|
(double_nn_sequence
(nn_series_increasing 0
(nn_series_increasing-1 nil 3408339793
("" (expand "increasing?")
(("" (expand "series")
(("" (skosimp*)
((""
(lemma "sigma_split"
("low" "0" "high" "y!1" "z" "x!1" "F" "v!1"))
(("" (assert)
((""
(lemma "sigma_ge_0"
("low" "x!1+1" "high" "y!1" "F" "v!1"))
(("" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
((series const-decl "sequence[real]" series "series/")
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans 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)
(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)
(T_low type-eq-decl nil sigma "reals/")
(T_high type-eq-decl nil sigma "reals/")
(<= const-decl "bool" reals nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(nnreal type-eq-decl nil real_types nil)
(sigma_split formula-decl nil sigma "reals/")
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(sigma_ge_0 formula-decl nil sigma "reals/")
(numfield nonempty-type-eq-decl nil number_fields nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(sigma_nnreal application-judgement "nnreal" sigma_nat "reals/")
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(even_minus_odd_is_odd application-judgement "odd_int" integers
nil)
(increasing? const-decl "bool" real_fun_preds "reals/"))
shostak))
(nn_index_scaf1_TCC1 0
(nn_index_scaf1_TCC1-1 nil 3408961994 ("" (subtype-tcc) nil nil) nil
nil))
(nn_index_scaf1_TCC2 0
(nn_index_scaf1_TCC2-1 nil 3408961994 ("" (subtype-tcc) nil nil)
((boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(NOT const-decl "[bool -> bool]" booleans 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)
(>= const-decl "bool" 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)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil))
nil))
(nn_index_scaf1 0
(nn_index_scaf1-1 nil 3408961995
("" (induct "n")
(("1" (skosimp)
(("1" (case-replace "double_index_n(0, 0)=0")
(("1" (expand "series")
(("1" (expand "sigma")
(("1" (expand "sigma")
(("1" (expand "single_index")
(("1" (lemma "double_index_ij_n" ("i" "0" "j" "0"))
(("1" (replace -2)
(("1" (flatten) (("1" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (hide 2)
(("2" (expand "double_index_n") (("2" (assert) nil nil))
nil))
nil))
nil))
nil)
("2" (skosimp*)
(("2" (expand "series")
(("2" (inst - "u!1")
(("2" (expand "sigma" 1 2)
(("2" (expand "sigma" 1 2)
(("2" (expand "sigma" 1 2)
(("2" (expand "sigma" 1 3)
(("2" (assert)
(("2"
(case "double_index_n(0, j!1))
(("1"
(lemma "sigma_split"
("low" "0" "high" "double_index_n(0, 1 + j!1)"
"z" "double_index_n(0, j!1)" "F"
"single_index(u!1)"))
(("1" (assert)
(("1" (replace -1)
(("1" (hide -1)
(("1"
(lemma
"sigma_sum"
("low"
"0"
"high"
"j!1"
"F"
"LAMBDA i:IF 0 > 1 - i + j!1 THEN 0
ELSE u!1(i, 1 - i + j!1)ENDIF"
"G"
"LAMBDA i: IF 0 > 1 - i + j!1 THEN 0
ELSE sigma(0, j!1 - i, LAMBDA j: u!1(i, j))ENDIF"))
(("1"
(assert)
(("1"
(case-replace
"(LAMBDA (i_1: nat):
IF 0 > 1 - i_1 + j!1 THEN 0
ELSE u!1(i_1, 1 - i_1 + j!1)
ENDIF
+
IF 0 > 1 - i_1 + j!1 THEN 0
ELSE sigma(0, j!1 - i_1, LAMBDA j: u!1(i_1, j))
ENDIF)=LAMBDA i:
IF 0 > 1 - i + j!1 THEN 0
ELSE u!1(i, 1 - i + j!1) +
sigma(0, j!1 - i, LAMBDA j: u!1(i, j))
ENDIF")
(("1"
(name-replace
"FF"
"LAMBDA i:
IF 0 > 1 - i + j!1 THEN 0
ELSE u!1(i, 1 - i + j!1) +
