|
(index_theorems
(finite_index 0
(finite_index-2 nil 3601907819
("" (skeep)
(("" (invoke (case "NOT %1") (! 1 1))
(("1" (hide 2)
(("1"
(name "G"
"LAMBDA (s2:(S2)): LET PI = inverse_image(f, singleton(s2)) IN
choose({b2: [(PI) -> below(d)]| bijective?(b2)})")
(("1" (name "F" "LAMBDA (s1:(S1)): (f(s1),G(f(s1))(s1))")
(("1" (inst + "F")
(("1" (expand "bijective?" 1)
(("1" (invoke (case "NOT %1") (! 1 1))
(("1" (hide 2)
(("1" (expand "injective?" 1)
(("1" (skolem 1 ("s1a" "s1b"))
(("1" (flatten)
(("1" (hide -2)
(("1" (expand "F" -1)
(("1"
(flatten)
(("1"
(replace -1 -2)
(("1"
(typepred "G(f(s1b))")
(("1"
(expand "bijective?" -1)
(("1"
(flatten)
(("1"
(expand "injective?" -1)
(("1"
(inst - "s1a" "s1b")
(("1" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (assert)
(("2" (expand "surjective?" 1)
(("2" (skolem 1 "s2ds")
(("2"
(case "NOT EXISTS (s2:(S2),id:below(d)): s2ds=(s2,id)")
(("1" (inst + "s2ds`1" "s2ds`2")
(("1" (decompose-equality 1) nil nil)) nil)
("2" (skeep -1)
(("2" (replaces -1)
(("2"
(typepred "G(s2)")
(("2"
(expand "bijective?" -1)
(("2"
(flatten)
(("2"
(expand "surjective?" -2)
(("2"
(inst - "id")
(("2"
(skolem - "s1")
(("2"
(inst + "s1")
(("2"
(expand "F" 1)
(("2"
(assert)
(("2"
(typepred "s1")
(("2"
(expand
"inverse_image"
-2)
(("2"
(expand
"member"
-2)
(("2"
(expand
"singleton"
-2)
(("2"
(assert)
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" (hide 2)
(("2" (skeep)
(("2" (expand "inverse_image" +)
(("2" (expand "member" 1)
(("2" (expand "singleton" +)
(("2" (propax) nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
("2" (skeep)
(("2" (split 1)
(("1" (skeep)
(("1" (replaces -1) (("1" (ground) nil nil)) nil)) nil)
("2" (assert)
(("2" (hide (-2 -3 2))
(("2" (invoke (name "A" "%1") (! 1 1))
(("1" (replace -1)
(("1" (expand "bijective?" 1)
(("1" (split)
(("1" (expand "injective?" 1)
(("1" (skolem 1 ("s1a" "s1b"))
(("1"
(flatten)
(("1"
(typepred "A")
(("1"
(expand "bijective?" -1)
(("1"
(flatten)
(("1"
(expand "injective?")
(("1"
(inst - "s1a" "s1b")
(("1" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (expand "surjective?")
(("2" (skolem 1 "id")
(("2"
(typepred "A")
(("2"
(expand "bijective?" -1)
(("2"
(flatten)
(("2"
(expand "surjective?" -2)
(("2"
(inst - "id")
(("2"
(skeep -)
(("2" (inst + "x") nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (hide 2)
(("2" (reveal -2)
(("2" (inst - "s2")
(("2" (skeep)
(("2" (expand "nonempty?")
(("2"
(expand "empty?")
(("2"
(expand "member")
(("2"
(inst - "b2")
(("1"
(expand "bijective?")
(("1"
(flatten)
(("1"
(split)
(("1"
(expand "injective?")
(("1"
(skeep)
(("1"
(inst - "x1" "x2")
(("1"
(assert)
nil
nil))
nil))
nil))
nil)
("2"
(expand "surjective?")
(("2"
(skeep)
(("2"
(inst - "y")
(("2"
(skeep)
(("2"
(inst + "x")
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(skeep)
(("2"
(replace -2)
(("2" (ground) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("3" (hide (-1 2))
(("3" (skeep)
(("3" (inst - "s2")
(("3" (assert)
(("3" (expand "nonempty?")
