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phanerozoic
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Why3

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fact
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5
124
type
stringclasses
3 values
library
stringclasses
5 values
imports
listlengths
0
177
filename
stringclasses
414 values
symbolic_name
stringlengths
1
57
docstring
stringclasses
1 value
is_partition(a: array int32) = (* at least one element *)
predicate
examples
[ "int.Int", "ref.Refint", "array.Array", "int.Int", "ref.Ref", "mach.int.Int32", "mach.array.Array32", "int.Int", "array.Array", "Conjugate" ]
examples/conjugate.mlw
is_partition
is_conjugate(a b: array int32) = b.length > a[0] &&
predicate
examples
[ "int.Int", "ref.Refint", "array.Array", "int.Int", "ref.Ref", "mach.int.Int32", "mach.array.Array32", "int.Int", "array.Array", "Conjugate" ]
examples/conjugate.mlw
is_conjugate
k_values(a: array int) = forall i: int. 0 <= i < length a -> 0 <= a[i] < k
predicate
examples
[ "export", "int.NumOf", "export", "export", "Spec", "ref.Refint", "Spec", "ref.Refint", "Spec", "InPlaceCountingSort" ]
examples/counting_sort.mlw
k_values
permut(a b: array int) = length a = length b /\
predicate
examples
[ "export", "int.NumOf", "export", "export", "Spec", "ref.Refint", "Spec", "ref.Refint", "Spec", "InPlaceCountingSort" ]
examples/counting_sort.mlw
permut
cube(x: int) : int
function
examples
[ "int.Int", "ref.Ref" ]
examples/cubic_root.mlw
cube
sum_of_list : forall l: list int.
lemma
examples
[ "int.Int", "int.Sum", "seq.Seq", "ref.Refint", "cursor.Cursor", "int.Int", "list.List", "seq.Seq", "seq.OfList", "int.Int", "int.Sum", "list.List", "list.Length", "list.Sum", "ref.Refint", "seq.Seq", "seq.OfList", "ListCursorImpl", "int.Int", "array.Array", "array.ToSeq", "...
examples/cursor_examples.mlw
sum_of_list
permitted(c: cursor 'a) = length c.visited <= length c.collection /\
predicate
examples
[ "int.Int", "int.Sum", "seq.Seq", "ref.Refint", "cursor.Cursor", "int.Int", "list.List", "seq.Seq", "seq.OfList", "int.Int", "int.Sum", "list.List", "list.Length", "list.Sum", "ref.Refint", "seq.Seq", "seq.OfList", "ListCursorImpl", "int.Int", "array.Array", "array.ToSeq", "...
examples/cursor_examples.mlw
permitted
complete(c: cursor 'a) = length c.visited = length c.collection
predicate
examples
[ "int.Int", "int.Sum", "seq.Seq", "ref.Refint", "cursor.Cursor", "int.Int", "list.List", "seq.Seq", "seq.OfList", "int.Int", "int.Sum", "list.List", "list.Length", "list.Sum", "ref.Refint", "seq.Seq", "seq.OfList", "ListCursorImpl", "int.Int", "array.Array", "array.ToSeq", "...
examples/cursor_examples.mlw
complete
permitted(c: cursor 'a) = length c.visited <= length c.collection /\
predicate
examples
[ "int.Int", "int.Sum", "seq.Seq", "ref.Refint", "cursor.Cursor", "int.Int", "list.List", "seq.Seq", "seq.OfList", "int.Int", "int.Sum", "list.List", "list.Length", "list.Sum", "ref.Refint", "seq.Seq", "seq.OfList", "ListCursorImpl", "int.Int", "array.Array", "array.ToSeq", "...
examples/cursor_examples.mlw
permitted
complete(c: cursor 'a) = length c.visited = length c.collection
predicate
examples
[ "int.Int", "int.Sum", "seq.Seq", "ref.Refint", "cursor.Cursor", "int.Int", "list.List", "seq.Seq", "seq.OfList", "int.Int", "int.Sum", "list.List", "list.Length", "list.Sum", "ref.Refint", "seq.Seq", "seq.OfList", "ListCursorImpl", "int.Int", "array.Array", "array.ToSeq", "...