sigma(0, j!1 - i, LAMBDA j: u!1(i, j))
ENDIF")
(("1"
(replace -2 1 rl)
(("1"
(hide -1 -2)
(("1"
(case-replace
"sigma(0, j!1,
LAMBDA i:
IF 0 > 1 - i + j!1 THEN 0
ELSE sigma(0, j!1 - i, LAMBDA j: u!1(i, j))
ENDIF)=sigma(0, double_index_n(0, j!1), single_index(u!1))")
(("1"
(assert)
(("1"
(hide -1 -3)
(("1"
(case
"forall n: sigma(1 + double_index_n(0, n), double_index_n(0, 1 + n),
single_index(u!1))
=
u!1(1 + n, 0) +
sigma(0, n,
LAMBDA i:
IF 0 > 1 - i + n THEN 0 ELSE u!1(i, 1 - i + n) ENDIF)")
(("1"
(inst - "j!1")
nil
nil)
("2"
(hide -1 2)
(("2"
(case
" FORALL n: u!1(1 + n, 0) +
sigma(0, n,
LAMBDA i:
IF 0 > 1 - i + n THEN 0 ELSE u!1(i, 1 - i + n) ENDIF) = sigma(0,n+1, LAMBDA i:
IF 0 > 1 - i + n THEN 0 ELSE u!1(i,1-i+n)endif)")
(("1"
(case
"FORALL n:
sigma(1 + double_index_n(0, n), double_index_n(0, 1 + n),
single_index(u!1))
=sigma(0, n + 1,
LAMBDA i:
IF 0 > 1 - i + n THEN 0 ELSE u!1(i, 1 - i + n) ENDIF)")
(("1"
(skosimp)
(("1"
(inst
-
"n!1")
(("1"
(inst
-
"n!1")
(("1"
(assert)
nil
nil))
nil))
nil))
nil)
("2"
(hide -1 2)
(("2"
(case
"FORALL n:
sigma(1 + double_index_n(0, n), double_index_n(0, 1 + n),
single_index(u!1))
=sigma(0, n + 1,
LAMBDA i:
IF 0 > 1 - i + n THEN 0 ELSE u!1(n+1-i,i) endif)")
(("1"
(case
"FORALL n:sigma(0, n + 1,
LAMBDA i:
IF 0 > 1 - i + n THEN 0 ELSE u!1(n + 1 - i, i) ENDIF) =
sigma(0, n + 1,
LAMBDA i:
IF 0 > 1 - i + n THEN 0 ELSE u!1(i, 1 - i + n) ENDIF)")
(("1"
(skosimp)
(("1"
(inst
-
"n!1")
(("1"
(inst
-
"n!1")
(("1"
(assert)
nil
nil))
nil))
nil))
nil)
("2"
(hide
-1
2)
(("2"
(skosimp)
(("2"
(case
"forall j: j <= n!1+1 => sigma(0, j,
LAMBDA i:
IF 0 > 1 - i + n!1 THEN 0 ELSE u!1(n!1 + 1 - i, i) ENDIF)
=
sigma(n!1+1-j, n!1 + 1,
LAMBDA i:
IF 0 > 1 - i + n!1 THEN 0 ELSE u!1(i, 1 - i + n!1) ENDIF)")
(("1"
(inst
-
"n!1+1")
(("1"
(assert)
nil
nil))
nil)
("2"
(hide
2)
(("2"
(induct
"j")
(("1"
(expand
"sigma")
(("1"
(expand
"sigma")
(("1"
(propax)
nil
nil))
nil))
nil)
("2"
(skosimp*)
(("2"
(expand
"sigma"
1
1)
(("2"
(assert)
(("2"
(replace
-1
1)
(("2"
(hide
-1)
(("2"
(lemma
"sigma_first"
("low"
"n!1 - j!2"
"high"
"1 + n!1"
"F"
"LAMBDA i:
IF 0 > 1 - i + n!1 THEN 0 ELSE u!1(i, 1 - i + n!1) ENDIF"))
(("1"
(assert)
nil
nil)
("2"
(skosimp)
(("2"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("3"
(skosimp)
(("3"
(skosimp)
(("3"
(assert)
nil
nil))
nil))
nil)
("4"
(skosimp)
(("4"
(assert)
nil
nil))
nil)
("5"
(skosimp)
(("5"
(skosimp)
(("5"
(assert)
nil
nil))
nil))
nil))
nil))
nil)
("3"
(skosimp)
(("3"
(skosimp)
(("3"
(assert)
nil
nil))
nil))
nil)
("4"
(skosimp)
(("4"
(assert)
nil
nil))
nil)
("5"
(skosimp)
(("5"
(skosimp)
(("5"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil)
("3"
(skosimp)
(("3"
(assert)
nil
nil))
nil)
("4"
(skosimp)
(("4"
(assert)
nil
nil))
nil))
nil)
("2"
(hide 2)
(("2"
(skosimp)
(("2"
(case
"forall j: j <=n!1+1=>sigma(1 + double_index_n(0, n!1), 1+double_index_n(0, n!1)+j,
single_index(u!1))
=
sigma(0, j,
LAMBDA i:
IF 0 > 1 - i + n!1 THEN 0 ELSE u!1(n!1 + 1 - i, i) ENDIF)")
(("1"
(inst
-
"n!1+1")
(("1"
(assert)
(("1"
(case-replace
"double_index_n(0, 1 + n!1)=2 + double_index_n(0, n!1) + n!1")
(("1"
(assert)
(("1"
(hide
-1
2)
(("1"
(expand
"double_index_n")
(("1"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(hide
2)
(("2"
(induct