(("3" (expand "empty?")
(("3" (expand "member")
(("3" (skeep)
(("3" (inst - "b2")
(("1" (expand "bijective?")
(("1"
(flatten)
(("1"
(split)
(("1"
(expand "injective?")
(("1"
(skeep)
(("1"
(inst - "x1" "x2")
(("1" (assert) nil nil))
nil))
nil))
nil)
("2"
(expand "surjective?")
(("2"
(skeep)
(("2"
(inst - "y")
(("2"
(skeep)
(("2" (inst + "x") nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (skeep)
(("2"
(replaces -1)
(("2" (ground) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (assert)
(("2" (replace -1)
(("2" (hide -3)
(("2"
(case "EXISTS (B:[[below(k),below(d)]->below(k*d)]): bijective?(B)")
(("1" (copy -3)
(("1" (copy -3)
(("1" (copy -3)
(("1" (skeep -1)
(("1" (skeep -2)
(("1" (skeep -3)
(("1"
(name "FF"
"LAMBDA (s1:(S1)): B(b1(b(s1)`1),b(s1)`2)")
(("1" (inst + "FF")
(("1"
(expand "bijective?")
(("1"
(flatten)
(("1"
(split)
(("1"
(expand "injective?" 1)
(("1"
(skeep)
(("1"
(expand "FF" -1)
(("1"
(expand "injective?" -3)
(("1"
(inst?)
(("1"
(assert)
(("1"
(flatten)
(("1"
(expand
"injective?"
-8)
(("1"
(inst?)
(("1"
(assert)
(("1"
(expand
"injective?"
-6)
(("1"
(inst?)
(("1"
(assert)
(("1"
(decompose-equality
2)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(expand "surjective?" 1)
(("2"
(skeep)
(("2"
(typepred "y")
(("2"
(expand "FF" 1)
(("2"
(expand "surjective?" -4)
(("2"
(inst - "y")
(("2"
(skolem - "xvv")
(("2"
(expand
"surjective?"
-8)
(("2"
(inst - "xvv`1")
(("2"
(skolem - "s2")
(("2"
(expand
"surjective?"
-6)
(("2"
(inst
-
"(s2,xvv`2)")
(("2"
(skolem
-
"xstar")
(("2"
(inst
+
"xstar")
(("2"
(replace
-6
+)
(("2"
(assert)
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" (hide-all-but 1)
(("2"
(case "EXISTS (B: [below(k * d)->[below(k), below(d)]]): bijective?(B)")
(("1" (skeep)
(("1" (inst + "inverse(B)")
(("1"
(rewrite "bijective_inverse_is_bijective" 1)
(("1" (hide 2)
(("1" (inst + "0")
(("1"
(lemma
"posreal_times_posreal_is_posreal")
(("1"
(inst?)
(("1" (assert) nil nil))
nil))
nil))
nil))
nil))
nil)
("2" (inst + "0")
(("2"
(lemma "posreal_times_posreal_is_posreal")
(("2" (inst?) (("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil)
("2" (hide 2)
(("2"
(name "BB"
"LAMBDA (i:below(k*d)): (floor(i/d),i-d*floor(i/d))")
(("2"
(case "NOT FORALL (i:below(k*d)): i = d*BB(i)`1+BB(i)`2")
(("1" (hide-all-but 1)
(("1" (skeep)
(("1" (typepred "i")
(("1"
(expand "BB")
(("1" (propax) nil nil))
nil))
nil))
nil))
nil)
("2" (inst + "BB")
(("1" (expand "bijective?")
(("1" (split)
(("1"
(expand "injective?")
(("1"
(skeep)
(("1"
(inst-cp - "x1")
(("1"
(inst - "x2")
(("1" (assert) nil nil))
nil))
nil))
nil))
nil)
("2"
(expand "surjective?")
