Quelle harmonic_polynomials.prf
Sprache: Lisp
(harmonic_polynomialsnil 3261618989 3276290504"" (skosimp*)"" (lemma "even_div2" ("i" "i!1" ))"" (rewrite "even_or_odd" ) (("" (assert ) nil nil )) nil )) nil ))nil )nil naturalnumbers nil )"bool" reals nil )nil booleans nil )nil integers nil )"[rational -> boolean]" integers nil )nil rationals nil )"[real -> boolean]" rationals nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )nil prelude_aux "../reals/" )nil naturalnumbers nil ))nil 3261619116 3261619125"" (grind) nil nil ) proved-completenil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil numbers nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"bool" reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )nil naturalnumbers nil )"bool" reals nil )nil integers nil )nil integers nil )"bool" integers nil )"boolean" notequal nil ))nil 3261619130 3261619134"" (grind) nil nil ) proved-complete"bool" integers nil )"boolean" notequal nil ))nil 3261619140 3261619145"" (grind) nil nil ) proved-completenil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil numbers nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"bool" reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )nil naturalnumbers nil )"bool" reals nil )nil integers nil )nil integers nil )"bool" integers nil )"boolean" notequal nil ))nil 3261619149 3261619153"" (grind) nil nil ) proved-completenil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil numbers nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"bool" reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )nil naturalnumbers nil )"bool" reals nil )nil integers nil )nil integers nil )"bool" integers nil )"boolean" notequal nil ))nil 3261619159 3261619167"" (grind) nil nil ) proved-complete"bool" integers nil )"boolean" notequal nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil numbers nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"bool" reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )nil naturalnumbers nil )nil integers nil ))nil 3261620027 3261620031"" (grind) nil nil ) proved-completenil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil numbers nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"bool" reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )nil naturalnumbers nil )nil integers nil ))nil 3261619175 3276290540"" (skosimp*)"" (lemma "odd_div2" ("i" "i!1" ))"" (rewrite "even_or_odd" ) (("" (assert ) nil nil )) nil )) nil ))nil )nil naturalnumbers nil )"bool" reals nil )nil booleans nil )nil integers nil )"[rational -> boolean]" integers nil )nil rationals nil )"[real -> boolean]" rationals nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )nil prelude_aux "../reals/" )nil naturalnumbers nil ))nil 3261619184 3261619188"" (grind) nil nil ) proved-completenil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil numbers nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"bool" reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )nil naturalnumbers nil )"bool" reals nil )nil integers nil )nil integers nil )"bool" integers nil )"boolean" notequal nil ))nil 3261619194 3261619199"" (grind) nil nil ) proved-completenil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil numbers nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"bool" reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )nil naturalnumbers nil )"bool" reals nil )nil integers nil )nil integers nil )"bool" integers nil )"boolean" notequal nil ))nil 3261619204 3261619209"" (grind) nil nil ) proved-completenil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil numbers nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"bool" reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )nil naturalnumbers nil )"bool" reals nil )nil integers nil )nil integers nil )"bool" integers nil )"boolean" notequal nil ))nil 3261620046 3261620052"" (grind) nil nil ) proved-complete"bool" integers nil )"boolean" notequal nil ))nil 3261619224 3261625898"" (skolem 1 ("x" "y" ))"" (expand "harmonic_poly_real" )"" (expand "sigma" )"" (expand "sigma" )"" (rewrite "expt_x0" )"" (rewrite "expt_x1" )"" (rewrite "C_0" )"" (case "odd?(0)" )"1" (expand "odd?" ) (("1" (propax) nil nil )) nil )"2" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"real" harmonic_polynomials nil )nil exponentiation nil )"bool" integers nil )nil naturalnumbers nil )"bool" reals nil )nil booleans nil )nil integers nil )"[rational -> boolean]" integers nil )nil rationals nil )"[real -> boolean]" rationals nil )nil binomial nil )"[numfield -> numfield]" number_fields nil )nil number_fields nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )nil exponentiation nil )"real" sigma "../reals/" ))nil 3261619351 3261625899"" (skolem 1 ("x" "y" ))"" (expand "harmonic_poly_imag" )"" (expand "sigma" )"" (expand "sigma" )"" (rewrite "expt_x1" )"" (rewrite "expt_x0" )"" (rewrite "C_n" )"" (case "even?(1)" )"1" (expand "even?" ) (("1" (propax) nil nil )) nil )"2" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"real" harmonic_polynomials nil )nil exponentiation nil )nil number_fields nil )"[numfield -> numfield]" number_fields nil )"bool" integers nil )nil naturalnumbers nil )"bool" reals nil )nil booleans nil )nil integers nil )"[rational -> boolean]" integers nil )nil rationals nil )"[real -> boolean]" rationals nil )nil binomial nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )nil exponentiation nil )"real" sigma "../reals/" ))nil 3261620367 3261625909"" (skolem 1 ("n" "x" "y" ))"" (expand "harmonic_poly_real" )"" (expand "harmonic_poly_imag" )"" "F1" "LAMBDA (i: nat): IF i > 1 + n OR odd?(i) THEN 0IF i = 0 THEN x ^ (1 + n)") "1" (replace -1)"1" "sigma_scal[nat]" "low" "0" "high" "n" "a" "x" "F" " LAMBDA (i: nat): IF i > n OR odd?(i) THEN 0IF i = 0 THEN x ^ n")) "1" (replace -1 1 rl)"1" (hide -1)"1" "F2" "LAMBDA (i_1: nat): LAMBDA (i: nat):IF i > n OR odd?(i) THEN 0IF i = 0 THEN x ^ n") "1" (replace -1)"1" "F3" "LAMBDA (i: nat): IF i > n OR even?(i) THEN 0IF i = n THEN y ^ n ELSE x ^ (n - i) * y ^ i ENDIF)") "1" (replace -1)"1" "sigma_scal[nat]" "low" "0" "high" "n" "F" "F3" "a" "y" ))"1" (replace -1 1 rl)"1" case "sigma(0, n, F2) = sigma(0, n+1, F2)" )"1" replace -1 1)"1" case "FORALL (n:nat): sigma(0, n, LAMBDA (i: nat): y * F3(i)) = sigma(0,n+1, LAMBDA (i:nat): IF i = 0 THEN 0 ELSE y*F3(i-1) ENDIF)" )"1" "n" )"1" replace -1 1)"1" "sigma_minus[nat]" "low" "0" "high" "n+1" "F" "F2" "G" "LAMBDA (i: nat): IF i = 0 THEN 0 ELSE y * F3(i - 1) ENDIF" ))"1" replace -1 1)"1" "1" "sigma_eq[nat]" "low" "0" "high" "n+1" "F" "F1" "G" "LAMBDA (i_1: nat): LAMBDA (i: nat): IF i = 0 THEN 0 ELSE y * F3(i - 1) ENDIF)")) "1" "1" assert )nil nil )"2" "2" "2" "n!1" )"2" expand "F1" )"2" "2" expand "F2" )"2" expand "F3" )"2" case "n!1=0" )"1" replace "1" rewrite "C_0" )"1" rewrite "C_0" )"1" rewrite "expt_x0" )"1" case "odd?