_negreal?")
(("" (skosimp*) (("" (inst 1 "x!2") nil nil)) nil)) nil))
nil))
nil))
nil)
((cauchy_negreal nonempty-type-eq-decl nil cauchy nil)
(cauchy_negreal? const-decl "bool" cauchy 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)
(negreal nonempty-type-eq-decl nil real_types nil)
(< const-decl "bool" reals nil)
(nonpos_real nonempty-type-eq-decl nil real_types nil)
(<= const-decl "bool" reals nil)
(nzreal nonempty-type-eq-decl nil reals nil)
(/= const-decl "boolean" notequal nil)
(cauchy_nzreal? const-decl "bool" cauchy nil))
shostak))
(subtype_TCC7 0
(subtype_TCC7-1 nil 3250063206
("" (skosimp*)
(("" (typepred "x!1")
(("" (expand "cauchy_npreal?")
(("" (expand "cauchy_negreal?")
(("" (skosimp*) (("" (inst 1 "x!2") nil nil)) nil)) nil))
nil))
nil))
nil)
((cauchy_negreal nonempty-type-eq-decl nil cauchy nil)
(cauchy_negreal? const-decl "bool" cauchy 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)
(negreal nonempty-type-eq-decl nil real_types nil)
(< const-decl "bool" reals nil)
(nonpos_real nonempty-type-eq-decl nil real_types nil)
(npreal type-eq-decl nil real_types nil)
(<= const-decl "bool" reals nil)
(cauchy_npreal? const-decl "bool" cauchy nil))
shostak))
(subtype_TCC8 0
(subtype_TCC8-1 nil 3250063206
("" (skosimp*)
(("" (typepred "x!1")
(("" (expand "cauchy_real?")
(("" (expand "cauchy_smallreal?")
(("" (skosimp*) (("" (inst 1 "sx!1") nil nil)) nil)) nil))
nil))
nil))
nil)
((cauchy_smallreal nonempty-type-eq-decl nil cauchy nil)
(cauchy_smallreal? const-decl "bool" cauchy 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)
(smallreal nonempty-type-eq-decl nil prelude_aux nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(< const-decl "bool" reals nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(cauchy_real? const-decl "bool" cauchy nil))
shostak))
(cauchy_zero_TCC1 0
(cauchy_zero_TCC1-1 nil 3250063205
("" (expand "cauchy_nnreal?")
(("" (inst 1 "0") (("" (grind) nil nil)) nil)) 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)
(nnreal type-eq-decl nil real_types nil)
(posnat_expt application-judgement "posnat" exponentiation nil)
(cauchy_prop const-decl "bool" cauchy nil)
(^ const-decl "real" exponentiation nil)
(cauchy_nnreal? const-decl "bool" cauchy nil))
nil))
(unique_cauchy_zero 0
(unique_cauchy_zero-1 nil 3250063205
("" (skosimp*)
(("" (expand "cauchy_prop")
(("" (expand "cauchy_zero")
(("" (lemma "trich_lt" ("x" "x!1" "y" "0"))
(("" (split -1)
(("1" (lemma "epsilon_log2" ("px" "-x!1"))
(("1" (skolem!)
(("1"
(lemma "div_mult_pos_lt1"
("z" "1" "py" "2^p!1" "x" "-x!1"))
(("1"
(lemma "both_sides_times_neg_lt1"
("y" "1" "nz" "-1" "x" "-x!1 * 2 ^ p!1"))
(("1" (split)
(("1" (flatten)
(("1" (inst - "p!1")
(("1" (assert) (("1" (grind) nil nil)) nil))
nil))
nil)
("2" (flatten 1)
(("2" (skolem!)
(("2" (replace -1)
(("2"
(lemma "expt_ge1" ("b" "2" "n" "p!2"))
(("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (assert) nil nil))
nil)
("2" (replace -1)
(("2" (split)
(("1" (assert) nil nil)
("2" (flatten)
(("2" (skolem!)
(("2" (lemma "expt_ge1" ("b" "2" "n" "p!1"))
(("2" (grind) nil nil)) nil))
nil))
nil))
nil))
nil)
("3" (lemma "epsilon_log2" ("px" "x!1"))
(("1" (skolem!)
