fact stringlengths 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 |
|---|---|---|---|---|---|---|
IEa : forall x y. | lemma | examples | [
"bv.BV32",
"int.Int",
"int.NumOf",
"bv.BV32",
"Utils",
"int.Int",
"int.NumOf",
"bool.Bool",
"bv.BV32",
"Utils"
] | examples/hackers-delight.mlw | IEa | |
IEb : forall x y. | lemma | examples | [
"bv.BV32",
"int.Int",
"int.NumOf",
"bv.BV32",
"Utils",
"int.Int",
"int.NumOf",
"bool.Bool",
"bv.BV32",
"Utils"
] | examples/hackers-delight.mlw | IEb | |
IE3 : forall x y. | lemma | examples | [
"bv.BV32",
"int.Int",
"int.NumOf",
"bv.BV32",
"Utils",
"int.Int",
"int.NumOf",
"bool.Bool",
"bv.BV32",
"Utils"
] | examples/hackers-delight.mlw | IE3 | |
IE4 : forall x y. | lemma | examples | [
"bv.BV32",
"int.Int",
"int.NumOf",
"bv.BV32",
"Utils",
"int.Int",
"int.NumOf",
"bool.Bool",
"bv.BV32",
"Utils"
] | examples/hackers-delight.mlw | IE4 | |
SR1 : forall x n. ult n size_bv -> | lemma | examples | [
"bv.BV32",
"int.Int",
"int.NumOf",
"bv.BV32",
"Utils",
"int.Int",
"int.NumOf",
"bool.Bool",
"bv.BV32",
"Utils"
] | examples/hackers-delight.mlw | SR1 | |
RS_left : forall x. | lemma | examples | [
"bv.BV32",
"int.Int",
"int.NumOf",
"bv.BV32",
"Utils",
"int.Int",
"int.NumOf",
"bool.Bool",
"bv.BV32",
"Utils"
] | examples/hackers-delight.mlw | RS_left | |
RS_right : forall x. | lemma | examples | [
"bv.BV32",
"int.Int",
"int.NumOf",
"bv.BV32",
"Utils",
"int.Int",
"int.NumOf",
"bool.Bool",
"bv.BV32",
"Utils"
] | examples/hackers-delight.mlw | RS_right | |
BP : forall a b c d x y. | lemma | examples | [
"bv.BV32",
"int.Int",
"int.NumOf",
"bv.BV32",
"Utils",
"int.Int",
"int.NumOf",
"bool.Bool",
"bv.BV32",
"Utils"
] | examples/hackers-delight.mlw | BP | |
max(x y : t) : t | function | examples | [
"bv.BV32",
"int.Int",
"int.NumOf",
"bv.BV32",
"Utils",
"int.Int",
"int.NumOf",
"bool.Bool",
"bv.BV32",
"Utils"
] | examples/hackers-delight.mlw | max | |
min(x y : t) : t | function | examples | [
"bv.BV32",
"int.Int",
"int.NumOf",
"bv.BV32",
"Utils",
"int.Int",
"int.NumOf",
"bool.Bool",
"bv.BV32",
"Utils"
] | examples/hackers-delight.mlw | min | |
count(bv : t) : t | function | examples | [
"bv.BV32",
"int.Int",
"int.NumOf",
"bv.BV32",
"Utils",
"int.Int",
"int.NumOf",
"bool.Bool",
"bv.BV32",
"Utils"
] | examples/hackers-delight.mlw | count | |
hammingD(a b : t) : t | function | examples | [
"bv.BV32",
"int.Int",
"int.NumOf",
"bv.BV32",
"Utils",
"int.Int",
"int.NumOf",
"bool.Bool",
"bv.BV32",
"Utils"
] | examples/hackers-delight.mlw | hammingD | |
fun_or(f g : 'a -> bool) : 'a -> bool | function | examples | [
"bv.BV32",
"int.Int",
"int.NumOf",
"bv.BV32",
"Utils",
"int.Int",
"int.NumOf",
"bool.Bool",
"bv.BV32",
"Utils"
] | examples/hackers-delight.mlw | fun_or | |
toGray(bv : t) : t | function | examples | [
"bv.BV32",
"int.Int",
"int.NumOf",
"bv.BV32",
"Utils",
"int.Int",
"int.NumOf",
"bool.Bool",
"bv.BV32",
"Utils"
] | examples/hackers-delight.mlw | toGray | |
fromGray(gr : t) : t | function | examples | [
"bv.BV32",