(0)" )"1" expand "odd?" )"1" nil nil ))nil )"2" assert )"2" expand "^" )"2" expand "expt" "2" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" assert )"2" case "n!1= 1+n" )"1" assert )"1" replace "1" rewrite "C_n" )"1" rewrite "C_n" )"1" case "even?(n)" )"1" case "odd?(n+1)" )"1" assert )nil nil )"2" "2" expand "even?" )"2" "2" replace "2" expand "odd?" )"2" "j!1" )nil nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" assert )"2" case "NOT (odd?(1+n))" )"1" assert )"1" rewrite "even_or_odd" )"1" "1" expand "odd?" )"1" "1" replace "1" "div_cancel1" "x" "j!1" "n0z" "2" ))"1" replace "1" "div_cancel1" "x" "j!1+1" "n0z" "2" ))"1" replace "1" replace "1" replace "1" "n" )"1" expand "^" "1" assert )"1" expand "expt" "1" expand "expt" "1" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" "2" expand "odd?" )"2" "2" replace "2" expand "even?" )"2" "j!1" )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" assert )"2" case "odd?(n!1)" )"1" case "even?(n!1-1)" )"1" assert )nil nil )"2" "2" expand "odd?" )"2" "2" replace "2" expand "even?" )"2" "j!1" )nil nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" case "NOT (even?(n!1-1))" )"1" assert )"1" rewrite "even_or_odd" )"1" "1" expand "odd?" )"1" "1" "div_cancel1" "x" "1+j!1" "n0z" "2" ))"1" "div_cancel1" "x" "j!1" "n0z" "2" ))"1" case "(n!1 - 2) / 2 = j!1" )"1" replace "1" case "(n!1) / 2 = j!1+1" )"1" replace "1" case "n!1=n" )"1" replace "1" rewrite "C_n" )"1" rewrite "C_n_1" )"1" rewrite "C_n_1" )"1" "expt_plus" "n0x" "-1" "i" "1" "j" "j!1" ))"1" rewrite "expt_x1" "1" replace "1" "K1" "(-1)^j!1" )"1" rewrite "expt_x1" "1" expand "^" "1" expand "expt" "1" expand "expt" "1" expand "expt" "1" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" assert )"2" "C_n_plus_1" "n" "n" "k" "n!1" ))"2" replace "2" "expt_plus" "n0x" "-1" "i" "1" "j" "j!1" ))"2" rewrite "expt_x1" "2" replace "2" "K10" "(-1)^j!1" )"2" "K11" "C(n,n!1-1)" )"2" "K12" "C(n,n!1)" )"2" expand "^" "2" expand "expt" "2" expand "expt" "2" expand "expt" "2" expand "expt" "2" expand "expt" "2" expand "expt" "2" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" "2" nil nil ))nil ))nil ))nil )"2" "2" nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" "2" expand "even?" )"2" "2" expand "odd?" )"2" "j!1" )"2" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" "2" nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" "2" "n" )"1" expand "sigma" )"1" expand "sigma" )"1" (propax) nil nil ))nil ))nil )"2" "i" ))"2" "2" expand "sigma" 1)"2" (assert ) nil nil ))nil ))nil ))nil )"3" "3" (grind) nil nil ))nil )"4" "4" (grind) nil nil ))nil ))nil ))nil )"3" "3" (grind) nil nil ))nil ))nil ))nil )"2" "2" expand "sigma" 1 2)"2" expand "F2" 1)"2" (propax) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (hide-all-but 1) (("2" (grind) nil nil ))nil )"3" (hide-all-but 1)"3" (skosimp*)"3" (rewrite "even_or_odd" )"3" expand "odd?" )"3" "3" "div_cancel1" "x" "j!1" "n0z" "2" ))"3" replace -2 2)"3" replace -1 2)"3" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"4" (hide-all-but 1) (("4" (grind) nil nil ))nil ))nil ))nil )"2" (hide-all-but 1) (("2" (grind) nil nil )) nil )"3" (hide-all-but 1)"3" (skosimp*)"3" (case "even?(i!1)" )"1" (expand "even?" )"1" (skosimp*)"1" "div_cancel1" "x" "j!1" "n0z" "2" ))"1" replace -2)"1" replace -1)"1" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil )"2" (rewrite "even_or_odd" ) nil nil ))nil ))nil ))nil )"4" (hide-all-but 1) (("4" (grind) nil nil ))nil ))nil ))nil ))nil )"2" (hide-all-but 1) (("2" (grind) nil nil )) nil )"3" (hide-all-but 1)"3" (skosimp*)"3" (case "even?