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Why3

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one_def : forall x : a. mem (x, x) one
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
one_def
unit_l : forall x. one * x = x
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
unit_l
unit_r : forall x. x * one = x
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
unit_r
assoc_mul : forall x y z. x * y * z = x * (y * z)
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
assoc_mul
le_mem : forall x y. x <= y <-> forall u. mem u x -> mem u y
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
le_mem
power_in_star : forall s : t, i, p : (a, a).
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
power_in_star
star_in_power : forall s x y.
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
star_in_power
star_spec : forall s : t, p : (a, a).
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
star_spec
star_unfold_l : forall x u. mem u (one + x * !x) -> mem u !x
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
star_unfold_l
star_unfold_r : forall x u. mem u (one + !x * x) -> mem u !x
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
star_unfold_r
star_induct_left_ind : forall x y z i. i >= 0 ->
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
star_induct_left_ind
star_induct_left_lem : forall x y z i. i >= 0 ->
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
star_induct_left_lem
star_induct_left : forall x y z.
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
star_induct_left
star_induct_right_ind : forall x y z i. i >= 0 ->
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
star_induct_right_ind
star_induct_right_lem : forall x y z i. i >= 0 ->
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
star_induct_right_lem
star_induct_right : forall x y z.
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
star_induct_right
matches_empty : forall a1 a2: array char, i1 i2: int.
lemma
examples
[ "int.Int", "ref.Ref", "array.Array" ]
examples/kmp.mlw
matches_empty
matches_right_extension : forall a1 a2: array char, i1 i2 n: int.
lemma
examples
[ "int.Int", "ref.Ref", "array.Array" ]
examples/kmp.mlw
matches_right_extension
matches_contradiction_at_first : forall a1 a2: array char, i1 i2 n: int.
lemma
examples
[ "int.Int", "ref.Ref", "array.Array" ]
examples/kmp.mlw
matches_contradiction_at_first
matches_contradiction_at_i : forall a1 a2: array char, i1 i2 i n: int.
lemma
examples
[ "int.Int", "ref.Ref", "array.Array" ]
examples/kmp.mlw
matches_contradiction_at_i
matches_right_weakening : forall a1 a2: array char, i1 i2 n n': int.
lemma
examples
[ "int.Int", "ref.Ref", "array.Array" ]
examples/kmp.mlw
matches_right_weakening
matches_left_weakening : forall a1 a2: array char, i1 i2 n n': int.
lemma
examples
[ "int.Int", "ref.Ref", "array.Array" ]
examples/kmp.mlw
matches_left_weakening
matches_sym : forall a1 a2: array char, i1 i2 n: int.
lemma
examples
[ "int.Int", "ref.Ref", "array.Array" ]
examples/kmp.mlw
matches_sym
matches_trans : forall a1 a2 a3: array char, i1 i2 i3 n: int.
lemma
examples
[ "int.Int", "ref.Ref", "array.Array" ]
examples/kmp.mlw
matches_trans
next_iteration : forall p a: array char, i j n: int.
lemma
examples
[ "int.Int", "ref.Ref", "array.Array" ]
examples/kmp.mlw
next_iteration
next_is_maximal : forall p a: array char, i j n k: int.
lemma
examples
[ "int.Int", "ref.Ref", "array.Array" ]
examples/kmp.mlw
next_is_maximal
next_1_0 : forall p: array char. 1 <= length p -> is_next p 1 0
lemma
examples
[ "int.Int", "ref.Ref", "array.Array" ]
examples/kmp.mlw
next_1_0
exists_prime : forall p: int -> int, u: int. 1 <= u -> first_primes p u ->
lemma
examples
[ "of", "int.Int", "int.ComputerDivision", "number.Parity", "number.Divisibility", "number.Prime", "ref.Refint", "map.Map", "array.Array" ]
examples/knuth_prime_numbers.mlw
exists_prime
no_prime_in(l u: int) = forall x: int. l < x < u -> not (prime x)
predicate
examples
[ "of", "int.Int", "int.ComputerDivision", "number.Parity", "number.Divisibility", "number.Prime", "ref.Refint", "map.Map", "array.Array" ]
examples/knuth_prime_numbers.mlw
no_prime_in
size_forest_nonneg : forall f.
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
size_forest_nonneg
count_forest_nonneg : forall f. count_forest f >= 1
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
count_forest_nonneg
mem_app : forall n st1 [@induction] st2.
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
mem_app
size_stack_nonneg : forall st.
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
size_stack_nonneg
white_forest_equiv : forall f c.