"int.Int",
"int.NumOf",
"bv.BV32",
"Utils",
"int.Int",
"int.NumOf",
"bool.Bool",
"bv.BV32",
"Utils"
] | examples/hackers-delight.mlw | fromGray | |
validAscii(b : t) = (nth_bv (count b) zeros) = False | predicate | examples | [
"bv.BV32",
"int.Int",
"int.NumOf",
"bv.BV32",
"Utils",
"int.Int",
"int.NumOf",
"bool.Bool",
"bv.BV32",
"Utils"
] | examples/hackers-delight.mlw | validAscii | |
addDontOverflow(a b : t) = ule b (add b a) /\ ule a (add b a) | predicate | examples | [
"bv.BV32",
"int.Int",
"int.NumOf",
"bv.BV32",
"Utils",
"int.Int",
"int.NumOf",
"bool.Bool",
"bv.BV32",
"Utils"
] | examples/hackers-delight.mlw | addDontOverflow | |
bucket_bounds : forall n: int. 0 < n -> | lemma | examples | [
"int.Int",
"int.ComputerDivision",
"option.Option",
"list.List",
"list.Mem",
"map.Map",
"map.Const",
"array.Array"
] | examples/hashtbl_impl.mlw | bucket_bounds | |
biginv(_b: big) = 89>55 (* used to enforce the type invariant *) | predicate | examples | [
"int.Int",
"int.MinMax",
"array.Array",
"int.Int",
"ref.Refint",
"fmap.MapImpInt",
"array.Array",
"int.Int",
"int.Abs",
"ref.Refint",
"array.Array",
"array.ArraySum",
"int.Int",
"int.Sum",
"int.Abs",
"ref.Ref",
"mach.int.Int32",
"mach.array.Array32"
] | examples/hillel_challenge.mlw | biginv | |
add_last : forall s: seq int, x. | lemma | examples | [
"int.Int",
"seq.Seq",
"seq.SortedInt",
"seq.SumInt"
] | examples/huffman_with_two_queues.mlw | add_last | |
sorted_tail : forall s. sorted s -> length s >= 1 -> sorted s[1 .. ] | lemma | examples | [
"int.Int",
"seq.Seq",
"seq.SortedInt",
"seq.SumInt"
] | examples/huffman_with_two_queues.mlw | sorted_tail | |
sorted_tail_tail : forall s. sorted s -> length s >= 2 -> sorted s[2 .. ] | lemma | examples | [
"int.Int",
"seq.Seq",
"seq.SortedInt",
"seq.SumInt"
] | examples/huffman_with_two_queues.mlw | sorted_tail_tail | |
last(s: seq int) : int | function | examples | [
"int.Int",
"seq.Seq",
"seq.SortedInt",
"seq.SumInt"
] | examples/huffman_with_two_queues.mlw | last | |
pr(k: int) = p k && p (k+1) | predicate | examples | [
"export",
"Hyps",
"Hyps",
"Hyps",
"Hyps",
"ref.Ref",
"Hyps",
"ref.Ref"
] | examples/induction.mlw | pr | |
p = pr, lemma base, lemma induction_step | predicate | examples | [
"export",
"Hyps",
"Hyps",
"Hyps",
"Hyps",
"ref.Ref",
"Hyps",
"ref.Ref"
] | examples/induction.mlw | p | |
p = p, constant bound = zero | predicate | examples | [
"export",
"Hyps",
"Hyps",
"Hyps",
"Hyps",
"ref.Ref",
"Hyps",
"ref.Ref"
] | examples/induction.mlw | p | |
le = le | predicate | examples | [
"of",
"int.Int",
"array.Array",
"array.IntArraySorted",
"array.ArrayPermut",
"array.ArrayEq",
"int.Int",
"array.Array",
"array.ArrayPermut",
"array.ArrayEq",
"int.Int",
"array.Array",
"array.ArraySwap",
"array.ArrayPermut"
] | examples/insertion_sort.mlw | le | |
sorted(a : array elt) = M.sorted_sub a.elts 0 a.length | predicate | examples | [
"of",
"int.Int",
"array.Array",
"array.IntArraySorted",
"array.ArrayPermut",
"array.ArrayEq",
"int.Int",
