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shostak))
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shostak))
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(("2" (label "Extspacename" -2)
(("2" (label "ffmember" 1)
(("2" (label "ExtExists" 2)
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(name "funchoose"
"LAMBDA (gg:(Extspace)): choose({rr:[INTab->real]|EXISTS (ffc:real):OE`space(rr) AND gg = rr + ffc * ff})" )
(("1" (label "funchoosename" -1)
(("1"
(name "constchoose"
"(LAMBDA (gg: (Extspace)):
choose({ffc: real |
EXISTS (rr: [INTab->real]):
OE`space(rr) AND gg = rr + ffc * ff}))")
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(case
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(("1"
(typepred "OE`space" )
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nil ))
nil )
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(hide-all-but (-2 -3 1))
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(decompose-equality +)
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(decompose-equality
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(decompose-equality
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(label "funchooseunique" -1)
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(("1"
(decompose-equality
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nil ))
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nil ))
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nil ))
nil ))
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nil )
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(hide-all-but
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(hide-all-but
(-1 -2 1 2))
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(decompose-equality
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("3"
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nil
nil )
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(hide-all-but
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(grind)
nil
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nil ))
nil )
("2"
(hide 2)
(("2"
(expand
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(("2"
(split +)
(("1"
(hide-all-but
(-1 1))
(("1"
(typepred
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(expand
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(("1"
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nil ))
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nil ))
nil ))
nil )
("2"
(hide-all-but
(-1 1))
(("2"
(inst
+
"fq"
"0" )
(("2"
(assert )
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(label "OEdecomp" -1)
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(("1"
(skosimp*)
(("1"
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(("1"
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(("1"
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nil
nil ))
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nil )
("2"
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1))
(("2"
(decompose-equality
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(name
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(("1"
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(("1"
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(("1"
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(("1"
(typepred
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(("1"
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(("1"
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(("1"
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("2"
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(("2"
(hide
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(("2"
(expand
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(("2"
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"fun_norm[a, b](spcfun + ff) * -constchoose(f!1) = fun_norm[a,b](funchoose(f!1) + constchoose(f!1)*ff)" )
(("1"
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("2"
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(("2"
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(("2"
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("3"
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("2"
(mult-by
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("3" (hide 2)
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real_props nil )
(real_plus_real_is_real application-judgement "real" reals nil )
(real_lt_is_strict_total_order name-judgement
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(+ const-decl "[numfield, numfield -> numfield]" number_fields nil )
(nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
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(member const-decl "bool" sets nil )
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(nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
real_types nil )
(both_sides_times_pos_le1_imp formula-decl nil extra_real_props
