|
(ellipsoid
(ellipsoid_TCC1 0
(ellipsoid_TCC1-1 nil 3504869522 ("" (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)
(>= const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(posnat nonempty-type-eq-decl nil integers nil)
(below type-eq-decl nil naturalnumbers nil)
(Matrix type-eq-decl nil matrices nil)
(square? const-decl "bool" matrices nil)
(Square type-eq-decl nil matrices nil)
(squareMat? const-decl "bool" matrices nil)
(SquareMat type-eq-decl nil matrices nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil))
nil))
(ellipsoid_TCC2 0
(ellipsoid_TCC2-1 nil 3504869522 ("" (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)
(>= const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(posnat nonempty-type-eq-decl nil integers nil)
(below type-eq-decl nil naturalnumbers nil)
(Matrix type-eq-decl nil matrices nil)
(square? const-decl "bool" matrices nil)
(Square type-eq-decl nil matrices nil)
(squareMat? const-decl "bool" matrices nil)
(SquareMat type-eq-decl nil matrices nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(T const-decl "[Mat(m, n) -> Map_linear(n, m)]" matrix_operator
nil)
(injective? const-decl "bool" functions nil)
(surjective? const-decl "bool" functions nil)
(bijective? const-decl "bool" functions nil)
(bijective? const-decl "bool" linear_map nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(real_times_real_is_real application-judgement "real" reals nil))
nil))
(ellipsoid_TCC3 0
(ellipsoid_TCC3-1 nil 3504869522 ("" (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)
(>= const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(posnat nonempty-type-eq-decl nil integers nil)
(below type-eq-decl nil naturalnumbers nil)
(Matrix type-eq-decl nil matrices nil)
(square? const-decl "bool" matrices nil)
(Square type-eq-decl nil matrices nil)
(squareMat? const-decl "bool" matrices nil)
(SquareMat type-eq-decl nil matrices nil)
(T const-decl "[Mat(m, n) -> Map_linear(n, m)]" matrix_operator
nil)
(injective? const-decl "bool" functions nil)
(surjective? const-decl "bool" functions nil)
(bijective? const-decl "bool" functions nil)
(bijective? const-decl "bool" linear_map nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(real_times_real_is_real application-judgement "real" reals nil))
nil))
(ellipsoid_TCC4 0
(ellipsoid_TCC4-1 nil 3508764162 ("" (subtype-tcc) nil nil)
((T const-decl "[Mat(m, n) -> Map_linear(n, m)]" matrix_operator
nil)
(injective? const-decl "bool" functions nil)
(surjective? const-decl "bool" functions nil)
(bijective? const-decl "bool" functions nil)
(bijective? const-decl "bool" linear_map nil)
(inverse const-decl "Maping" linear_map nil)
(inverse const-decl "D" function_inverse nil)
(L const-decl "[Map_linear(n, m) -> Mat(m, n)]" matrix_operator
nil)
(inv const-decl "[Matrix_inv(n) -> Matrix_inv(n)]" matrix_operator
nil)
(real_times_real_is_real application-judgement "real" reals nil)
(int_minus_int_is_int application-judgement "int" integers nil))
nil))
(ellipsoid_TCC5 0
(ellipsoid_TCC5-1 nil 3508764162 ("" (subtype-tcc) nil nil)
((T const-decl "[Mat(m, n) -> Map_linear(n, m)]" matrix_operator
nil)
(injective? const-decl "bool" functions nil)
(surjective? const-decl "bool" functions nil)
(bijective? const-decl "bool" functions nil)
(bijective? const-decl "bool" linear_map nil)
(inverse const-decl "Maping" linear_map nil)
(inverse const-decl "D" function_inverse nil)
(L const-decl "[Map_linear(n, m) -> Mat(m, n)]" matrix_operator
nil)
(inv const-decl "[Matrix_inv(n) -> Matrix_inv(n)]" matrix_operator
nil)
(real_times_real_is_real application-judgement "real" reals nil)
(int_minus_int_is_int application-judgement "int" integers nil))
nil))
(ellipsoid_TCC6 0
(ellipsoid_TCC6-1 nil 3508764162 ("" (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)
