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quadratic.prf
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quadratic.prf
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(quadratic
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(real_plus_real_is_real application-judgement "real" reals nil)
(sq const-decl "nonneg_real" sq nil))
nil))
(discr_symm 0
(discr_symm-1 nil 3427107841
("" (expand "discr")
(("" (skeep) (("" (rewrite "sq_neg") (("" (assert) nil nil)) nil)) nil))
nil)
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(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)
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(minus_real_is_real application-judgement "real" reals nil)
(minus_nzreal_is_nzreal application-judgement "nzreal" real_types nil)
(real_times_real_is_real application-judgement "real" reals nil))
shostak))
(discr_scalar 0
(discr_scalar-1 nil 3427287214
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(("" (rewrite "sq_times")
(("" (expand "sq" 1 5) (("" (assert) nil nil)) nil)) nil))
nil))
nil)
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(nzreal_times_nzreal_is_nzreal application-judgement "nzreal" real_types
nil)
(discr const-decl "real" quadratic nil)
(sq const-decl "nonneg_real" sq nil)
(nnreal_times_nnreal_is_nnreal application-judgement "nnreal" real_types
nil)
(nzreal nonempty-type-eq-decl nil reals nil)
(/= const-decl "boolean" notequal nil)
(real nonempty-type-from-decl nil reals nil)
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(number_field_pred const-decl "[number -> boolean]" number_fields nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(sq_times formula-decl nil sq nil))
shostak))
(a_gt_0_discr_gt_0 0
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nil))
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nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
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nil)
(a_gt_0_discr_gt_0-1 nil 3253574939
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nil))
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nil))
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("2" (hide -2 2) (("2" (grind-reals) nil nil)) nil))
nil))
nil))
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nil))
nil))
nil)
((sq const-decl "nonneg_real" sq nil)) nil))
(a_gt_0_discr_ge_0 0
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nil)
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nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
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(pos_times_ge formula-decl nil real_props nil)
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(bool nonempty-type-eq-decl nil booleans nil)
(real_plus_real_is_real application-judgement "real" reals nil)
(nonzero_real nonempty-type-eq-decl nil reals nil)
(/= const-decl "boolean" notequal 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))
nil)
(a_gt_0_discr_ge_0-2 nil 3253620357
("" (skolem 1 ("a" "b" "c" "x"))
(("" (flatten)
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("2" (hide -2 2) (("2" (grind-reals) nil nil)) nil))
nil))
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nil))
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((sq const-decl "nonneg_real" sq nil)) nil))
(a_lt_0_discr_gt_0 0
(a_lt_0_discr_gt_0-1 nil 3253574939
("" (skeep)
(("" (lemma "a_gt_0_discr_gt_0")
(("" (inst -1 "-a" "-b" "-c" "x")
(("" (assert)
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nil))
nil))
nil)
((a_gt_0_discr_gt_0 formula-decl nil quadratic nil)
(real_times_real_is_real application-judgement "real" reals nil)
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(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(discr_symm formula-decl nil quadratic nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(nonzero_real nonempty-type-eq-decl nil reals nil)
(/= const-decl "boolean" notequal 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)
(minus_nzreal_is_nzreal application-judgement "nzreal" real_types nil)
(minus_real_is_real application-judgement "real" reals nil))
nil))
(a_lt_0_discr_ge_0 0
(a_lt_0_discr_ge_0-2 nil 3430213579
("" (skeep)
(("" (lemma "a_gt_0_discr_ge_0")
(("" (inst -1 "-a" "-b" "-c" "x")
(("" (assert)
(("" (rewrite "discr_symm") (("" (assert) nil nil)) nil)) nil))
nil))
nil))
nil)
((a_gt_0_discr_ge_0 formula-decl nil quadratic nil)
(real_le_is_total_order name-judgement "(total_order?[real])" real_props
nil)
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"(strict_total_order?[real])" real_props nil)
(real_times_real_is_real application-judgement "real" reals nil)
(real_plus_real_is_real application-judgement "real" reals nil)
(real_ge_is_total_order name-judgement "(total_order?[real])" real_props
nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
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(/= const-decl "boolean" notequal nil)
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(minus_real_is_real application-judgement "real" reals nil))
nil)
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