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(real_ge_is_total_order name-judgement "(total_order?[real])"
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(abs_mult formula-decl nil real_props nil )
(OE skolem-const-decl "Op_Pair" riesz_hahn_banach nil )
(rr!1 skolem-const-decl "[INTab[a, b] -> real]" riesz_hahn_banach
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(funs_const_closed? const-decl "bool" riesz_function_sets nil )
(funs_bounded? const-decl "bool" riesz_function_sets nil )
(funs_contain_constants? const-decl "bool" riesz_function_sets nil )
(Continuous_Function type-eq-decl nil riesz_interval_funs nil )
(continuous_on_int? const-decl "bool" riesz_interval_funs nil )
(f!1 skolem-const-decl "[INTab[a, b] -> real]" riesz_hahn_banach
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(continuous_implies_bounded formula-decl nil riesz_interval_funs
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(funs_contain_continuous? const-decl "bool" riesz_function_sets
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(fq!1 skolem-const-decl "[INTab[a, b] -> real]" riesz_hahn_banach
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(- const-decl "[T -> real]" real_fun_ops "reals/" )
(yy skolem-const-decl "(OE`space)" riesz_hahn_banach nil )
(hh skolem-const-decl "(OE`space)" riesz_hahn_banach nil )
(fun_norm_triangle formula-decl nil riesz_interval_funs nil )
(nzint_abs_is_pos application-judgement "{j: posint | j >= i}"
real_defs nil )
(empty? const-decl "bool" sets nil )
(zerfun skolem-const-decl "[INTab[a, b] -> naturalnumber]"
riesz_hahn_banach nil )
(naturalnumber type-eq-decl nil naturalnumbers 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 )
(zerfun skolem-const-decl "[INTab[a, b] -> naturalnumber]"
riesz_hahn_banach nil )
(upper_bound? const-decl "bool" bounded_real_defs nil )
(hh!1 skolem-const-decl "(OE`space)" riesz_hahn_banach nil )
(OEnorm skolem-const-decl "{M: nnreal |
(FORALL (f: ((OE`space))): abs(OE`Lop(f)) <= M * fun_norm(f)) AND
(FORALL (M1: real):
M1 < M IMPLIES
(EXISTS (f: ((OE`space))):
abs(OE`Lop(f)) > M1 * fun_norm(f)))}"
riesz_hahn_banach nil )
(Aset skolem-const-decl "[real -> boolean]" riesz_hahn_banach nil )
(lub const-decl "{x | least_upper_bound?(x, SA)}" bounded_real_defs
nil )
(least_upper_bound? const-decl "bool" bounded_real_defs nil )
(bounded_above? const-decl "bool" bounded_real_defs nil )
(f!1 skolem-const-decl "(Extspace)" riesz_hahn_banach nil )
(triangle formula-decl nil real_props nil )
(spcfun skolem-const-decl "[INTab[a, b] -> real]" riesz_hahn_banach
nil )
(constchoose skolem-const-decl "[gg: (Extspace) ->
({ffc: real |
EXISTS (rr: [INTab -> real]): OE`space(rr) AND gg = rr + ffc * ff})]"
riesz_hahn_banach nil )
(const_inv_op? const-decl "bool" riesz_linear_functionals nil )
(linear_op? const-decl "bool" riesz_linear_functionals nil )
(fun_norm_scal formula-decl nil riesz_interval_funs nil )
(Extop skolem-const-decl "[(Extspace) -> real]" riesz_hahn_banach
nil )
(Extn skolem-const-decl
"[# Lop: [(Extspace) -> real], space: [[INTab[a, b] -> real] -> boolean] #]"
riesz_hahn_banach nil )
(IFF const-decl "[bool, bool -> bool]" booleans nil )
(<= const-decl "bool" riesz_hahn_banach nil )
(Op_Extension type-eq-decl nil riesz_hahn_banach nil )
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil )
(f!1 skolem-const-decl "((OE`space))" riesz_hahn_banach nil )
(IF const-decl "[boolean, T, T -> T]" if_def nil )
(subset? const-decl "bool" sets nil )
(additive_op? const-decl "bool" riesz_linear_functionals nil )
(g!1 skolem-const-decl "(Extspace)" riesz_hahn_banach nil )
(f!1 skolem-const-decl "(Extspace)" riesz_hahn_banach nil )
(c!1 skolem-const-decl "real" riesz_hahn_banach nil )
(f!1 skolem-const-decl "(Extspace)" riesz_hahn_banach nil )
(both_sides_times1_imp formula-decl nil extra_real_props nil )
(fq skolem-const-decl "[INTab[a, b] -> real]" riesz_hahn_banach
nil )
(fq skolem-const-decl "(OE`space)" riesz_hahn_banach nil )
(gg skolem-const-decl "(Extspace)" riesz_hahn_banach nil )
(rr!1 skolem-const-decl "[INTab[a, b] -> real]" riesz_hahn_banach
nil )
(fq skolem-const-decl "(OE`space)" riesz_hahn_banach nil )
(gg skolem-const-decl "(Extspace)" riesz_hahn_banach nil )
(div_cancel4 formula-decl nil real_props nil )
(nonzero_real nonempty-type-eq-decl nil reals nil )
(times_div2 formula-decl nil real_props nil )
(real_div_nzreal_is_real application-judgement "real" reals nil )
(ff skolem-const-decl "Bounded_Function[a, b]" riesz_hahn_banach
nil )
(funchoose skolem-const-decl "[gg: (Extspace) ->
({rr: [INTab -> real] |
EXISTS (ffc: real): OE`space(rr) AND gg = rr + ffc * ff})]"
riesz_hahn_banach nil )
(gg skolem-const-decl "(Extspace)" riesz_hahn_banach nil )
(fq skolem-const-decl "[INTab[a, b] -> real]" riesz_hahn_banach
nil )
(- const-decl "[numfield, numfield -> numfield]" number_fields nil )
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil )
(nznum nonempty-type-eq-decl nil number_fields nil )