(>= const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(posnat nonempty-type-eq-decl nil integers nil)
(below type-eq-decl nil naturalnumbers nil)
(Matrix type-eq-decl nil matrices nil)
(square? const-decl "bool" matrices nil)
(Square type-eq-decl nil matrices nil)
(squareMat? const-decl "bool" matrices nil)
(SquareMat type-eq-decl nil matrices 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_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)
(Vector type-eq-decl nil vectors "vectors/")
(Index type-eq-decl nil vectors "vectors/")
(< const-decl "bool" reals nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(T const-decl "[Mat(m, n) -> Map_linear(n, m)]" matrix_operator
nil)
(inverse const-decl "Maping" linear_map nil)
(inverse const-decl "D" function_inverse nil)
(L const-decl "[Map_linear(n, m) -> Mat(m, n)]" matrix_operator
nil)
(inv const-decl "[Matrix_inv(n) -> Matrix_inv(n)]" matrix_operator
nil)
(- const-decl "real" vectors "vectors/")
(* const-decl "Vector[M`rows]" matrices nil)
(* const-decl "real" vectors "vectors/")
(injective? const-decl "bool" functions nil)
(surjective? const-decl "bool" functions nil)
(bijective? const-decl "bool" functions nil)
(bijective? const-decl "bool" linear_map nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(real_times_real_is_real application-judgement "real" reals nil)
(real_minus_real_is_real application-judgement "real" reals nil))
nil))
(ellipsoid_TCC7 0
(ellipsoid_TCC7-1 nil 3520826443 ("" (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)
(>= const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(posnat nonempty-type-eq-decl nil integers nil)
(below type-eq-decl nil naturalnumbers nil)
(Matrix type-eq-decl nil matrices nil)
(square? const-decl "bool" matrices nil)
(Square type-eq-decl nil matrices nil)
(squareMat? const-decl "bool" matrices nil)
(SquareMat type-eq-decl nil matrices 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_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)
(Vector type-eq-decl nil vectors "vectors/")
(Index type-eq-decl nil vectors "vectors/")
(< const-decl "bool" reals nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(T const-decl "[Mat(m, n) -> Map_linear(n, m)]" matrix_operator
nil)
(inverse const-decl "Maping" linear_map nil)
(inverse const-decl "D" function_inverse nil)
(L const-decl "[Map_linear(n, m) -> Mat(m, n)]" matrix_operator
nil)
(inv const-decl "[Matrix_inv(n) -> Matrix_inv(n)]" matrix_operator
nil)
(- const-decl "real" vectors "vectors/")
(* const-decl "Vector[M`rows]" matrices nil)
(* const-decl "real" vectors "vectors/")
(injective? const-decl "bool" functions nil)
(surjective? const-decl "bool" functions nil)
(bijective? const-decl "bool" functions nil)
(bijective? const-decl "bool" linear_map nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(real_times_real_is_real application-judgement "real" reals nil)
(real_minus_real_is_real application-judgement "real" reals nil))
nil))
(ellipsoid_TCC8 0
(ellipsoid_TCC8-1 nil 3520826443 ("" (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)
(>= const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(posnat nonempty-type-eq-decl nil integers nil)
(below type-eq-decl nil naturalnumbers nil)
(Matrix type-eq-decl nil matrices nil)
(square? const-decl "bool" matrices nil)
(Square type-eq-decl nil matrices nil)
(squareMat? const-decl "bool" matrices nil)
(SquareMat type-eq-decl nil matrices 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_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)
(Vector type-eq-decl nil vectors "vectors/")
(Index type-eq-decl nil vectors "vectors/")
(< const-decl "bool" reals nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(T const-decl "[Mat(m, n) -> Map_linear(n, m)]" matrix_operator