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
white_forest_equiv
any_forest_frame : forall f c1 c2.
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
any_forest_frame
any_stack_frame : forall st c1 c2.
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
any_stack_frame
inverse_frame : forall st c1 c2 c3.
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
inverse_frame
inverse_frame2 : forall st c1 c2 c3.
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
inverse_frame2
inverse_final : forall f st c1 c2.
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
inverse_final
inverse_white : forall f st c1 c2.
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
inverse_white
final_unique : forall f c1 c2.
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
final_unique
sub_not_nil : forall st f c. sub st f c -> st <> Nil
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
sub_not_nil
sub_empty : forall st f0 c. st <> Nil -> sub (Cons E st) f0 c ->
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
sub_empty
sub_mem : forall n st f c.
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
sub_mem
sub_weaken1 : forall st i f1 f2 f0 c.
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
sub_weaken1
sub_weaken2 : forall st i f1 f2 f0 c.
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
sub_weaken2
not_mem_st : forall i f st c.
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
not_mem_st
sub_frame : forall st f0 c c'.
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
sub_frame
sub_no_rep : forall f st' f0 c.
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
sub_no_rep
sub_no_rep2 : forall f st' f0 c.
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
sub_no_rep2
white_valid : forall f c.
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
white_valid
final_valid : forall f c.
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
final_valid
valid_coloring_frame : forall f c1 c2.
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
valid_coloring_frame
valid_coloring_set : forall f i c.
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
valid_coloring_set
head_and_tail : forall f1 f2: 'a, st1 st2: list 'a.
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
head_and_tail
sub_valid_coloring_f1 : forall i f1 f2 c i1.
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
sub_valid_coloring_f1
sub_valid_coloring : forall f0 i f1 f2 st c1.
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
sub_valid_coloring
sub_Cons_N : forall f st i f1 f2 c.
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
sub_Cons_N
white_white : forall f c i.
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
white_white
count_stack_nonneg : forall st. count_stack st >= 1
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
count_stack_nonneg
solution_eq : forall n f c1 c2.
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
solution_eq
solution_product : forall n i f1 f2 c1 c2 c.
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
solution_product
solution_white_or_black : forall n i f1 f2 c.
lemma
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
solution_white_or_black
size_forest(f: forest) : int
function
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
size_forest
count_forest(f: forest) : int
function
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
count_forest
size_stack(st: stack) : int
function
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
size_stack
count_stack(st: stack) : int
function
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
count_stack
disjoint(f1 f2: forest) = forall x. mem_forest x f1 -> mem_forest x f2 -> false
predicate
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
disjoint
no_repeated_forest(f: forest) = match f with
predicate
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
no_repeated_forest
even_forest(f: forest) = match f with
predicate
examples
[ "map.Map", "list.List", "list.Append", "int.Int", "map.Map", "list.List", "list.Append", "int.Int", "KodaRuskey_Spec", "seq.Seq", "seq.Seq", "list.List", "KodaRuskey_Spec", "Lemmas", "map.Map", "array.Array", "int.Int", "ref.Ref", "seq.Seq", "map.Map", "map.Const", "list.Li...
examples/koda_ruskey.mlw
even_forest
not_eqseq : forall a: array int, x y: int, i: int. 0 <= i ->
lemma
examples
[ "int.Int", "ref.Refint", "array.Array" ]
examples/lcp.mlw
not_eqseq
size_nonneg : forall t: tree 'a. 0 <= size t
lemma
examples
[ "int.Int", "TreeRank", "int.Int", "TreeRank", "int.Int", "TreeRank", "export", "export", "int.Int", "int.MinMax" ]
examples/leftist_heap.mlw
size_nonneg
size_empty : forall t: tree 'a. 0 = size t <-> t = E
lemma
examples
[ "int.Int", "TreeRank", "int.Int", "TreeRank", "int.Int", "TreeRank", "export", "export", "int.Int", "int.MinMax" ]
examples/leftist_heap.mlw
size_empty
occ_nonneg : forall x:'a, t. 0 <= occ x t
lemma
examples
[ "int.Int", "TreeRank", "int.Int", "TreeRank", "int.Int", "TreeRank", "export", "export", "int.Int", "int.MinMax" ]
examples/leftist_heap.mlw
occ_nonneg
le_root_trans : forall x y h. le x y -> le_root y h -> le_root x h
lemma
examples
[ "int.Int", "TreeRank", "int.Int", "TreeRank", "int.Int", "TreeRank", "export", "export", "int.Int", "int.MinMax" ]
examples/leftist_heap.mlw
le_root_trans
size(t: tree 'a) : int
function
examples
[ "int.Int", "TreeRank", "int.Int", "TreeRank", "int.Int", "TreeRank", "export", "export", "int.Int", "int.MinMax" ]
examples/leftist_heap.mlw
size
rank(h: t) : int
function
examples
[ "int.Int", "TreeRank", "int.Int", "TreeRank", "int.Int", "TreeRank", "export", "export", "int.Int", "int.MinMax" ]
examples/leftist_heap.mlw
rank
rel = le, axiom .