examples/cursor_examples.mlw
complete
decrease1(a: array int) = forall i: int. 0 <= i < length a - 1 -> a[i+1] >= a[i] - 1
predicate
examples
[ "of", "int.Int", "ref.Ref", "array.Array" ]
examples/decrease1.mlw
decrease1
size_e_pos : forall e: expr. size_e e >= 1
lemma
examples
[ "export", "Expr", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "Defunctionalization", "Expr", "DirectSem", "Defunctionalization", "Expr", "SemWithError", "Defunctionalization" ]
examples/defunctionalization.mlw
size_e_pos
size_c_pos : forall c: cont. size_c c >= 0
lemma
examples
[ "export", "Expr", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "Defunctionalization", "Expr", "DirectSem", "Defunctionalization", "Expr", "SemWithError", "Defunctionalization" ]
examples/defunctionalization.mlw
size_c_pos
cps_correct_expr : forall e: expr. forall k:value -> 'a. eval_1 e k = k (eval_0 e)
lemma
examples
[ "export", "Expr", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "Defunctionalization", "Expr", "DirectSem", "Defunctionalization", "Expr", "SemWithError", "Defunctionalization" ]
examples/defunctionalization.mlw
cps_correct_expr
cps_correct : forall p. interpret_1 p = interpret_0 p
lemma
examples
[ "export", "Expr", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "Defunctionalization", "Expr", "DirectSem", "Defunctionalization", "Expr", "SemWithError", "Defunctionalization" ]
examples/defunctionalization.mlw
cps_correct
cps2_correct_expr_aux : forall k: int -> 'a, e1 e2, kerr: unit -> 'a.
lemma
examples
[ "export", "Expr", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "Defunctionalization", "Expr", "DirectSem", "Defunctionalization", "Expr", "SemWithError", "Defunctionalization" ]
examples/defunctionalization.mlw
cps2_correct_expr_aux
cps2_correct_expr : forall e, kerr: unit->'a, k:int -> 'a. eval_2 e k kerr =
lemma
examples
[ "export", "Expr", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "Defunctionalization", "Expr", "DirectSem", "Defunctionalization", "Expr", "SemWithError", "Defunctionalization" ]
examples/defunctionalization.mlw
cps2_correct_expr
cps2_correct : forall p. interpret_2 p = interpret_0 p
lemma
examples
[ "export", "Expr", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "Defunctionalization", "Expr", "DirectSem", "Defunctionalization", "Expr", "SemWithError", "Defunctionalization" ]
examples/defunctionalization.mlw
cps2_correct
cps3_correct : forall p. interpret_3 p = interpret_0 p
lemma
examples
[ "export", "Expr", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "Defunctionalization", "Expr", "DirectSem", "Defunctionalization", "Expr", "SemWithError", "Defunctionalization" ]
examples/defunctionalization.mlw
cps3_correct
size_e_pos : forall e: expr. size_e e >= 1
lemma
examples
[ "export", "Expr", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "Defunctionalization", "Expr", "DirectSem", "Defunctionalization", "Expr", "SemWithError", "Defunctionalization" ]
examples/defunctionalization.mlw
size_e_pos
size_c_pos : forall c: cont. size_c c >= 0
lemma
examples
[ "export", "Expr", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "Defunctionalization", "Expr", "DirectSem", "Defunctionalization", "Expr", "SemWithError", "Defunctionalization" ]
examples/defunctionalization.mlw
size_c_pos
size_c_pos : forall c: context. size_c c >= 0
lemma
examples
[ "export", "Expr", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "Defunctionalization", "Expr", "DirectSem", "Defunctionalization", "Expr", "SemWithError", "Defunctionalization" ]
examples/defunctionalization.mlw
size_c_pos
size_c_pos : forall c: context. size_c c >= 0
lemma
examples
[ "export", "Expr", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "Defunctionalization", "Expr", "DirectSem", "Defunctionalization", "Expr", "SemWithError", "Defunctionalization" ]
examples/defunctionalization.mlw
size_c_pos
eval_0(e:expr) : int
function
examples
[ "export", "Expr", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "Defunctionalization", "Expr", "DirectSem", "Defunctionalization", "Expr", "SemWithError", "Defunctionalization" ]
examples/defunctionalization.mlw
eval_0
interpret_0(p:prog) : int
function
examples
[ "export", "Expr", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "Defunctionalization", "Expr", "DirectSem", "Defunctionalization", "Expr", "SemWithError", "Defunctionalization" ]
examples/defunctionalization.mlw
interpret_0
size_e(e:expr) : int
function
examples