(i!1)" )"1" (expand "even?" )"1" (skosimp*)"1" (replace -1)"1" "div_cancel1" ("x" "j!1" "n0z" "2" ))"1" (replace -1) (("1" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil )"2" (rewrite "even_or_odd" ) nil nil ))nil ))nil ))nil )"4" (hide-all-but 1) (("4" (grind) nil nil )) nil )"5" (hide-all-but 1) (("5" (grind) nil nil )) nil ))nil ))nil )"2" (hide 2) (("2" (grind) nil nil )) nil )"3" (hide 2)"3" (skosimp*)"3" (case "even?(i!1)" )"1" (expand "even?" )"1" (skosimp*)"1" (lemma "div_cancel1" ("x" "j!1" "n0z" "2" ))"1" (replace -2)"1" (replace -1) (("1" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil )"2" (rewrite "even_or_odd" ) nil nil ))nil ))nil ))nil )"4" (hide 2) (("4" (grind) nil nil )) nil ))nil ))nil ))nil ))nil )"real" harmonic_polynomials nil )"[numfield, numfield -> numfield]" number_fields nil )"[numfield, nznum -> numfield]" number_fields nil )nil number_fields nil )"[numfield -> numfield]" number_fields nil )"real" exponentiation nil )"boolean" notequal nil )"posnat" binomial nil )"bool" reals nil )"[numfield, numfield -> numfield]" number_fields nil )"bool" integers nil )nil integers nil )nil integers nil )"[numfield, numfield -> numfield]" number_fields nil )"bool" reals nil )OR const-decl "[bool, bool -> bool]" booleans nil )IF const-decl "[boolean, T, T -> T]" if_def nil )"[T, T -> boolean]" equalities nil )nil number_fields nil )nil naturalnumbers nil )"bool" reals nil )nil booleans nil )nil integers nil )"[rational -> boolean]" integers nil )nil rationals nil )"[real -> boolean]" rationals nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )NOT const-decl "[bool -> bool]" booleans nil )AND const-decl "[bool, bool -> bool]" booleans nil )"[bool, bool -> bool]" booleans nil )nil sigma "../reals/" )nil integers nil )nil naturalnumbers nil )nil defined_types nil )nil sigma "../reals/" ) nil nil nil binomial nil )nil exponentiation nil )"real" exponentiation nil )nil real_props nil )nil reals nil )nil naturalnumbers nil )nil binomial nil )nil binomial nil )nil binomial nil )nil exponentiation nil )nil reals nil )nil rationals nil )nil exponentiation nil ) nil nil integers nil )nil sigma "../reals/" )"real" sigma "../reals/" )"bool" integers nil )"real" harmonic_polynomials nil ))nil 3261625972 3261628417"" (skolem 1 ("n" "x" "y" ))"" (expand "harmonic_poly_imag" )"" (expand "harmonic_poly_real" )"" "F1" "LAMBDA (i: nat): IF i > n OR odd?(i) THEN 0IF i = 0 THEN x ^ n") "1" "F2" "LAMBDA (i: nat): IF i > n OR even?(i) THEN 0IF i = n THEN y ^ n ELSE x ^ (n - i) * y ^ i ENDIF)") "1" "F3" "LAMBDA (i: nat): IF i > 1 + n OR even?(i) THEN 0IF i = 1 + n THEN y ^ (1 + n)") "1" "sigma_scal" "low" "0" "high" "n" "a" "x" "F" "F2" ))"1" (replace -1 1 rl)"1" "sigma_scal" "low" "0" "high" "n" "a" "y" "F" "F1" ))"1" (replace -1 1 rl)"1" (hide -1 -2)"1" case "FORALL (n:nat): sigma(0, n, LAMBDA (i: nat): y * F1(i)) = sigma(0,n+1, LAMBDA (i:nat): IF i=0 THEN 0 ELSE y*F1(i-1) ENDIF)" )"1" (inst - "n" )"1" (replace -1)"1" case "sigma(0, n, LAMBDA (i: nat): x * F2(i)) = sigma(0, n+1 LAMBDA (i: nat): x * F2(i))") "1" replace -1 1)"1" "sigma_sum" "low" "0" "high" "1+n" "F" "LAMBDA (i: nat): x * F2(i)" "G" "LAMBDA (i: nat): IF i = 0 THEN 0 ELSE y * F1(i - 1) ENDIF" ))"1" replace -1 1)"1" "1" "sigma_eq[nat]" "low" "0" "high" "1+n" "F" "F3" "G" "LAMBDA (i_1: nat): LAMBDA (i: nat): x * F2(i))(i_1) +LAMBDA (i: nat): IF i = 0 THEN 0 ELSE y * F1(i - 1) ENDIF)")) "1" "1" (propax) nil nil )"2" "2" "i" ))"2" "i" )"2" expand "F3" )"2" expand "F2" )"2" expand "F1" )"2" case "even?