Quelle finite_fubini_tonelli.prf
Sprache: Lisp
(finite_fubini_tonellinil 3458551591"" (typepred "S1" )"" (expand "sigma_algebra?" )"" (expand "subset_algebra_empty?" )"" (flatten)"" (expand "member" ) (("" (propax) nil nil )) nil )) nil ))nil ))nil ))nil )"bool" sets nil )"bool" subset_algebra_def nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil finite_fubini_tonelli nil )nil defined_types nil )nil sets nil )"bool" subset_algebra_def nil )nil subset_algebra_def nil )"sigma_algebra[T1]" finite_fubini_tonellinil ))nil ))nil 3458551591"" (typepred "S2" )"" (expand "sigma_algebra?" )"" (expand "subset_algebra_empty?" )"" (flatten)"" (expand "member" ) (("" (propax) nil nil )) nil )) nil ))nil ))nil ))nil )"bool" sets nil )"bool" subset_algebra_def nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil finite_fubini_tonelli nil )nil defined_types nil )nil sets nil )"bool" subset_algebra_def nil )nil subset_algebra_def nil )"sigma_algebra[T2]" finite_fubini_tonellinil ))nil ))nil 3458552933"" (skosimp)"" (split)"1" (flatten)"1" (typepred "h!1" )"1" (expand "nn_measurable?" )"1" (flatten)"1" "nn_integrable_is_nn_integrable" ("f" "h!1" ))"1" (split)"1" (hide -4)"1" (lemma "nn_integral_def" ("f" "h!1" ))"1" (skolem - "HH" )"1" (flatten)"1" (typepred "HH" )"1" (case "FORALL (n: nat): isf?(HH(n))" )"1" case "FORALL (n: nat,z:[T1,T2]): HH(n)(z)>=0" )"1" "FF" "lambda (n:nat): lambda (x:T1): isf_integral(lambda (y:T2): HH(n)(x,y))" )"1" case "FORALL (n: nat): integrable?[T1, S1, to_measure(mu)](FF(n))" )"1" case "forall (n:nat): integral[T1,S1,to_measure(mu)](FF(n))=integral[[T1,T2],sigma_times(S1,S2),to_measure(fm_times(mu,nu))](HH(n))" )"1" "(isf_integral o HH)=integral o FF" )"1" case "forall (n:nat,x:T1): FF(n)(x)>=0" )"1" case "pointwise_increasing?(FF)" )"1" case "bounded?(integral o FF)" )"1" "monotone_convergence[T1, S1, to_measure(mu)]" "F" "FF" ))"1" "1" "1" "1" "1" "F" )"1" "F" )"1" assert )"1" "F" )"1" expand "integrable1?" )"1" expand "ae_convergence?" )"1" expand "fullset" )"1" expand "ae_convergence_in?" )"1" expand "ae_in?" )"1" "1" expand "member" )"1" "E!1" )"1" expand "negligible_set?" )"1" "N1" )"1" "1" "N1" "F" )"1" "1" expand "subset?" )"1" "x!1" )"1" expand "member" )"1" "x!1" )"1" assert )"1" "monotone_convergence_scaf[T2,S2,to_measure(nu)]" "f" "LAMBDA (y: T2): h!1(x!1, y)" "F" "lambda (n:nat): lambda (y:T2): HH(n)(x!1,y)" ))"1" "1" "1" replace "1" "LHS" "integral(LAMBDA (y: T2): h!1(x!1, y))" )"1" "(integral o LAMBDA (n: nat): LAMBDA (y: T2): HH(n)(x!1, y)))=LAMBDA (n:nat): FF(n)(x!1)") "1" expand "converges_upto?" )"1" "1" "1" "hausdorff_convergence.unique_limit" "u" "LAMBDA (n: nat): FF(n)(x!1)" "l1" "LHS" "l2" "F(x!1)" ))"1" assert )nil nil ))nil ))nil ))nil ))nil )"2" "1" expand "FF" "1" expand "o" "1" "x!2" )"1" "isf_x_section" "x" "x!1" "i" "HH(x!2)" ))"1" rewrite "isf_integral" nil nil ))nil ))nil ))nil ))nil )"2" "2" "n!1" )"2" "isf_x_section" "x" "x!1" "i" "HH(n!1)" ))"2" "isf_is_integrable[T2, S2, to_measure(nu)]" )"2" "LAMBDA (y: T2): HH(n!1)(x!1, y)" )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" "2" expand "increasing_nn_isf?" )"2" expand "pointwise_converges_upto?" )"2" "1" expand "pointwise_convergence?" )"1" "y!1" )"1" "(x!1,y!1)" )nil nil ))nil ))nil )"2" expand "pointwise_increasing?" )"2" "y!1" )"2" "(x!1,y!1)" )nil nil ))nil ))nil ))nil ))nil ))nil ))nil )"3" replace "3" "3" expand "FF" )"3" expand "o " )"3" expand "pointwise_increasing?" )"3" "x!1" )"3" "3" expand "bounded?" )"3" "1" expand "bounded_above?" )"1" "F(x!1)" )"1" "n!1" )"1" "n!1" )"1" "isf_x_section" "i" "HH(n!1)" "x" "x!1" ))"1" rewrite "isf_integral" )"1" rewrite "metric_convergence_def" )"1" expand "metric_converges_to" )"1" "isf_integral(LAMBDA (y: T2): HH(n!1)(x!1, y))-F(x!1)" )"1" "1" "n!1+n!2" )"1" assert )"1" expand "ball" )"1" expand "increasing?" )"1" "n!1" "n!1+n!2" )"1" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" assert )nil nil ))nil ))nil )"2" "2" rewrite "isf_x_section" )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" expand "bounded_below?" )"2" "0" )"2" "n!1" )"2" "n!1" )"2" "isf_x_section" "i" "HH(n!1)" "x" "x!1" ))"2" rewrite "isf_integral" "2" "n!1" "x!1" )"2" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" "2" "n!1" )"2" "isf_x_section" "i" "HH(n!1)" "x" "x!1" ))"2" "isf_is_integrable[T2, S2, to_measure(nu)]" )"2" "LAMBDA (y: T2): HH(n!1)(x!1, y)" )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" "2" expand "bounded?" )"2" "2" "1" expand "bounded_above?" )"1" "c!1" )"1" "n!1" )"1" "n!1" )"1" assert )nil nil ))nil ))nil ))nil ))nil )"2" expand "bounded_below?" )"2" "-c!1" )"2" "n!1" )"2" "n!1" )"2" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" "2" expand "ae_increasing?" )"2" "emptyset" )"2" "2" expand "pointwise_increasing?" )"2" "x!1" )"2" expand "increasing?" )"2" quality 98%
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2026-03-28