[ "export", "Expr", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "Defunctionalization", "Expr", "DirectSem", "Defunctionalization", "Expr", "SemWithError", "Defunctionalization" ]
examples/defunctionalization.mlw
size_e
size_c(c:cont) : int
function
examples
[ "export", "Expr", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "Defunctionalization", "Expr", "DirectSem", "Defunctionalization", "Expr", "SemWithError", "Defunctionalization" ]
examples/defunctionalization.mlw
size_c
eval_0(e:expr) : value
function
examples
[ "export", "Expr", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "Defunctionalization", "Expr", "DirectSem", "Defunctionalization", "Expr", "SemWithError", "Defunctionalization" ]
examples/defunctionalization.mlw
eval_0
interpret_0(p:prog) : value
function
examples
[ "export", "Expr", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "Defunctionalization", "Expr", "DirectSem", "Defunctionalization", "Expr", "SemWithError", "Defunctionalization" ]
examples/defunctionalization.mlw
interpret_0
interpret_1(p : prog) : value
function
examples
[ "export", "Expr", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "Defunctionalization", "Expr", "DirectSem", "Defunctionalization", "Expr", "SemWithError", "Defunctionalization" ]
examples/defunctionalization.mlw
interpret_1
interpret_2(p : prog) : value
function
examples
[ "export", "Expr", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "Defunctionalization", "Expr", "DirectSem", "Defunctionalization", "Expr", "SemWithError", "Defunctionalization" ]
examples/defunctionalization.mlw
interpret_2
interpret_3(p : prog) : value
function
examples
[ "export", "Expr", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "Defunctionalization", "Expr", "DirectSem", "Defunctionalization", "Expr", "SemWithError", "Defunctionalization" ]
examples/defunctionalization.mlw
interpret_3
size_e(e:expr) : int
function
examples
[ "export", "Expr", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "Defunctionalization", "Expr", "DirectSem", "Defunctionalization", "Expr", "SemWithError", "Defunctionalization" ]
examples/defunctionalization.mlw
size_e
size_c(c:cont) : int
function
examples
[ "export", "Expr", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "Defunctionalization", "Expr", "DirectSem", "Defunctionalization", "Expr", "SemWithError", "Defunctionalization" ]
examples/defunctionalization.mlw
size_c
size_e(e:expr) : int
function
examples
[ "export", "Expr", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "Defunctionalization", "Expr", "DirectSem", "Defunctionalization", "Expr", "SemWithError", "Defunctionalization" ]
examples/defunctionalization.mlw
size_e
size_c(c:context) : int
function
examples
[ "export", "Expr", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "Defunctionalization", "Expr", "DirectSem", "Defunctionalization", "Expr", "SemWithError", "Defunctionalization" ]
examples/defunctionalization.mlw
size_c
size_e(e:expr) : int
function
examples
[ "export", "Expr", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "Defunctionalization", "Expr", "DirectSem", "Defunctionalization", "Expr", "SemWithError", "Defunctionalization" ]
examples/defunctionalization.mlw
size_e
size_c(c:context) : int
function
examples
[ "export", "Expr", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "Defunctionalization", "Expr", "DirectSem", "Defunctionalization", "Expr", "SemWithError", "Defunctionalization" ]
examples/defunctionalization.mlw
size_c
is_a_redex(e:expr) = match e with
predicate
examples
[ "export", "Expr", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "Defunctionalization", "Expr", "DirectSem", "Defunctionalization", "Expr", "SemWithError", "Defunctionalization" ]
examples/defunctionalization.mlw
is_a_redex
is_a_value(e:expr) = match e with
predicate
examples
[ "export", "Expr", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "Defunctionalization", "Expr", "DirectSem", "Defunctionalization", "Expr", "SemWithError", "Defunctionalization" ]
examples/defunctionalization.mlw
is_a_value
is_empty_context(c:context) = match c with
predicate
examples
[ "export", "Expr", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "DirectSem", "Expr", "Defunctionalization", "Expr", "DirectSem", "Defunctionalization", "Expr", "SemWithError", "Defunctionalization" ]
examples/defunctionalization.mlw
is_empty_context
empty_notin_r1 : not (mem empty r1)
lemma
examples
[ "option.Option", "seq.Seq" ]
examples/dfa_example.mlw
empty_notin_r1
words_in_r1_end_with_one : forall w: word.