"j")
(("1"
(assert)
(("1"
(expand
"sigma")
(("1"
(assert)
(("1"
(expand
"sigma")
(("1"
(case-replace
"1 + double_index_n(0, n!1)=double_index_n(n!1+1,0)")
(("1"
(expand
"single_index")
(("1"
(lemma
"double_index_ij_n"
("i"
"1+n!1"
"j"
"0"))
(("1"
(flatten)
(("1"
(assert)
nil
nil))
nil))
nil))
nil)
("2"
(hide
2)
(("2"
(expand
"double_index_n")
(("2"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(skosimp*)
(("2"
(expand
"sigma"
1)
(("2"
(assert)
(("2"
(replace
-1)
(("2"
(hide
-1)
(("2"
(assert)
(("2"
(case-replace
"2 + double_index_n(0, n!1) + j!2=double_index_n(n!1-j!2,1+j!2)")
(("1"
(expand
"single_index")
(("1"
(lemma
"double_index_ij_n"
("i"
"n!1-j!2"
"j"
"1+j!2"))
(("1"
(flatten)
(("1"
(assert)
nil
nil))
nil))
nil))
nil)
("2"
(hide
2)
(("2"
(expand
"double_index_n")
(("2"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("3"
(skosimp)
(("3"
(skosimp)
(("3"
(assert)
nil
nil))
nil))
nil)
("4"
(skosimp)
(("4"
(assert)
nil
nil))
nil)
("5"
(skosimp)
(("5"
(assert)
nil
nil))
nil))
nil))
nil)
("3"
(skosimp)
(("3"
(skosimp)
(("3"
(assert)
nil
nil))
nil))
nil)
("4"
(skosimp)
(("4"
(assert)
nil
nil))
nil))
nil))
nil))
nil)
("3"
(skosimp)
(("3"
(assert)
nil
nil))
nil))
nil))
nil)
("3"
(skosimp)
(("3"
(assert)
nil
nil))
nil))
nil)
("2"
(hide 2)
(("2"
(skosimp)
(("2"
(lemma
"sigma_last"
("low"
"0"
"high"
"n!1+1"
"F"
"LAMBDA i:
IF 0 > 1 - i + n!1 THEN 0 ELSE u!1(i, 1 - i + n!1) ENDIF"))
(("1"
(assert)
nil
nil)
("2"
(skosimp)
(("2"
(assert)
nil
nil))
nil))
nil))
nil))
nil)
("3"
(skosimp)
(("3"
(assert)
nil
nil))
nil))
nil))
nil)
("3"
(skosimp)
(("3"
(assert)
nil
nil))
nil)
("4"
(skosimp)
(("4"
(assert)
nil
nil))
nil)
("5"
(skosimp)
(("5"
(assert)
nil
nil))
nil))
nil))
nil))
nil)
("2"
(hide 2)
(("2"
(replace -2)
(("2"
(hide -2)
(("2"
(lemma
"sigma_restrict_eq"
("low"
"0"
"high"
"j!1"
"F"
"LAMBDA i:
IF 0 > 1 - i + j!1 THEN 0
ELSE sigma(0, j!1 - i, LAMBDA j: u!1(i, j))
ENDIF"
"G"
"LAMBDA i: sigma(0, j!1 - i, LAMBDA j: u!1(i, j))"))
(("1"
(split -1)
(("1"
(propax)
nil
nil)
("2"
(hide 2)
(("2"
(expand
"restrict")
(("2"
(propax)
nil
nil))
nil))
nil))
nil)
("2"
(skosimp)
(("2"
(inst + "j!1")
(("2"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(hide -1 2)
(("2"
(apply-extensionality :hide? t)
(("1"
(case-replace
"0 > 1 - x!1 + j!1")
(("1" (assert) nil nil)
("2" (assert) nil nil))
nil)
("2"
(skosimp)
(("2"
(inst + "j!1")
(("2" (assert) nil nil))
nil))
nil)
("3"
(skosimp)
(("3" (assert) nil nil))
nil))
nil))
nil))
nil))
nil)
("2"
(skosimp)
(("2"
(inst + "j!1")
(("2" (assert) nil nil))
nil))
nil)
("3"
(skosimp)
(("3" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (hide-all-but 1)
(("2" (expand "double_index_n")
(("2" (rewrite "sq_rew")
(("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("3" (skosimp) (("3" (inst + "n!2") (("3" (assert) nil nil)) nil))
nil))
nil)
((< const-decl "bool" reals nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(even_minus_odd_is_odd application-judgement "odd_int" integers
nil)
(nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(even_plus_even_is_even application-judgement "even_int" integers
nil)
(j!1 skolem-const-decl "nat" double_nn_sequence nil)
(restrict const-decl "[T -> real]" sigma "reals/")
(sigma_restrict_eq formula-decl nil sigma "reals/")