(("2"
(skeep)
(("2"
(inst + "d*y`1 + y`2")
(("1"
(expand "BB" 1)
(("1"
(case
"floor((d * y`1 + y`2) / d) = y`1")
(("1"
(replace -1)
(("1" (assert) nil nil))
nil)
("2"
(assert)
(("2"
(case
"(d * y`1 + y`2) / d =y`1 + y`2/d")
(("1"
(replace -1)
(("1"
(assert)
(("1"
(case
"y`2/d>=0 AND y`2/d<1")
(("1"
(ground)
nil
nil)
("2"
(split)
(("1"
(cross-mult 1)
nil
nil)
("2"
(cross-mult 1)
nil
nil))
nil))
nil))
nil))
nil)
("2" (assert) nil nil))
nil))
nil))
nil))
nil)
("2"
(assert)
(("2"
(typepred "y`1")
(("2"
(typepred "y`2")
(("2"
(case "y`1+1<=k")
(("1"
(mult-by -1 "d")
(("1" (assert) nil nil))
nil)
("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (assert)
(("2" (expand "BB" 1)
(("2"
(assert)
(("2"
(skolem 1 "i")
(("2"
(typepred "floor(i/d)")
(("2"
(cross-mult -1)
(("2"
(cross-mult -2)
(("2"
(assert)
(("2"
(typepred "i")
(("2"
(case "i/d)
(("1" (assert) nil nil)
("2"
(cross-mult 1)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(BB skolem-const-decl
"[i: below(k * d) -> [{i_1 | i_1 <= i / d & i / d < 1 + i_1}, numfield]]"
index_theorems nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(div_mult_pos_le2 formula-decl nil real_props nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(y skolem-const-decl "[below(k), below(d)]" index_theorems nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(nnrat_plus_nnrat_is_nnrat application-judgement "nonneg_rat"
rationals nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(div_mult_pos_ge1 formula-decl nil real_props nil)
(div_mult_pos_lt1 formula-decl nil real_props nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(both_sides_times_pos_le1_imp formula-decl nil extra_real_props
nil)
(nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
rationals nil)
(integer nonempty-type-from-decl nil integers nil)
(<= const-decl "bool" reals nil)
(/= const-decl "boolean" notequal nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(floor const-decl "{i | i <= x & x < i + 1}" floor_ceil nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(bijective_inverse_is_bijective judgement-tcc nil function_inverse
nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(posreal_times_posreal_is_posreal judgement-tcc nil real_types nil)
(inverse const-decl "D" function_inverse nil)
(TRUE const-decl "bool" booleans nil)
(d skolem-const-decl "posnat" index_theorems nil)
(k skolem-const-decl "posnat" index_theorems nil)
(FF skolem-const-decl "[(S1) -> below(k * d)]" index_theorems nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(posint_times_posint_is_posint application-judgement "posint"
integers nil)
(s2 skolem-const-decl "(S2)" index_theorems nil)
(PI skolem-const-decl "set[(S1)]" index_theorems nil)
(empty? const-decl "bool" sets nil)
(S1 skolem-const-decl "set[T1]" index_theorems nil)
(S2 skolem-const-decl "set[T2]" index_theorems nil)
(f skolem-const-decl "[(S1) -> (S2)]" index_theorems nil)
(s2 skolem-const-decl "(S2)" index_theorems nil)
(PI skolem-const-decl "set[(S1)]" index_theorems nil)
(member const-decl "bool" sets nil)
(surjective? const-decl "bool" functions nil)
(F skolem-const-decl "[(S1) -> [(S2), below(d)]]" index_theorems
nil)
(injective? const-decl "bool" functions nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(IFF const-decl "[bool, bool -> bool]" booleans nil)
(nonempty_singleton_finite application-judgement
"non_empty_finite_set" finite_sets nil)