lemma
examples
[ "option.Option", "seq.Seq" ]
examples/dfa_example.mlw
words_in_r1_end_with_one
words_in_r1_suffix_in_r1 : forall c c': char. forall w: word.
lemma
examples
[ "option.Option", "seq.Seq" ]
examples/dfa_example.mlw
words_in_r1_suffix_in_r1
zero_w_in_r1 : forall w: word. mem w r1 <-> mem (cons Zero w) r1
lemma
examples
[ "option.Option", "seq.Seq" ]
examples/dfa_example.mlw
zero_w_in_r1
zero_w_in_r2 : forall w: word. mem w r1 <-> mem (cons Zero w) r2
lemma
examples
[ "option.Option", "seq.Seq" ]
examples/dfa_example.mlw
zero_w_in_r2
one_w_in_r2 : forall w: word. mem w r2 <-> mem (cons One w) r2
lemma
examples
[ "option.Option", "seq.Seq" ]
examples/dfa_example.mlw
one_w_in_r2
reformulation : forall marked: marks.
lemma
examples
[ "bool.Bool", "map.Map", "ref.Ref" ]
examples/dfs.mlw
reformulation
edge(x y: loc) = x <> null && (left x = y || right x = y)
predicate
examples
[ "bool.Bool", "map.Map", "ref.Ref" ]
examples/dfs.mlw
edge
only_descendants_are_marked(marked: marks) = forall x: loc. x <> null && marked[x] = True -> path root x
predicate
examples
[ "bool.Bool", "map.Map", "ref.Ref" ]
examples/dfs.mlw
only_descendants_are_marked
well_colored(marked busy: marks) = forall x y: loc. edge x y -> y <> null ->
predicate
examples
[ "bool.Bool", "map.Map", "ref.Ref" ]
examples/dfs.mlw
well_colored
all_descendants_are_marked(marked: marks) = root <> null ->
predicate
examples
[ "bool.Bool", "map.Map", "ref.Ref" ]
examples/dfs.mlw
all_descendants_are_marked
Length_nonneg : forall x y: vertex. forall d: int. path x y d -> d >= 0
lemma
examples
[ "map.Map", "map.Const", "int.Int", "ref.Ref" ]
examples/dijkstra.mlw
Length_nonneg
Path_inversion : forall src v:vertex. forall d:int. path src v d ->
lemma
examples
[ "map.Map", "map.Const", "int.Int", "ref.Ref" ]
examples/dijkstra.mlw
Path_inversion
Path_shortest_path : forall src v: vertex. forall d: int. path src v d ->
lemma
examples
[ "map.Map", "map.Const", "int.Int", "ref.Ref" ]
examples/dijkstra.mlw
Path_shortest_path
Main_lemma : forall src v: vertex. forall d: int.
lemma
examples
[ "map.Map", "map.Const", "int.Int", "ref.Ref" ]
examples/dijkstra.mlw
Main_lemma
Completeness_lemma : forall s: set.
lemma
examples
[ "map.Map", "map.Const", "int.Int", "ref.Ref" ]
examples/dijkstra.mlw
Completeness_lemma
inside_or_exit : forall s, src, v, d. mem src s -> path src v d ->
lemma
examples
[ "map.Map", "map.Const", "int.Int", "ref.Ref" ]
examples/dijkstra.mlw
inside_or_exit
create(x: 'a) : t 'a
function
examples
[ "map.Map", "map.Const", "int.Int", "ref.Ref" ]
examples/dijkstra.mlw
create
g_succ(_x: vertex) : fset vertex
function
examples
[ "map.Map", "map.Const", "int.Int", "ref.Ref" ]
examples/dijkstra.mlw
g_succ
original_included : forall e. pe e -> pe' e
lemma
examples
[ "int.Int", "list.ListRich" ]
examples/disamb.mlw
original_included
original_equiv_disambiguation : forall e. pe e <-> pe' e
lemma
examples
[ "int.Int", "list.ListRich" ]
examples/disamb.mlw
original_equiv_disambiguation
dyck_word_first : forall w: word. dyck w ->
lemma
examples
[ "export", "export", "Dyck", "list.Length", "ref.Ref" ]
examples/dyck.mlw
dyck_word_first
fall(p s: word) = dyck p /\
predicate
examples
[ "export", "export", "Dyck", "list.Length", "ref.Ref" ]
examples/dyck.mlw
fall
first_last_explicit : forall u: word, a: char.