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(posrat_plus_nnrat_is_posrat application-judgement "posrat"
rationals nil)
(posrat_div_posrat_is_posrat application-judgement "posrat"
rationals nil)
(nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
rationals nil)
(n!1 skolem-const-decl "nat" double_nn_sequence nil)
(real_minus_real_is_real application-judgement "real" reals nil)
(sigma_0_neg formula-decl nil sigma_nat "reals/")
(odd_minus_even_is_odd application-judgement "odd_int" integers
nil)
(even_minus_even_is_even application-judgement "even_int" integers
nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(sigma_first formula-decl nil sigma "reals/")
(n!1 skolem-const-decl "nat" double_nn_sequence nil)
(sigma_last formula-decl nil sigma "reals/")
(minus_odd_is_odd application-judgement "odd_int" integers nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(> const-decl "bool" reals nil)
(IF const-decl "[boolean, T, T -> T]" if_def nil)
(sigma_sum formula-decl nil sigma "reals/")
(int_plus_int_is_int application-judgement "int" integers nil)
(sigma_split formula-decl nil sigma "reals/")
(posreal_div_posreal_is_posreal application-judgement "posreal"
real_types nil)
(posreal_plus_nnreal_is_posreal application-judgement "posreal"
real_types nil)
(nnreal_div_posreal_is_nnreal application-judgement "nnreal"
real_types nil)
(sq_rew formula-decl nil sq "reals/")
(sigma_nnreal application-judgement "nnreal" sigma_nat "reals/")
(real_le_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)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(real_plus_real_is_real application-judgement "real" reals nil)
(double_index_ij_n formula-decl nil code_product nil)
(nat_induction formula-decl nil naturalnumbers nil)
(sigma def-decl "real" sigma "reals/")
(T_high type-eq-decl nil sigma "reals/")
(T_low type-eq-decl nil sigma "reals/")
(double_index_n const-decl "nat" code_product nil)
(single_index const-decl "[nat -> T]" double_index nil)
(series const-decl "sequence[real]" series "series/")
(sequence type-eq-decl nil sequences nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(nnreal type-eq-decl nil real_types nil)
(pred type-eq-decl nil defined_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)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(<= const-decl "bool" reals nil)
(int_minus_int_is_int application-judgement "int" integers nil))
shostak))
(nn_double_index_incr 0
(nn_double_index_incr-1 nil 3408979981
("" (skosimp)
(("" (expand "double_index_n") (("" (propax) nil nil)) nil)) nil)
((nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(double_index_n const-decl "nat" code_product nil))
shostak))
(nn_index_scaf2 0
(nn_index_scaf2-1 nil 3408975051
("" (skosimp)
(("" (rewrite "nn_index_scaf1")
((""
(lemma "sigma_split"
("low" "0" "high" "2*n!1" "z" "n!1" "F"
"LAMBDA i: sigma(0, 2 * n!1 - i, LAMBDA j: u!1(i, j))"))
(("1" (assert)
(("1" (replace -1)
(("1" (hide -1)
(("1"
(lemma "sigma_le"
("low" "0" "high" "n!1" "F"
"LAMBDA i: sigma(0, n!1, LAMBDA j: u!1(i, j))" "G"
"LAMBDA i: sigma(0, 2 * n!1 - i, LAMBDA j: u!1(i, j))"))
(("1" (split -1)
(("1"
(lemma "sigma_ge_0"
("low" "1+n!1" "high" "2*n!1" "F"
"LAMBDA i: sigma(0, 2 * n!1 - i, LAMBDA j: u!1(i, j))"))