(inverse_image const-decl "set[D]" function_image nil)
(singleton? const-decl "bool" sets nil)
(singleton const-decl "(singleton?)" sets nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(nonempty? const-decl "bool" sets nil)
(choose const-decl "(p)" sets nil)
(bijective? const-decl "bool" functions nil)
(below type-eq-decl nil naturalnumbers nil)
(posnat 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)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals 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)
(number nonempty-type-decl nil numbers nil)
(T2 formal-type-decl nil index_theorems nil)
(set type-eq-decl nil sets nil)
(T1 formal-type-decl nil index_theorems nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil))
nil)
(finite_index-1 nil 3601832556
("" (skeep)
(("" (invoke (case "NOT %1") (! 1 1))
(("1" (hide 2)
(("1"
(name "G"
"LAMBDA (s2:(S2)): LET PI = inverse_image(f, singleton(s2)) IN
choose({b2: [(PI) -> below(d)]| bijective?(b2)})")
(("1" (name "F" "LAMBDA (s1:(S1)): (f(s1),G(f(s1))(s1))")
(("1" (inst + "F")
(("1" (expand "bijective?" 1)
(("1" (invoke (case "NOT %1") (! 1 1))
(("1" (hide 2)
(("1" (expand "injective?" 1)
(("1" (skolem 1 ("s1a" "s1b"))
(("1" (flatten)
(("1" (hide -2)
(("1" (expand "F" -1)
(("1"
(flatten)
(("1"
(replace -1 -2)
(("1"
(typepred "G(f(s1b))")
(("1"
(expand "bijective?" -1)
(("1"
(flatten)
(("1"
(expand "injective?" -1)
(("1"
(inst - "s1a" "s1b")
(("1" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (assert)
(("2" (expand "surjective?" 1)
(("2" (skolem 1 "s2ds")
(("2"
(case "NOT EXISTS (s2:(S2),id:below(d)): s2ds=(s2,id)")
(("1" (inst + "s2ds`1" "s2ds`2")
(("1" (decompose-equality 1) nil nil)) nil)
("2" (skeep -1)
(("2" (replaces -1)
(("2"
(typepred "G(s2)")
(("2"
(expand "bijective?" -1)
(("2"
(flatten)
(("2"
(expand "surjective?" -2)
(("2"
(inst - "id")
(("2"
(skolem - "s1")
(("2"
(inst + "s1")
(("2"
(expand "F" 1)
(("2"
(assert)
(("2"
(typepred "s1")
(("2"
(expand
"inverse_image"
-2)
(("2"
(expand
"member"
-2)
(("2"
(expand
"singleton"
-2)
(("2"
(assert)
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" (hide 2)
(("2" (skeep)
(("2" (expand "inverse_image" +)
(("2" (expand "member" 1)
(("2" (expand "singleton" +)
(("2" (propax) nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
("2" (skeep)
(("2" (split 1)
(("1" (skeep)
(("1" (replaces -1) (("1" (ground) nil nil)) nil)) nil)
("2" (assert)
(("2" (hide (-2 -3 2))
(("2" (invoke (name "A" "%1") (! 1 1))
(("1" (replace -1)
(("1" (expand "bijective?" 1)
(("1" (split)
(("1" (expand "injective?" 1)
(("1" (skolem 1 ("s1a" "s1b"))
(("1"
(flatten)
(("1"
(typepred "A")
(("1"
(expand "bijective?" -1)
(("1"
(flatten)
(("1"
(expand "injective?")
(("1"
(inst - "s1a" "s1b")
(("1" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (expand "surjective?")
(("2" (skolem 1 "id")
(("2"
(typepred "A")
(("2"
(expand "bijective?" -1)
(("2"
(flatten)
(("2"
(expand "surjective?" -2)
(("2"
(inst - "id")
(("2"
(skeep -)
(("2" (inst + "x") nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (hide 2)
(("2" (reveal -2)
(("2" (inst - "s2")
(("2" (skeep)
(("2" (expand "nonempty?")
(("2"
(expand "empty?")
(("2"
(expand "member")
(("2"
(inst - "b2")
(("1"
(expand "bijective?")
(("1"
(flatten)
(("1"
(split)
(("1"
(expand "injective?")
(("1"
(skeep)
(("1"
(inst - "x1" "x2")
(("1"
(assert)
nil
nil))
nil))
nil))
nil)
("2"
(expand "surjective?")