predicate
examples
[ "int.Int", "TreeRank", "int.Int", "TreeRank", "int.Int", "TreeRank", "export", "export", "int.Int", "int.MinMax" ]
examples/leftist_heap.mlw
rel
rel = le, axiom .
predicate
examples
[ "int.Int", "TreeRank", "int.Int", "TreeRank", "int.Int", "TreeRank", "export", "export", "int.Int", "int.MinMax" ]
examples/leftist_heap.mlw
rel
is_heap(h: t) = match h with
predicate
examples
[ "int.Int", "TreeRank", "int.Int", "TreeRank", "int.Int", "TreeRank", "export", "export", "int.Int", "int.MinMax" ]
examples/leftist_heap.mlw
is_heap
leftist(h: t) = match h with
predicate
examples
[ "int.Int", "TreeRank", "int.Int", "TreeRank", "int.Int", "TreeRank", "export", "export", "int.Int", "int.MinMax" ]
examples/leftist_heap.mlw
leftist
leftist_heap(h: t) = is_heap h && leftist h
predicate
examples
[ "int.Int", "TreeRank", "int.Int", "TreeRank", "int.Int", "TreeRank", "export", "export", "int.Int", "int.MinMax" ]
examples/leftist_heap.mlw
leftist_heap
next(n i: int) : int
function
examples
[ "int.Int", "int.Int", "int.ComputerDivision", "option.Option", "list.Mem", "map.Map", "map.Const", "ref.Ref", "array.Array", "int.NumOf" ]
examples/linear_probing.mlw
next
between(l j r: int) = l <= j < r || r < l <= j || j < r < l
predicate
examples
[ "int.Int", "int.Int", "int.ComputerDivision", "option.Option", "list.Mem", "map.Map", "map.Const", "ref.Ref", "array.Array", "int.NumOf" ]
examples/linear_probing.mlw
between
non_empty_seq : forall s: seq 'a. length s > 0 ->
lemma
examples
[ "any", "map.Map", "ref.Ref", "int.Int", "list.List", "list.Quant", "list.Append", "list.Mem", "list.Length", "export", "int.Int", "map.Map", "seq.Seq", "seq.Mem", "seq.Reverse", "ref.Ref", "int.Int", "map.Map", "int.Int", "int.NumOf", "map.Map" ]
examples/linked_list_rev.mlw
non_empty_seq
list_seg_frame_ext : forall next1 next2: next, p q r v: loc, pM: seq loc.
lemma
examples
[ "any", "map.Map", "ref.Ref", "int.Int", "list.List", "list.Quant", "list.Append", "list.Mem", "list.Length", "export", "int.Int", "map.Map", "seq.Seq", "seq.Mem", "seq.Reverse", "ref.Ref", "int.Int", "map.Map", "int.Int", "int.NumOf", "map.Map" ]
examples/linked_list_rev.mlw
list_seg_frame_ext
seq_tail_append : forall l1 l2: seq 'a.
lemma
examples
[ "any", "map.Map", "ref.Ref", "int.Int", "list.List", "list.Quant", "list.Append", "list.Mem", "list.Length", "export", "int.Int", "map.Map", "seq.Seq", "seq.Mem", "seq.Reverse", "ref.Ref", "int.Int", "map.Map", "int.Int", "int.NumOf", "map.Map" ]
examples/linked_list_rev.mlw
seq_tail_append
get_tail : forall i: int, s: seq 'a. 0 <= i < length s - 1 -> s[1..][i] = s[i+1]
lemma
examples
[ "any", "map.Map", "ref.Ref", "int.Int", "list.List", "list.Quant", "list.Append", "list.Mem", "list.Length", "export", "int.Int", "map.Map", "seq.Seq", "seq.Mem", "seq.Reverse", "ref.Ref", "int.Int", "map.Map", "int.Int", "int.NumOf", "map.Map" ]
examples/linked_list_rev.mlw
get_tail
tail_suffix : forall i: int, s: seq 'a. 0 <= i < length s -> s[1..][i..] == s[i+1..]