(("1" (assert) nil nil)) nil)
("2" (hide 2)
(("2" (skosimp)
(("2" (typepred "n!2")
(("2"
(lemma "sigma_split"
("low" "0" "high" "2*n!1-n!2" "z" "n!1" "F"
"LAMBDA j: u!1(n!2, j)"))
(("2" (assert)
(("2" (replace -1)
(("2"
(hide -1)
(("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (skosimp) (("2" (assert) nil nil)) nil))
nil))
nil))
nil)
((nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(nn_index_scaf1 formula-decl nil double_nn_sequence 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)
(numfield nonempty-type-eq-decl nil number_fields nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(nnreal type-eq-decl nil real_types nil)
(real_le_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)
(int_minus_int_is_int application-judgement "int" integers nil)
(sigma_nnreal application-judgement "nnreal" sigma_nat "reals/")
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(even_minus_odd_is_odd application-judgement "odd_int" integers
nil)
(nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(sigma_ge_0 formula-decl nil sigma "reals/")
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(subrange type-eq-decl nil integers nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(sigma_le formula-decl nil sigma "reals/")
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(sigma def-decl "real" sigma "reals/")
(T_high type-eq-decl nil sigma "reals/")
(T_low type-eq-decl nil sigma "reals/")
(<= const-decl "bool" reals nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(sigma_split formula-decl nil sigma "reals/"))
shostak))
(nn_index_scaf3 0
(nn_index_scaf3-1 nil 3408981469
("" (skolem + ("i!1" "j!1" "u!1"))
(("" (lemma "nn_index_scaf2" ("u" "u!1" "n" "i!1+j!1"))
(("" (inst + "double_index_n(0, 2 * (i!1 + j!1))")
((""
(name-replace "RHS"
"series(single_index(u!1))(double_index_n(0, 2 * (i!1 + j!1)))")
((""
(lemma "sigma_split"
("low" "0" "high" "i!1+j!1" "z" "i!1" "F"
"LAMBDA i: sigma(0, i!1 + j!1, LAMBDA j: u!1(i, j))"))
(("" (assert)
(("" (replace -1)
(("" (hide -1)
((""
(lemma "sigma_ge_0"
("low" "1+i!1" "high" "i!1+j!1" "F"
"LAMBDA i: sigma(0, i!1 + j!1, LAMBDA j: u!1(i, j))"))
(("" (split -1)
(("1"
(name-replace "DRL1" "sigma(1 + i!1, i!1 + j!1,
LAMBDA i: sigma(0, i!1 + j!1, LAMBDA j: u!1(i, j)))")
(("1"
(lemma "sigma_sum"
("low" "0" "high" "i!1" "F"
"LAMBDA i: sigma(0, j!1, LAMBDA j: u!1(i, j))"
"G"
"LAMBDA i: sigma(j!1+1, i!1+j!1,LAMBDA j: u!1(i, j))"))
(("1" (assert)
(("1"
(case-replace "(LAMBDA (i_1: nat):
sigma(0, j!1, LAMBDA j: u!1(i_1, j)) +
sigma(1 + j!1, i!1 + j!1, LAMBDA j: u!1(i_1, j)))=LAMBDA i: sigma(0, i!1 + j!1, LAMBDA j: u!1(i, j))")
(("1"
(replace -2 -4 rl)
(("1" (assert) nil nil))
nil)
("2"
(apply-extensionality 1 :hide? t)
(("2"
(hide-all-but 1)
(("2"
(lemma
"sigma_split"
("low"
"0"
"high"
"i!1+j!1"
"z"
"j!1"
"F"
"LAMBDA j: u!1(x!1, j)"))
(("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (skosimp)
(("2" (hide-all-but 1)
(("2" (rewrite "sigma_ge_0") nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((nnreal type-eq-decl nil real_types nil)
--> --------------------
--> maximum size reached
--> --------------------
¤ Dauer der Verarbeitung: 0.121 Sekunden
(vorverarbeitet)
¤
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