(("2"
(skeep)
(("2"
(inst - "y")
(("2"
(skeep)
(("2"
(inst + "x")
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(skeep)
(("2"
(replace -2)
(("2" (ground) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("3" (hide (-1 2))
(("3" (skeep)
(("3" (inst - "s2")
(("3" (assert)
(("3" (expand "nonempty?")
(("3" (expand "empty?")
(("3" (expand "member")
(("3" (skeep)
(("3" (inst - "b2")
(("1" (expand "bijective?")
(("1"
(flatten)
(("1"
(split)
(("1"
(expand "injective?")
(("1"
(skeep)
(("1"
(inst - "x1" "x2")
(("1" (assert) nil nil))
nil))
nil))
nil)
("2"
(expand "surjective?")
(("2"
(skeep)
(("2"
(inst - "y")
(("2"
(skeep)
(("2" (inst + "x") nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (skeep)
(("2"
(replaces -1)
(("2" (ground) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (assert)
(("2" (replace -1)
(("2" (hide -3)
(("2"
(case "EXISTS (B:[[below(k),below(d)]->below(k*d)]): bijective?(B)")
(("1" (copy -3)
(("1" (copy -3)
(("1" (copy -3)
(("1" (skeep -1)
(("1" (skeep -2)
(("1" (skeep -3)
(("1"
(name "FF"
"LAMBDA (s1:(S1)): B(b1(b(s1)`1),b(s1)`2)")
(("1" (inst + "FF")
(("1"
(expand "bijective?")
(("1"
(flatten)
(("1"
(split)
(("1"
(expand "injective?" 1)
(("1"
(skeep)
(("1"
(expand "FF" -1)
(("1"
(expand "injective?" -3)
(("1"
(inst?)
(("1"
(assert)
(("1"
(flatten)
(("1"
(expand
"injective?"
-8)
(("1"
(inst?)
(("1"
(assert)
(("1"
(expand
"injective?"
-6)
(("1"
(inst?)
(("1"
(assert)
(("1"
(decompose-equality
2)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(expand "surjective?" 1)
(("2"
(skeep)
(("2"
(typepred "y")
(("2"
(expand "FF" 1)
(("2"
(expand "surjective?" -4)
(("2"
(inst - "y")
(("2"
(skolem - "xvv")
(("2"
(expand
"surjective?"
-8)
(("2"
(inst - "xvv`1")
(("2"
(skolem - "s2")
(("2"
(expand
"surjective?"
-6)
(("2"
(inst
-
"(s2,xvv`2)")
(("2"
(skolem
-
"xstar")
(("2"
(inst
+
"xstar")
(("2"
(replace
-6
+)
(("2"
(assert)
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" (hide-all-but 1)
(("2"
(case "EXISTS (B: [below(k * d)->[below(k), below(d)]]): bijective?(B)")
(("1" (skeep)
(("1" (inst + "inverse(B)")
(("1"
(rewrite "bijective_inverse_is_bijective" 1)
(("1" (hide 2)
(("1" (inst + "0")
(("1"
(lemma
"posreal_times_posreal_is_posreal")
(("1"
(inst?)
(("1" (assert) nil nil))
nil))
nil))
nil))
nil))
nil)
("2" (inst + "0")
(("2"
(lemma "posreal_times_posreal_is_posreal")
(("2" (inst?) (("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil)
("2" (hide 2)
(("2"
(name "BB"
"LAMBDA (i:below(k*d)): (floor(i/d),i-floor(i/d))")
(("2" (inst + "BB")
(("1" (expand "bijective?")
(("1" (split)
(("1"
(case "NOT FORALL (i:below(k*d)): i = d*BB(i)`1+BB(i)`2")
(("1"
(hide-all-but 1)
(("1" (postpone) nil nil))
nil)
("2" (postpone) nil nil))
nil)
("2" (postpone) nil nil))
nil))
nil)
("2" (postpone) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
nil shostak)))
¤ Dauer der Verarbeitung: 0.91 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.
|