(("1"
(lemma "div_mult_pos_lt1"
("z" "1" "py" "2^p!1" "x" "x!1"))
(("1" (split 1)
(("1" (flatten 1)
(("1" (inst - "p!1")
(("1" (assert) (("1" (grind) nil nil)) nil))
nil))
nil)
("2" (flatten 1)
(("2" (skolem!)
(("2" (replace -1) (("2" (grind) nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
((posint_exp application-judgement "posint" exponentiation nil)
(cauchy_prop const-decl "bool" cauchy 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)
(trich_lt formula-decl nil real_props nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields 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)
(epsilon_log2 formula-decl nil appendix nil)
(minus_real_is_real application-judgement "real" reals nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(^ const-decl "real" exponentiation nil)
(/= const-decl "boolean" notequal nil)
(OR const-decl "[bool, bool -> bool]" 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)
(div_mult_pos_lt1 formula-decl nil real_props nil)
(posnat_expt application-judgement "posnat" exponentiation nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(posrat_div_posrat_is_posrat application-judgement "posrat"
rationals nil)
(odd_times_odd_is_odd application-judgement "odd_int" integers nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(expt_ge1 formula-decl nil exponentiation nil)
(above nonempty-type-eq-decl nil integers nil)
(minus_even_is_even application-judgement "even_int" integers nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(negreal nonempty-type-eq-decl nil real_types nil)
(< const-decl "bool" reals nil)
(nonpos_real nonempty-type-eq-decl nil real_types nil)
(<= const-decl "bool" reals nil)
(both_sides_times_neg_lt1 formula-decl nil real_props nil)
(real_times_real_is_real application-judgement "real" reals nil)
(minus_odd_is_odd application-judgement "odd_int" integers nil)
(cauchy_zero const-decl "cauchy_nnreal" cauchy nil))
nil))
(unique_cauchy_zero2 0
(unique_cauchy_zero2-1 nil 3250063205
("" (skosimp)
(("" (split)
(("1" (flatten)
(("1" (expand "cauchy_prop")
(("1" (skolem!)
(("1" (expand "cauchy_zero")
(("1" (inst - "p!1")
(("1" (flatten)
(("1" (rewrite "zero_times1")
(("1" (rewrite "lt_equiv_le_plus_one" -1)
(("1" (rewrite "lt_plus_one_equiv_le" -2)
(("1" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (flatten)
(("2"
(lemma "extensionality_postulate"
("f" "cx!1" "g" "cauchy_zero"))
(("2" (lemma "unique_cauchy_zero" ("x" "0"))
(("2" (grind) nil nil)) nil))
nil))
nil))
nil))
nil)
((posint_exp application-judgement "posint" exponentiation nil)
(cauchy_prop const-decl "bool" cauchy nil)
(cauchy_zero const-decl "cauchy_nnreal" cauchy nil)
(cauchy_real nonempty-type-eq-decl nil cauchy nil)
(cauchy_real? const-decl "bool" cauchy nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(lt_equiv_le_plus_one formula-decl nil prelude_aux nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(lt_plus_one_equiv_le formula-decl nil prelude_aux nil)
(^ const-decl "real" exponentiation nil)
(/= const-decl "boolean" notequal nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(zero_times1 formula-decl nil real_props 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)
(cauchy_nnreal nonempty-type-eq-decl nil cauchy nil)
(cauchy_nnreal? const-decl "bool" cauchy nil)
(extensionality_postulate formula-decl nil functions nil)
(posnat_expt application-judgement "posnat" exponentiation nil)
(unique_cauchy_zero formula-decl nil cauchy nil))
nil))
(unique_cauchy_zero3 0
(unique_cauchy_zero3-1 nil 3250063205
("" (skosimp*)
((""
(lemma "extensionality_postulate" ("f" "cx!1" "g" "cauchy_zero"))
(("" (lemma "unique_cauchy_zero2" ("cx" "cx!1"))
(("" (grind) nil nil)) nil))
nil))
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)
(cauchy_zero const-decl "cauchy_nnreal" cauchy nil)
(cauchy_nnreal nonempty-type-eq-decl nil cauchy nil)
(cauchy_nnreal? const-decl "bool" cauchy nil)
(cauchy_real nonempty-type-eq-decl nil cauchy nil)
(cauchy_real? const-decl "bool" cauchy nil)
(extensionality_postulate formula-decl nil functions nil)
(unique_cauchy_zero2 formula-decl nil cauchy nil))
nil)))
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