(i)" )"1" case "odd?(i-1)" )"1" assert )nil nil )"2" "2" expand "even?" )"2" "2" replace "2" expand "odd?" )"2" "j!1-1" )"2" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" case "NOT (odd?(i-1))" )"1" assert )"1" "1" case "i= 1+n" )"1" replace "1" assert )"1" rewrite "C_n" )"1" rewrite "C_n" )"1" expand "^" "1" expand "^" "1" expand "expt" "1" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" assert )"2" case "i=0" )"1" replace "1" expand "even?" )"1" "0" )"1" assert )nil nil ))nil ))nil ))nil )"2" case "i=1" )"1" replace "1" assert )"1" rewrite "expt_x0" )"1" rewrite "expt_x1" )"1" rewrite "C_0" )"1" rewrite "C_1" )"1" rewrite "C_1" )"1" case "n=1" )"1" replace "1" rewrite "expt_x1" )"1" rewrite "expt_x1" )"1" assert )nil nil ))nil ))nil ))nil )"2" assert )"2" expand "^" "2" expand "expt" "2" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" assert )"2" "C_n_plus_1" "n" "n" "k" "i" ))"2" replace "2" expand "^" "2" expand "^" "2" expand "^" "2" expand "^" "2" expand "^" "2" expand "^" "2" expand "expt" "2" expand "^" "2" expand "^" "2" case "i=n" )"1" replace "1" assert )"1" expand "expt" "1" expand "expt" "1" expand "expt" "1" assert )nil nil ))nil ))nil ))nil ))nil ))nil )"2" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" "2" expand "odd?" )"2" "2" expand "even?" )"2" "1+j!1" )"2" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" "2" (grind) nil nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" "2" expand "sigma" 1 2)"2" expand "F2" )"2" (propax) nil nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (hide 2)"2" (induct "n" )"1" (grind) nil nil )"2" "j" ))"2" "2" expand "sigma" 1)"2" (assert ) nil nil ))nil ))nil ))nil )"3" "3" (grind) nil nil ))nil )"4" "4" (grind) nil nil ))nil ))nil ))nil )"3" (hide 2) (("3" (grind) nil nil )) nil )"4" (hide 2) (("4" (grind) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (hide 2) (("2" (grind) nil nil )) nil )"3" (hide 2)"3" (skosimp*)"3" (rewrite "even_or_odd" )"3" (expand "odd?" )"3" (skosimp*)"3" (replace -1 2)"3" "div_cancel1" ("x" "j!1" "n0z" "2" ))"3" (replace -1) (("3" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"4" (hide 2) (("4" (grind) nil nil )) nil ))nil )"2" (hide 2) (("2" (grind) nil nil )) nil )"3" (hide 2)"3" (skosimp*)"3" (rewrite "even_or_odd" )"3" (expand "odd?" )"3" (skosimp*)"3" (replace -1)"3" "div_cancel1" ("x" "j!1" "n0z" "2" ))"3" (replace -1) (("3" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"4" (hide 2) (("4" (grind) nil nil )) nil ))nil )"2" (hide 2) (("2" (grind) nil nil )) nil )"3" (hide 2)"3" (skosimp*)"3" (case "even?(i!1)" )"1" (expand "even?" )"1" (skosimp*)"1" (replace -1)"1" (lemma "div_cancel1" ("x" "j!1" "n0z" "2" ))"1" (replace -1) (("1" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil )"2" (rewrite "even_or_odd" ) nil nil ))nil ))nil ))nil )"4" (hide 2) (("4" (grind) nil nil )) nil ))nil ))nil ))nil ))nil )"real" harmonic_polynomials nil )"[bool, bool -> bool]" booleans nil )AND const-decl "[bool, bool -> bool]" booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil numbers nil )nil booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )nil booleans nil )"bool" reals nil )nil naturalnumbers nil )nil number_fields nil )"[T, T -> boolean]" equalities nil )IF const-decl "[boolean, T, T -> T]" if_def nil )OR const-decl "[bool, bool -> bool]" booleans