(real_order_ep
(real_ord_ep_well_founded 0
(real_ord_ep_well_founded-1 nil 3595171480
("" (skeep)
(("" (expand "well_founded?")
(("" (skeep)
(("" (skolem - "a")
((""
(name "Kset"
"{kk:nat | EXISTS (x:(p)): kk = floor(abs(x)/epsil)}")
(("" (name "mm" "min(Kset)")
(("1" (typepred "mm")
(("1" (copy -1)
(("1" (expand "Kset" -1)
(("1" (skolem - "yy")
(("1" (inst + "yy")
(("1" (skeep)
(("1" (inst - "floor(abs(x)/epsil)")
(("1" (split -)
(("1"
(expand "real_ord_ep")
(("1" (assert) nil nil))
nil)
("2"
(expand "Kset" 1)
(("2" (inst + "x") nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (hide 2)
(("2" (expand "nonempty?")
(("2" (expand "empty?")
(("2" (expand "member")
(("2" (inst - "floor(abs(a)/epsil)")
(("2" (expand "Kset" 1)
(("2" (inst + "a") nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((well_founded? const-decl "bool" orders nil)
(set type-eq-decl nil sets nil)
(nonempty? const-decl "bool" sets nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(min const-decl "{a | S(a) AND (FORALL x: S(x) IMPLIES a <= x)}"
min_nat nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_ord_ep const-decl "bool" real_order_ep nil)
(Kset skolem-const-decl "[nat -> boolean]" real_order_ep nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(member const-decl "bool" sets nil)
(a skolem-const-decl "real" real_order_ep nil)
(p skolem-const-decl "pred[real]" real_order_ep nil)
(empty? const-decl "bool" sets nil)
(nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
(nnreal_div_posreal_is_nnreal application-judgement "nnreal"
real_types 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)
(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)
(= const-decl "[T, T -> boolean]" equalities nil)
(pred type-eq-decl nil defined_types nil)
(integer nonempty-type-from-decl nil integers nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(<= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(floor const-decl "{i | i <= x & x < i + 1}" floor_ceil nil)
(/= const-decl "boolean" notequal nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil)
(> const-decl "bool" reals nil)
(posreal nonempty-type-eq-decl nil real_types nil))
nil))
(real_ord_ep_decreases_halves 0
(real_ord_ep_decreases_halves-1 nil 3595172081
("" (skeep)
(("" (case "FORALL (y:real): y>=1 IMPLIES floor(y/2) < floor(y)")
(("1" (inst - "abs(x)/epsil")
(("1" (assert)
(("1" (split -1)
(("1" (expand "real_ord_ep")
(("1" (assert)
(("1" (expand "abs")
(("1" (lift-if)
(("1" (lift-if)
(("1" (lift-if) (("1" (ground) nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
("2" (cross-mult 1) nil nil))
nil))
nil))
nil)
("2" (hide-all-but 1)
(("2" (skeep) (("2" (ground) nil nil)) nil)) nil))
nil))
nil)
((/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/= const-decl "boolean" notequal nil)
(floor const-decl "{i | i <= x & x < i + 1}" floor_ceil nil)
(+ const-decl "[numfield, 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)
(integer nonempty-type-from-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)
(< const-decl "bool" reals nil) (>= const-decl "bool" reals nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans 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)
(real_div_nzreal_is_real application-judgement "real" reals nil)
(real_ord_ep_well_founded application-judgement
"(well_founded?[real])" real_order_ep nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(div_mult_pos_ge1 formula-decl nil real_props nil)
(posreal_times_posreal_is_posreal application-judgement "posreal"
real_types nil)
(real_ord_ep const-decl "bool" real_order_ep nil)
(minus_real_is_real application-judgement "real" reals nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil)
(> const-decl "bool" reals nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(nnreal_div_posreal_is_nnreal application-judgement "nnreal"
real_types nil))
shostak)))
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