nil)
(inverse const-decl "Maping" linear_map nil)
(inverse const-decl "D" function_inverse nil)
(L const-decl "[Map_linear(n, m) -> Mat(m, n)]" matrix_operator
nil)
(inv const-decl "[Matrix_inv(n) -> Matrix_inv(n)]" matrix_operator
nil)
(- const-decl "real" vectors "vectors/")
(* const-decl "Vector[M`rows]" matrices nil)
(* const-decl "real" vectors "vectors/")
(injective? const-decl "bool" functions nil)
(surjective? const-decl "bool" functions nil)
(bijective? const-decl "bool" functions nil)
(bijective? const-decl "bool" linear_map nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(real_times_real_is_real application-judgement "real" reals nil)
(real_minus_real_is_real application-judgement "real" reals nil))
nil))
(ellipsoid_TCC9 0
(ellipsoid_TCC9-1 nil 3520826443 ("" (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)
(>= const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(posnat nonempty-type-eq-decl nil integers nil)
(below type-eq-decl nil naturalnumbers nil)
(Matrix type-eq-decl nil matrices nil)
(square? const-decl "bool" matrices nil)
(Square type-eq-decl nil matrices nil)
(squareMat? const-decl "bool" matrices nil)
(SquareMat type-eq-decl nil matrices 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_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(T const-decl "[Mat(m, n) -> Map_linear(n, m)]" matrix_operator
nil)
(injective? const-decl "bool" functions nil)
(surjective? const-decl "bool" functions nil)
(bijective? const-decl "bool" functions nil)
(bijective? const-decl "bool" linear_map nil)
(inverse const-decl "Maping" linear_map nil)
(inverse const-decl "D" function_inverse nil)
(L const-decl "[Map_linear(n, m) -> Mat(m, n)]" matrix_operator
nil)
(inv const-decl "[Matrix_inv(n) -> Matrix_inv(n)]" matrix_operator
nil)
(- const-decl "real" vectors "vectors/")
(* const-decl "Vector[M`rows]" matrices nil)
(* const-decl "real" vectors "vectors/")
(transpose const-decl "Matrix" matrices nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(real_times_real_is_real application-judgement "real" reals nil)
(real_minus_real_is_real application-judgement "real" reals nil))
nil))
(ellipsoid_TCC10 0
(ellipsoid_TCC10-1 nil 3520826443 ("" (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)
(>= const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(posnat nonempty-type-eq-decl nil integers nil)
(below type-eq-decl nil naturalnumbers nil)
(Matrix type-eq-decl nil matrices nil)
(square? const-decl "bool" matrices nil)
(Square type-eq-decl nil matrices nil)
(squareMat? const-decl "bool" matrices nil)
(SquareMat type-eq-decl nil matrices 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_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(T const-decl "[Mat(m, n) -> Map_linear(n, m)]" matrix_operator
nil)
(injective? const-decl "bool" functions nil)
(surjective? const-decl "bool" functions nil)
(bijective? const-decl "bool" functions nil)
(bijective? const-decl "bool" linear_map nil)
(inverse const-decl "Maping" linear_map nil)
(inverse const-decl "D" function_inverse nil)
(L const-decl "[Map_linear(n, m) -> Mat(m, n)]" matrix_operator
nil)
(inv const-decl "[Matrix_inv(n) -> Matrix_inv(n)]" matrix_operator
nil)
(- const-decl "real" vectors "vectors/")
(* const-decl "Vector[M`rows]" matrices nil)
(* const-decl "real" vectors "vectors/")
(transpose const-decl "Matrix" matrices nil)
(* const-decl "Matrix" matrices nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(real_times_real_is_real application-judgement "real" reals nil)
(real_minus_real_is_real application-judgement "real" reals nil))
nil))
(ellipsoid_TCC11 0
(tcc "tcc" 3520936757
("" (skosimp)
(("" (split)
(("1" (grind) nil nil)
("2" (expand "squareMat?")