lemma
examples
[ "export", "export", "export", "export", "export", "Word", "list.Length", "ref.Ref", "array.Array" ]
examples/edit_distance.mlw
first_last_explicit
first_last : forall a: char, u: word. exists v: word, b: char.
lemma
examples
[ "export", "export", "export", "export", "export", "Word", "list.Length", "ref.Ref", "array.Array" ]
examples/edit_distance.mlw
first_last
key_lemma_right : forall w1 w'2: word, m: int, a: char.
lemma
examples
[ "export", "export", "export", "export", "export", "Word", "list.Length", "ref.Ref", "array.Array" ]
examples/edit_distance.mlw
key_lemma_right
dist_symetry : forall w1 w2: word, n: int. dist w1 w2 n -> dist w2 w1 n
lemma
examples
[ "export", "export", "export", "export", "export", "Word", "list.Length", "ref.Ref", "array.Array" ]
examples/edit_distance.mlw
dist_symetry
key_lemma_left : forall w1 w2: word, m: int, a: char.
lemma
examples
[ "export", "export", "export", "export", "export", "Word", "list.Length", "ref.Ref", "array.Array" ]
examples/edit_distance.mlw
key_lemma_left
dist_concat_left : forall u v w: word, n: int.
lemma
examples
[ "export", "export", "export", "export", "export", "Word", "list.Length", "ref.Ref", "array.Array" ]
examples/edit_distance.mlw
dist_concat_left
dist_concat_right : forall u v w: word, n: int.
lemma
examples
[ "export", "export", "export", "export", "export", "Word", "list.Length", "ref.Ref", "array.Array" ]
examples/edit_distance.mlw
dist_concat_right
min_dist_equal : forall w1 w2: word, a: char, n: int.
lemma
examples
[ "export", "export", "export", "export", "export", "Word", "list.Length", "ref.Ref", "array.Array" ]
examples/edit_distance.mlw
min_dist_equal
min_dist_diff : forall w1 w2: word, a b: char, m p: int.
lemma
examples
[ "export", "export", "export", "export", "export", "Word", "list.Length", "ref.Ref", "array.Array" ]
examples/edit_distance.mlw
min_dist_diff
min_dist_eps : forall w: word, a: char, n: int.
lemma
examples
[ "export", "export", "export", "export", "export", "Word", "list.Length", "ref.Ref", "array.Array" ]
examples/edit_distance.mlw
min_dist_eps
min_dist_eps_length : forall w: word. min_dist Nil w (length w)
lemma
examples
[ "export", "export", "export", "export", "export", "Word", "list.Length", "ref.Ref", "array.Array" ]
examples/edit_distance.mlw
min_dist_eps_length
suffix_length : forall a: array char, i: int.
lemma
examples
[ "export", "export", "export", "export", "export", "Word", "list.Length", "ref.Ref", "array.Array" ]
examples/edit_distance.mlw
suffix_length
word_of(a: array char) : word
function
examples
[ "export", "export", "export", "export", "export", "Word", "list.Length", "ref.Ref", "array.Array" ]
examples/edit_distance.mlw
word_of
eq(x y: char) : bool ensures { result <-> x
function
examples
[ "int.Int", "seq.Seq", "seq.FreeMonoid", "an" ]
examples/equality_up_to_spaces.mlw
eq
remove_spaces(s: char_string) : char_string
function
examples
[ "int.Int", "seq.Seq", "seq.FreeMonoid", "an" ]
examples/equality_up_to_spaces.mlw
remove_spaces
div_succ_1 : forall x y:int. x >= 0 /\ y > 0 ->
lemma
examples
[ "int.Int", "int.ComputerDivision", "int.Int", "int.ComputerDivision", "int.Div2", "DivModHints", "int.Int", "int.ComputerDivision", "TriangularNumbers", "DivModHints", "SumMultiple", "int.Int", "mach.int.Int", "io.StdIO", "ref.Ref" ]
examples/euler001.mlw
div_succ_1
div_succ_2 : forall x y:int. x >= 0 /\ y > 0 ->
lemma
examples
[ "int.Int", "int.ComputerDivision", "int.Int", "int.ComputerDivision", "int.Div2", "DivModHints", "int.Int", "int.ComputerDivision", "TriangularNumbers", "DivModHints", "SumMultiple", "int.Int", "mach.int.Int", "io.StdIO", "ref.Ref" ]