(/= const-decl "boolean" notequal nil )
(real_minus_real_is_real application-judgement "real" reals nil )
(nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
real_types nil )
(minus_odd_is_odd application-judgement "odd_int" integers nil )
(choose const-decl "(p)" sets nil )
(nonempty? const-decl "bool" sets nil )
(Bounded_Function type-eq-decl nil riesz_interval_funs nil )
(* const-decl "[T -> real]" real_fun_ops "reals/" )
(+ const-decl "[T -> real]" real_fun_ops "reals/" )
(FALSE const-decl "bool" booleans nil )
(extend const-decl "R" extend nil )
(fullset const-decl "set" sets 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 )
(AND const-decl "[bool, bool -> bool]" booleans nil )
(<= const-decl "bool" reals nil )
(a formal-const-decl "real" riesz_hahn_banach nil )
(< const-decl "bool" reals nil )
(b formal-const-decl "{bb: real | a < bb}" riesz_hahn_banach nil )
(INTab type-eq-decl nil riesz_interval_funs nil )
(set type-eq-decl nil sets nil )
(bounded_linear_subspace? const-decl "bool" riesz_function_sets
nil )
(Operator type-eq-decl nil riesz_linear_functionals nil )
(bounded_linear_operator? const-decl "bool"
riesz_bounded_functionals nil )
(Op_Pair type-eq-decl nil riesz_hahn_banach nil )
(bounded_op? const-decl "bool" riesz_bounded_functionals nil )
(>= const-decl "bool" reals nil )
(nnreal type-eq-decl nil real_types nil )
(nonneg_real nonempty-type-eq-decl nil real_types nil )
(numfield nonempty-type-eq-decl nil number_fields nil )
(- const-decl "[numfield -> numfield]" number_fields nil )
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil )
(* const-decl "[numfield, numfield -> numfield]" number_fields nil )
(bounded_on_int? const-decl "bool" riesz_interval_funs nil )
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil )
(> const-decl "bool" reals nil )
(fun_norm const-decl "{M: nnreal |
(FORALL (x): abs(f(x)) <= M) AND
(FORALL (M1: real): M1 < M IMPLIES (EXISTS (x): abs(f(x)) > M1))}"
riesz_interval_funs nil )
(op_norm const-decl "{M: nnreal |
(FORALL (f: Funs): abs(L(f)) <= M * fun_norm(f)) AND
(FORALL (M1: real):
M1 < M IMPLIES
(EXISTS (f: Funs): abs(L(f)) > M1 * fun_norm(f)))}"
riesz_bounded_functionals nil )
(TRUE const-decl "bool" booleans nil )
(= const-decl "[T, T -> boolean]" equalities nil )
(bool nonempty-type-eq-decl nil booleans nil )
(boolean nonempty-type-decl nil booleans nil ))
nil )
(Op_Extension_exists-4 nil 3565654845
(""
(deftactic step_assert (step)
(branch step ((skip) (finalize (assert )))))
(("" (skeep)
(("" (name "OEnorm" "op_norm[a, b, ((OE`space))](OE`Lop)" )
(("1" (label "OEnormname" -1)
(("1"
(name "Extspace"
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(("1" (case "NOT bounded_linear_subspace?[a,b](Extspace)" )
(("1" (hide 3)
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(inst - "x!1" )
(("1"
(grind)
nil )))))))))))))
("2"
(skosimp*)
(("2"
(inst
+
"rr!1+rr!2"
"ffc!1+ffc!2" )
(("2"
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(inst
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("2"
(replace -3)
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(("2"
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("2" (expand "funs_const_closed?" )
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(expand "*" )
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(("1"
(assert )
nil )))))))))))))))))))))
("2"
(skosimp*)
(("2"
(inst + "c!1*rr!1" "c!1*ffc!1" )
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("3" (expand "funs_bounded?" )
(("3" (skosimp*)
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(("3" (flatten) nil )))))))))
("4" (ground)
(("4" (expand "funs_contain_constants?" )
(("4" (skosimp*)
(("4" (expand "Extspace" +)
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(split)
(("1"
(expand "bounded_on_int?" )
(("1"
(inst + "abs(c!1)" )
(("1" (grind) nil )))))
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(("5" (skosimp*)
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("2" (label "bls" -1)
(("2" (label "Extspacename" -2)
(("2" (label "ffmember" 1)
(("2" (label "ExtExists" 2)
(("2"
(name "funchoose"
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(("1" (label "funchoosename" -1)
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(name "constchoose"
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(("1" (label "constchoosename" -1)
(("1"
(case
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(("1"
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(("1"
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"funchoose(gg)"
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(("1"
(expand
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(("1"
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"fq"
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(("1"
(step_assert
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"fq + (-1) * funchoose(gg)"
"(1 / (rr - constchoose(gg)))" ))
(("1"
(assert )
nil )))))))
("2"