(("2" (assert)
(("2" (typepred "M!1")
(("2" (typepred "Q!1")
(("2" (expand "squareMat?")
(("2" (assert) (("2" (grind) nil nil)) nil)) nil))
nil))
nil))
nil))
nil)
("3" (lemma "bijec_prod")
(("3" (inst?)
(("1" (assert)
(("1" (split)
(("1" (assert)
(("1" (typepred "Q!1")
(("1" (typepred "M!1")
(("1" (expand "square?")
(("1" (assert) (("1" (grind) nil nil)) nil))
nil))
nil))
nil))
nil)
("2" (typepred "Q!1")
(("2" (typepred "M!1")
(("2" (expand "square?") (("2" (grind) nil nil))
nil))
nil))
nil)
("3" (lemma "bijec_prod")
(("3" (inst?)
(("1" (assert)
(("1" (split)
(("1" (assert)
(("1" (hide 2 3)
(("1"
(typepred "M!1")
(("1" (grind) nil nil))
nil))
nil))
nil)
("2" (typepred "M!1")
(("2" (hide 2 3) (("2" (grind) nil nil))
nil))
nil)
("3" (lemma "bijec_transpose")
(("3" (inst?) (("3" (assert) nil nil))
nil))
nil))
nil))
nil)
("2" (typepred "M!1")
(("2" (hide 2 3) (("2" (grind) nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
("2" (typepred "Q!1")
(("2" (typepred "M!1")
(("2" (expand "square?")
(("2" (assert)
(("2" (hide 2) (("2" (grind) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((transpose const-decl "Matrix" matrices nil)
(* const-decl "Matrix" matrices nil)
(square? const-decl "bool" matrices nil)
(real_times_real_is_real application-judgement "real" reals
nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_plus_real_is_real application-judgement "real" reals nil)
(sigma def-decl "real" sigma "reals/")
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(posnat nonempty-type-eq-decl nil integers nil)
(below type-eq-decl nil naturalnumbers nil)
(real nonempty-type-from-decl nil reals nil)
(Matrix type-eq-decl nil matrices nil)
(Square type-eq-decl nil matrices 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)
(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)
(>= const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(SquareMat type-eq-decl nil matrices nil)
(squareMat? const-decl "bool" matrices nil)
(M!1 skolem-const-decl "SquareMat(n!1)" ellipsoid nil)
(Q!1 skolem-const-decl "SquareMat(n!1)" ellipsoid nil)
(n!1 skolem-const-decl "posnat" ellipsoid nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(bijec_transpose formula-decl nil matrix_operator nil)
(bijec_prod formula-decl nil matrix_operator nil))
shostak)
(ellipsoid_TCC11-1 nil 3520826443 ("" (subtype-tcc) nil nil)
((transpose const-decl "Matrix" matrices nil)
(square? const-decl "bool" matrices nil)
(sigma def-decl "real" sigma "reals/")
(Matrix type-eq-decl nil matrices nil)
(Square type-eq-decl nil matrices nil)
(SquareMat type-eq-decl nil matrices nil)
(squareMat? const-decl "bool" matrices nil)
(bijec_transpose formula-decl nil matrix_operator nil)
(bijec_prod formula-decl nil matrix_operator nil))
nil))
(ellipsoid_TCC12 0
(ellipsoid_TCC12-1 nil 3520826443 ("" (subtype-tcc) nil nil)
((T const-decl "[Mat(m, n) -> Map_linear(n, m)]" matrix_operator