examples/euler001.mlw
div_succ_2
mod2_mul2 : forall x:int. mod (2 * x) 2 = 0
lemma
examples
[ "int.Int", "int.ComputerDivision", "int.Int", "int.ComputerDivision", "int.Div2", "DivModHints", "int.Int", "int.ComputerDivision", "TriangularNumbers", "DivModHints", "SumMultiple", "int.Int", "mach.int.Int", "io.StdIO", "ref.Ref" ]
examples/euler001.mlw
mod2_mul2
mod2_mul2_aux : forall x y:int. mod (y * (2 * x)) 2 = 0
lemma
examples
[ "int.Int", "int.ComputerDivision", "int.Int", "int.ComputerDivision", "int.Div2", "DivModHints", "int.Int", "int.ComputerDivision", "TriangularNumbers", "DivModHints", "SumMultiple", "int.Int", "mach.int.Int", "io.StdIO", "ref.Ref" ]
examples/euler001.mlw
mod2_mul2_aux
mod2_mul2_aux2 : forall x y z t:int. mod (y * (2 * x) + z * (2 * t)) 2 = 0
lemma
examples
[ "int.Int", "int.ComputerDivision", "int.Int", "int.ComputerDivision", "int.Div2", "DivModHints", "int.Int", "int.ComputerDivision", "TriangularNumbers", "DivModHints", "SumMultiple", "int.Int", "mach.int.Int", "io.StdIO", "ref.Ref" ]
examples/euler001.mlw
mod2_mul2_aux2
div2_mul2 : forall x:int. div (2 * x) 2 = x
lemma
examples
[ "int.Int", "int.ComputerDivision", "int.Int", "int.ComputerDivision", "int.Div2", "DivModHints", "int.Int", "int.ComputerDivision", "TriangularNumbers", "DivModHints", "SumMultiple", "int.Int", "mach.int.Int", "io.StdIO", "ref.Ref" ]
examples/euler001.mlw
div2_mul2
div2_mul2_aux : forall x y:int. div (y * (2 * x)) 2 = y * x
lemma
examples
[ "int.Int", "int.ComputerDivision", "int.Int", "int.ComputerDivision", "int.Div2", "DivModHints", "int.Int", "int.ComputerDivision", "TriangularNumbers", "DivModHints", "SumMultiple", "int.Int", "mach.int.Int", "io.StdIO", "ref.Ref" ]
examples/euler001.mlw
div2_mul2_aux
div2_add : forall x y:int. mod x 2 = 0 /\ mod y 2 = 0 ->
lemma
examples
[ "int.Int", "int.ComputerDivision", "int.Int", "int.ComputerDivision", "int.Div2", "DivModHints", "int.Int", "int.ComputerDivision", "TriangularNumbers", "DivModHints", "SumMultiple", "int.Int", "mach.int.Int", "io.StdIO", "ref.Ref" ]
examples/euler001.mlw
div2_add
div2_sub : forall x y:int. mod x 2 = 0 /\ mod y 2 = 0 ->
lemma
examples
[ "int.Int", "int.ComputerDivision", "int.Int", "int.ComputerDivision", "int.Div2", "DivModHints", "int.Int", "int.ComputerDivision", "TriangularNumbers", "DivModHints", "SumMultiple", "int.Int", "mach.int.Int", "io.StdIO", "ref.Ref" ]
examples/euler001.mlw
div2_sub
tr_mod_2 : forall n:int. n >= 0 -> mod (n*(n+1)) 2 = 0
lemma
examples
[ "int.Int", "int.ComputerDivision", "int.Int", "int.ComputerDivision", "int.Div2", "DivModHints", "int.Int", "int.ComputerDivision", "TriangularNumbers", "DivModHints", "SumMultiple", "int.Int", "mach.int.Int", "io.StdIO", "ref.Ref" ]
examples/euler001.mlw
tr_mod_2
tr_repr : forall n:int. n >= 0 -> n*(n+1) = 2 * tr n
lemma
examples
[ "int.Int", "int.ComputerDivision", "int.Int", "int.ComputerDivision", "int.Div2", "DivModHints", "int.Int", "int.ComputerDivision", "TriangularNumbers", "DivModHints", "SumMultiple", "int.Int", "mach.int.Int", "io.StdIO", "ref.Ref" ]
examples/euler001.mlw
tr_repr
tr_succ : forall n:int. n >= 0 -> tr (n+1) = tr n + n + 1
lemma
examples
[ "int.Int", "int.ComputerDivision", "int.Int", "int.ComputerDivision", "int.Div2", "DivModHints", "int.Int", "int.ComputerDivision", "TriangularNumbers", "DivModHints", "SumMultiple", "int.Int", "mach.int.Int", "io.StdIO", "ref.Ref" ]
examples/euler001.mlw
tr_succ
mod_15 : forall n:int.