lemma
examples
[ "any", "map.Map", "ref.Ref", "int.Int", "list.List", "list.Quant", "list.Append", "list.Mem", "list.Length", "export", "int.Int", "map.Map", "seq.Seq", "seq.Mem", "seq.Reverse", "ref.Ref", "int.Int", "map.Map", "int.Int", "int.NumOf", "map.Map" ]
examples/linked_list_rev.mlw
tail_suffix
eq_loc(l1 l2:loc) : bool
function
examples
[ "any", "map.Map", "ref.Ref", "int.Int", "list.List", "list.Quant", "list.Append", "list.Mem", "list.Length", "export", "int.Int", "map.Map", "seq.Seq", "seq.Mem", "seq.Reverse", "ref.Ref", "int.Int", "map.Map", "int.Int", "int.NumOf", "map.Map" ]
examples/linked_list_rev.mlw
eq_loc
null : loc
function
examples
[ "any", "map.Map", "ref.Ref", "int.Int", "list.List", "list.Quant", "list.Append", "list.Mem", "list.Length", "export", "int.Int", "map.Map", "seq.Seq", "seq.Mem", "seq.Reverse", "ref.Ref", "int.Int", "map.Map", "int.Int", "int.NumOf", "map.Map" ]
examples/linked_list_rev.mlw
null
eq_loc(l1 l2:loc) : bool
function
examples
[ "any", "map.Map", "ref.Ref", "int.Int", "list.List", "list.Quant", "list.Append", "list.Mem", "list.Length", "export", "int.Int", "map.Map", "seq.Seq", "seq.Mem", "seq.Reverse", "ref.Ref", "int.Int", "map.Map", "int.Int", "int.NumOf", "map.Map" ]
examples/linked_list_rev.mlw
eq_loc
no_repet(l:list loc) = match l with
predicate
examples
[ "any", "map.Map", "ref.Ref", "int.Int", "list.List", "list.Quant", "list.Append", "list.Mem", "list.Length", "export", "int.Int", "map.Map", "seq.Seq", "seq.Mem", "seq.Reverse", "ref.Ref", "int.Int", "map.Map", "int.Int", "int.NumOf", "map.Map" ]
examples/linked_list_rev.mlw
no_repet
no_repet(s: seq loc) = forall i. 0 <= i < length s -> not (mem s[i] s[i+1..])
predicate
examples
[ "any", "map.Map", "ref.Ref", "int.Int", "list.List", "list.Quant", "list.Append", "list.Mem", "list.Length", "export", "int.Int", "map.Map", "seq.Seq", "seq.Mem", "seq.Reverse", "ref.Ref", "int.Int", "map.Map", "int.Int", "int.NumOf", "map.Map" ]
examples/linked_list_rev.mlw
no_repet
path_shorten : forall mem x n y. list mem x n y -> n > 0 -> list mem mem[x] (n - 1) y
lemma
examples
[ "int.Int", "map.Map" ]
examples/list_removal.mlw
path_shorten
path_extend : forall mem x n y. n >= 0 -> list mem y n x -> x <> null ->
lemma
examples
[ "int.Int", "map.Map" ]
examples/list_removal.mlw
path_extend
rel = lt, axiom .
predicate
examples
[ "int.Int", "seq.Seq", "int.Int", "seq.Seq", "seq.FreeMonoid", "Spec" ]
examples/longest_increasing_subsequence.mlw
rel
sum_ind : forall i: int. i < n -> forall j: int.
lemma
examples
[ "int.Int", "option.Option", "int.Int", "map.Map", "map.Map", "map.Const", "int.Int", "map.Map", "int.Int", "int.MinMax", "ref.Ref", "Bitset", "map.Map", "option.Option", "HashTable" ]
examples/max_matrix.mlw
sum_ind
below(n: int) : set
function
examples
[ "int.Int", "option.Option", "int.Int", "map.Map", "map.Map", "map.Const", "int.Int", "map.Map", "int.Int", "int.MinMax", "ref.Ref", "Bitset", "map.Map", "option.Option", "HashTable" ]
examples/max_matrix.mlw
below
create(x: 'a) : t 'a
function
examples
[ "int.Int", "option.Option", "int.Int", "map.Map", "map.Map", "map.Const", "int.Int", "map.Map", "int.Int", "int.MinMax", "ref.Ref", "Bitset", "map.Map", "option.Option", "HashTable" ]
examples/max_matrix.mlw
create