nil)
(injective? const-decl "bool" functions nil)
(surjective? const-decl "bool" functions nil)
(bijective? const-decl "bool" functions nil)
(bijective? const-decl "bool" linear_map nil)
(inverse const-decl "Maping" linear_map nil)
(inverse const-decl "D" function_inverse nil)
(L const-decl "[Map_linear(n, m) -> Mat(m, n)]" matrix_operator
nil)
(inv const-decl "[Matrix_inv(n) -> Matrix_inv(n)]" matrix_operator
nil)
(- const-decl "real" vectors "vectors/")
(* const-decl "Vector[M`rows]" matrices nil)
(* const-decl "real" vectors "vectors/")
(transpose const-decl "Matrix" matrices nil)
(* const-decl "Matrix" matrices nil)
(real_minus_real_is_real application-judgement "real" reals nil)
(real_times_real_is_real application-judgement "real" reals nil)
(int_minus_int_is_int application-judgement "int" integers nil))
nil))
(ellipsoid_TCC13 0
(ellipsoid_TCC13-1 nil 3520826443 ("" (subtype-tcc) nil nil)
((T const-decl "[Mat(m, n) -> Map_linear(n, m)]" matrix_operator
nil)
(injective? const-decl "bool" functions nil)
(surjective? const-decl "bool" functions nil)
(bijective? const-decl "bool" functions nil)
(bijective? const-decl "bool" linear_map nil)
(inverse const-decl "Maping" linear_map nil)
(inverse const-decl "D" function_inverse nil)
(L const-decl "[Map_linear(n, m) -> Mat(m, n)]" matrix_operator
nil)
(inv const-decl "[Matrix_inv(n) -> Matrix_inv(n)]" matrix_operator
nil)
(- const-decl "real" vectors "vectors/")
(* const-decl "Vector[M`rows]" matrices nil)
(* const-decl "real" vectors "vectors/")
(transpose const-decl "Matrix" matrices nil)
(* const-decl "Matrix" matrices nil)
(real_minus_real_is_real application-judgement "real" reals nil)
(real_times_real_is_real application-judgement "real" reals nil)
(int_minus_int_is_int application-judgement "int" integers nil))
nil))
(ellipsoid 0
(thm "thm" 3521305299
("" (skosimp)
(("" (replace -4)
(("" (assert)
(("" (lemma "add_cancel_neg2[n!1]")
(("" (inst -1 "b!1" "M!1 * x!1")
(("1" (typepred "M!1")
(("1" (expand "squareMat?")
(("1" (replace -2 :actuals? t :hide? t)
(("1" (hide -1)
(("1" (replace -1 :hide? t)
(("1" (lemma "left_distributive_vect")
(("1" (inst -1 "M!1" "x!1" "c!1")
(("1" (typepred "M!1")
(("1" (expand "squareMat?")
(("1"
(replace -2 :actuals? t :hide? t)
(("1"
(hide -1)
(("1"
(replace -1)
(("1"
(lemma "prod_inv_oper")
(("1"
(inst
-1
"M!1"
"Q!1*transpose(M!1)"
"n!1")
(("1"
(assert)
(("1"
(case
"square?(Q!1 * transpose(M!1)) AND
squareMat?(n!1)(Q!1 * transpose(M!1)) AND
bijective?(n!1)(T(n!1, n!1)(Q!1 * transpose(M!1)))")
(("1"
(flatten)
(("1"
(assert)
(("1"
(hide -1 -2 -3)
(("1"
(replace -1)
(("1"
(lemma
"mult_assoc_vect")
(("1"
(inst
-1
"inv(n!1)(Q!1*transpose(M!1))"
"inv(n!1)(M!1)"
"M!1*(x!1-c!1)")
(("1"
(reveal -8)
(("1"
(expand
"square?")
(("1"
(reveal
-9)
(("1"
(replace
-2
:dir
rl
:actuals?
t
:hide?
t)
(("1"
(replace
-1
:actuals?
t
:hide?