lemma
examples
[ "int.Int", "int.ComputerDivision", "int.Int", "int.ComputerDivision", "int.Div2", "DivModHints", "int.Int", "int.ComputerDivision", "TriangularNumbers", "DivModHints", "SumMultiple", "int.Int", "mach.int.Int", "io.StdIO", "ref.Ref" ]
examples/euler001.mlw
mod_15
Closed_formula_0 : p 0
lemma
examples
[ "int.Int", "int.ComputerDivision", "int.Int", "int.ComputerDivision", "int.Div2", "DivModHints", "int.Int", "int.ComputerDivision", "TriangularNumbers", "DivModHints", "SumMultiple", "int.Int", "mach.int.Int", "io.StdIO", "ref.Ref" ]
examples/euler001.mlw
Closed_formula_0
Closed_formula_n : forall n:int. n > 0 -> p (n-1) ->
lemma
examples
[ "int.Int", "int.ComputerDivision", "int.Int", "int.ComputerDivision", "int.Div2", "DivModHints", "int.Int", "int.ComputerDivision", "TriangularNumbers", "DivModHints", "SumMultiple", "int.Int", "mach.int.Int", "io.StdIO", "ref.Ref" ]
examples/euler001.mlw
Closed_formula_n
Closed_formula_n_3 : forall n:int. n > 0 -> p (n-1) ->
lemma
examples
[ "int.Int", "int.ComputerDivision", "int.Int", "int.ComputerDivision", "int.Div2", "DivModHints", "int.Int", "int.ComputerDivision", "TriangularNumbers", "DivModHints", "SumMultiple", "int.Int", "mach.int.Int", "io.StdIO", "ref.Ref" ]
examples/euler001.mlw
Closed_formula_n_3
Closed_formula_n_5 : forall n:int. n > 0 -> p (n-1) ->
lemma
examples
[ "int.Int", "int.ComputerDivision", "int.Int", "int.ComputerDivision", "int.Div2", "DivModHints", "int.Int", "int.ComputerDivision", "TriangularNumbers", "DivModHints", "SumMultiple", "int.Int", "mach.int.Int", "io.StdIO", "ref.Ref" ]
examples/euler001.mlw
Closed_formula_n_5
Closed_formula_n_15 : forall n:int. n > 0 -> p (n-1) ->
lemma
examples
[ "int.Int", "int.ComputerDivision", "int.Int", "int.ComputerDivision", "int.Div2", "DivModHints", "int.Int", "int.ComputerDivision", "TriangularNumbers", "DivModHints", "SumMultiple", "int.Int", "mach.int.Int", "io.StdIO", "ref.Ref" ]
examples/euler001.mlw
Closed_formula_n_15
Closed_formula_ind : forall n:int. 0 <= n -> p n
lemma
examples
[ "int.Int", "int.ComputerDivision", "int.Int", "int.ComputerDivision", "int.Div2", "DivModHints", "int.Int", "int.ComputerDivision", "TriangularNumbers", "DivModHints", "SumMultiple", "int.Int", "mach.int.Int", "io.StdIO", "ref.Ref" ]
examples/euler001.mlw
Closed_formula_ind
div_15 : forall n:int. 0 <= n -> div n 15 >= 0
lemma
examples
[ "int.Int", "int.ComputerDivision", "int.Int", "int.ComputerDivision", "int.Div2", "DivModHints", "int.Int", "int.ComputerDivision", "TriangularNumbers", "DivModHints", "SumMultiple", "int.Int", "mach.int.Int", "io.StdIO", "ref.Ref" ]
examples/euler001.mlw
div_15
div_5 : forall n:int. 0 <= n -> div n 5 >= 0
lemma
examples
[ "int.Int", "int.ComputerDivision", "int.Int", "int.ComputerDivision", "int.Div2", "DivModHints", "int.Int", "int.ComputerDivision", "TriangularNumbers", "DivModHints", "SumMultiple", "int.Int", "mach.int.Int", "io.StdIO", "ref.Ref" ]
examples/euler001.mlw
div_5