nil )"bool" reals nil )nil integers nil )nil integers nil )"bool" integers nil )"[numfield, numfield -> numfield]" number_fields nil )"bool" reals nil )"posnat" binomial nil )"boolean" notequal nil )"real" exponentiation nil )"[numfield -> numfield]" number_fields nil )nil number_fields nil )"[numfield, nznum -> numfield]" number_fields nil )"[numfield, numfield -> numfield]" number_fields nil )"[numfield, numfield -> numfield]" number_fields nil )"real" sigma "../reals/" )nil integers nil )nil sigma "../reals/" )nil integers nil ) nil "real" exponentiation nil )nil binomial nil )nil binomial nil )nil exponentiation nil )nil binomial nil )nil binomial nil )nil exponentiation nil ) nil nil nil sigma "../reals/" )nil defined_types nil )nil naturalnumbers nil )nil sigma "../reals/" )nil reals nil )nil real_props nil )nil naturalnumbers nil )"bool" integers nil )"real" harmonic_polynomials nil ))nil 3261625909 3261625944"" (grind) nil nil ) proved-complete"nonneg_real" sq "../reals/" )) 3629 210 t shostak))nil 3261625059 3261625911"" (skolem 1 ("_" "x" "y" ))"" (induct "pn" )"1" (assert ) nil nil ) ("2" (assert ) nil nil )"3" (skolem 1 ("i" ))"3" (flatten)"3" (case "i=0" )"1" (replace -1)"1" (hide -1 -2 -3)"1" (rewrite "harmonic_polynomial_real_n1" )"1" (rewrite "harmonic_polynomial_imag_n1" )"1" (rewrite "expt_x1" ) nil nil )) nil ))nil ))nil ))nil )"2" (assert )"2" (hide -2 1)"2" (rewrite "harmonic_polynomial_real_rec" 1)"2" (rewrite "harmonic_polynomial_imag_rec" 1)"2" "U" "harmonic_poly_real(i, x, y)" )"2" "V" "harmonic_poly_imag(i, x, y)" )"2" (expand "sq" )"2" (case "x=0" )"1" (replace -1)"1" case "y=0" )"1" replace -1)"1" expand "^" 1)"1" expand "expt" )"1" (assert ) nil nil ))nil ))nil ))nil )"2" "sq_nz_pos" ("nz" "y" ))"1" expand "sq" )"1" "expt_plus" "n0x" "y*y" "i" "1" "j" "i" ))"1" rewrite "expt_x1" -1)"1" replace -1 2)"1" (assert ) nil nil ))nil ))nil )"2" (assert ) nil nil ))nil ))nil )"2" (assert ) nil nil ))nil ))nil ))nil )"2" (lemma "sq_pos" ("a" "y" ))"2" "sq_nz_pos" ("nz" "x" ))"1" expand "sq" )"1" "expt_plus" "n0x" "x*x+y*y" "i" "1" "j" "i" ))"1" rewrite "expt_x1" -1)"1" replace -1 2)"1" replace -4 2 rl)"1" (assert ) nil nil ))nil ))nil ))nil )"2" (assert ) nil nil ))nil ))nil )"2" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )nil numbers nil )nil booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )nil booleans nil )"bool" reals nil )nil naturalnumbers nil )nil defined_types nil )"[bool, bool -> bool]" booleans nil )"bool" reals nil )"[T, T -> boolean]" equalities nil )nil number_fields nil )"[numfield, numfield -> numfield]" number_fields nil )nil real_types nil )"nonneg_real" sq "../reals/" )nil integers nil )nil integers nil )"real" harmonic_polynomials nil )"real" harmonic_polynomials nil )OR const-decl "[bool, bool -> bool]" booleans nil )"boolean" notequal nil )"real" exponentiation nil )nil naturalnumbers nil )AND const-decl "[bool, bool -> bool]" booleans nil )"[numfield, numfield -> numfield]" number_fields nil )nil harmonic_polynomialsnil )nil sq "../reals/" )nil sq "../reals/" )nil reals nil )nil exponentiation nil )"[numfield, numfield -> numfield]" number_fields nil )"real" exponentiation nil )nil harmonic_polynomialsnil )nil harmonic_polynomialsnil )nil exponentiation nil )nil harmonic_polynomialsnil ))
Messung V0.5 in Prozent C=100 H=100 G=100
¤ Dauer der Verarbeitung: 0.97 Sekunden
(vorverarbeitet am 2026-05-01)
¤ *© Formatika GbR, Deutschland
2026-05-26