(assert )
(("2"
(typepred
"funchoose(gg)" )
(("2"
(skosimp*)
nil )))))))))))))))
("2"
(hide-all-but (-2 -3 1))
(("2"
(decompose-equality +)
(("2"
(decompose-equality
-)
(("2"
(decompose-equality
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(("2"
(inst - "x!1" )
(("2"
(inst - "x!1" )
(("2"
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(expand
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("2"
(label "funchooseunique" -1)
(("2"
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(("1"
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(("1"
(case
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(("1"
(replace -1)
(("1"
(hide-all-but
(-3 -4 1))
(("1"
(decompose-equality
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(("1"
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(("1"
(decompose-equality
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(inst - "x!1" )
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(inst
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"x!1" )
(("1"
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(case
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(("1"
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"fq"
"-1 * funchoose(gg)" ))
(("1"
(step_assert
(inst
-
"fq + -1 * funchoose(gg)"
"(1 / (ffc!1 - constchoose(gg)))" ))
(("1"
(assert )
nil )))))))))))))))))
("2"
(hide-all-but
(-2 -3 1))
(("2"
(decompose-equality
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(("2"
(decompose-equality
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(("2"
(decompose-equality
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(("2"
(inst - "x!1" )
(("2"
(inst
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(("2"
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(grind
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nil )))))))))))))))))))))))
("3"
(assert )
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("2"
(label "funchooseunique2" -1)
(("2"
(case
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(("1"
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(inst
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(assert )
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(label "ggdecomp" -1)
(("2"
(case
"NOT FORALL (gg: (Extspace), fq: (OE`space), rr:real):
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"fq"
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(("1"
(inst
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(assert )
nil )))
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(typepred
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(skosimp*)
(("2"
(assert )
nil )))))
("3"
(assert )
nil )))))))))))))))
("2"
(hide-all-but
(-1 -2 1 2))
(("2"
(decompose-equality
+)
(("2"
(decompose-equality
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(("2"
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(inst
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"x!1" )
(("2"
(inst
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"x!1" )
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(assert )
nil )))))))))))
("2"
(label "decompunique" -1)
(("2"
(case
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(("1"
(inst
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"fq"
"fq"
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(ground)
nil )
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(hide-all-but
1)
(("2"
(decompose-equality
+)
(("2"
(grind)
nil )))))))))
("2"
(hide 2)
(("2"
(expand
"Extspace" )
(("2"
(split +)
(("1"
(hide-all-but
(-1 1))
(("1"
(typepred
"OE`space" )
(("1"
(expand
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(("1"
(expand
"funs_bounded?" )
(("1"
(flatten)
(("1"
(inst
-
"fq" )
nil )))))))))))
("2"
(hide-all-but
(-1 1))
(("2"
(inst
+
"fq"
"0" )
(("2"
(assert )
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(decompose-equality
+)
(("2"
(grind)
nil )))))))))))))))))))
("2"
(label "OEdecomp" -1)
(("2"
(case
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(("1"
(label
"betadef"
-1)
(("1"
(skosimp*)
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(("1"
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(("1"
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(("1"
(skosimp*)
(("1"
(expand
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+)
(("1"
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(("1"
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(inst
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"f!1" )
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(("1"
(inst
-
"funchoose(f!1)" )
(("1"
(assert )
nil )))))
("2"
(replace
-2)
(("2"
(hide-all-but
(-1
1))
(("2"
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(("2"
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--> --------------------
--> maximum size reached
--> --------------------
Messung V0.5 in Prozent C=100 H=100 G=100
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