t)
(("1"
(replace
-1)
(("1"
(assert)
(("1"
(case
"inv(n!1)(M!1) * (M!1 * (x!1 - c!1))=x!1-c!1")
(("1"
(replace
-1)
(("1"
(lemma
"prod_inv_oper")
(("1"
(inst
-1
"Q!1"
"transpose(M!1)"
"n!1")
(("1"
(assert)
(("1"
(case
"square?(transpose(M!1)) AND
squareMat?(n!1)(transpose(M!1)) AND
bijective?(n!1)(T(n!1, n!1)(transpose(M!1)))")
(("1"
(flatten)
(("1"
(assert)
(("1"
(hide
-1
-2
-3)
(("1"
(replace
-1)
(("1"
(lemma
"mult_assoc_vect")
(("1"
(inst
-1
"inv(n!1)(transpose(M!1))"
"inv(n!1)(Q!1)"
"x!1-c!1")
(("1"
(replace
-1)
(("1"
(lemma
"trans_mat_scal")
(("1"
(inst
-1
"inv(n!1)(transpose(M!1))"
"M!1*(x!1-c!1)"
"inv(n!1)(Q!1)*(x!1-c!1)")
(("1"
(case
"inv(n!1)(transpose(M!1))`rows = n!1")
(("1"
(replace
-1
:actuals?
t
:hide?
t)
(("1"
(replace
-1)
(("1"
(case
"(transpose(inv(n!1)(transpose(M!1))) * (M!1 * (x!1 - c!1)))=x!1-c!1")
(("1"
(replace
-1)
(("1"
(assert)
(("1"
(hide-all-but
(-11
1))
(("1"
(case
"transpose(inv(n!1)(transpose(M!1)))`rows = n!1")
(("1"
(replace
-1
:actuals?
t
:hide?
t)
(("1"
(propax)
nil
nil))
nil)
("2"
(assert)
(("2"
(hide-all-but
1)
(("2"
(grind)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(hide
-1
-2
-3)
(("2"
(hide
2)
(("2"
(lemma
"tran_inv_oper")
(("2"
(inst
-1
"M!1"
"n!1")
(("2"
(assert)
(("2"
(replace
-1)
(("2"
(lemma
"transpose2")
(("2"
(inst
-1
"inv(n!1)(M!1)")
(("2"
(replace
-1)
(("2"
(propax)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("3"
(hide-all-but
1)
(("3"
(grind)
nil
nil))
nil))
nil))
nil))
nil)
("2"
(hide-all-but
1)
(("2"
(grind)
nil
nil))
nil))
nil)
("2"
(hide-all-but
1)
(("2"
(grind)
(("1"
(reveal
-24)
(("1"
(assert)
nil
nil))
nil)
("2"
(reveal
-24)
(("2"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(hide
2)
(("2"
(split)
(("1"
(hide-all-but
1)
(("1"
(typepred
"M!1")
(("1"
(grind)
nil
nil))
nil))
nil)
("2"
(hide-all-but
1)
(("2"
(typepred
"M!1")
(("2"
(grind)
nil
nil))
nil))
nil)
("3"
(lemma
"bijec_transpose")
(("3"
(inst
-1
"M!1"
"n!1")
(("3"
(assert)
nil
nil))
nil))
nil))
nil))
nil)
("3"
(flatten)
(("3"
(hide
2)
(("3"
(grind)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(hide
2)
(("2"
(assert)
(("2"
(lemma
"mult_assoc_vect")
(("2"
(inst
-1
"inv(n!1)(M!1)"
"M!1"
"x!1-c!1")
(("1"
(replace
-1
:dir
rl)
(("1"
(assert)
(("1"
(lemma
"iso_inv")
(("1"
(inst
-1
"M!1"
"n!1")
(("1"
(assert)
(("1"
(flatten)
(("1"
(replace
-1)
(("1"
(assert)
(("1"
(lemma
"ident_vect")
(("1"
(inst
-1
"I(n!1)"
"x!1-c!1")
nil
nil))
nil))
nil))
nil))
nil))
--> --------------------
--> maximum size reached
--> --------------------
¤ Dauer der Verarbeitung: 0.76 Sekunden
(vorverarbeitet)
¤
|
Haftungshinweis
Die Informationen auf dieser Webseite wurden
nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit,
noch Qualität der bereit gestellten Informationen zugesichert.
Bemerkung:
Die farbliche Syntaxdarstellung ist noch experimentell.
|