"array.Array",
"array.ArrayPermut",
"array.ArrayEq",
"int.Int",
"array.Array",
"array.ArraySwap",
"array.ArrayPermut"
] | examples/insertion_sort.mlw | sorted | |
rel = le, axiom . | predicate | examples | [
"list.List",
"list.Permut",
"a",
"int.Int",
"list.List",
"list.NumOcc",
"list.Permut",
"int.Int",
"list.List",
"list.NumOcc",
"list.Permut"
] | examples/insertion_sort_list.mlw | rel | |
le = le, goal Transitive.Trans | predicate | examples | [
"list.List",
"list.Permut",
"a",
"int.Int",
"list.List",
"list.NumOcc",
"list.Permut",
"int.Int",
"list.List",
"list.NumOcc",
"list.Permut"
] | examples/insertion_sort_list.mlw | le | |
rel = le, axiom . | predicate | examples | [
"list.List",
"list.Permut",
"a",
"int.Int",
"list.List",
"list.NumOcc",
"list.Permut",
"int.Int",
"list.List",
"list.NumOcc",
"list.Permut"
] | examples/insertion_sort_list.mlw | rel | |
le = le, goal Transitive.Trans | predicate | examples | [
"list.List",
"list.Permut",
"a",
"int.Int",
"list.List",
"list.NumOcc",
"list.Permut",
"int.Int",
"list.List",
"list.NumOcc",
"list.Permut"
] | examples/insertion_sort_list.mlw | le | |
ge(x y: elt) = le y x | predicate | examples | [
"list.List",
"list.Permut",
"a",
"int.Int",
"list.List",
"list.NumOcc",
"list.Permut",
"int.Int",
"list.List",
"list.NumOcc",
"list.Permut"
] | examples/insertion_sort_list.mlw | ge | |
le = ge, goal Transitive.Trans | predicate | examples | [
"list.List",
"list.Permut",
"a",
"int.Int",
"list.List",
"list.NumOcc",
"list.Permut",
"int.Int",
"list.List",
"list.NumOcc",
"list.Permut"
] | examples/insertion_sort_list.mlw | le | |
gt(x y: elt) = ge x y && not (eq x y) | predicate | examples | [
"list.List",
"list.Permut",
"a",
"int.Int",
"list.List",
"list.NumOcc",
"list.Permut",
"int.Int",
"list.List",
"list.NumOcc",
"list.Permut"
] | examples/insertion_sort_list.mlw | gt | |
rel = le, axiom . | predicate | examples | [
"list.List",
"list.Permut",
"a",
"int.Int",
"list.List",
"list.NumOcc",
"list.Permut",
"int.Int",
"list.List",
"list.NumOcc",
"list.Permut"
] | examples/insertion_sort_list.mlw | rel | |
le = le, goal Transitive.Trans | predicate | examples | [
"list.List",
"list.Permut",
"a",
"int.Int",
"list.List",
"list.NumOcc",
"list.Permut",
"int.Int",
"list.List",
"list.NumOcc",
"list.Permut"
] | examples/insertion_sort_list.mlw | le | |
ge(x y: elt) = le y x | predicate | examples | [
"list.List",
"list.Permut",
"a",
"int.Int",
"list.List",
"list.NumOcc",
"list.Permut",
"int.Int",
"list.List",
"list.NumOcc",
"list.Permut"
] | examples/insertion_sort_list.mlw | ge | |
le = ge, goal Transitive.Trans | predicate | examples | [
"list.List",
"list.Permut",
"a",
"int.Int",
"list.List",
"list.NumOcc",
"list.Permut",
"int.Int",
"list.List",
"list.NumOcc",
"list.Permut"
] | examples/insertion_sort_list.mlw | le | |
list_le(ul vl: list elt) = match ul, vl with | predicate | examples | [
"list.List",
"list.Permut",
"a",
"int.Int",
"list.List",
"list.NumOcc",
"list.Permut",
"int.Int",
"list.List",
"list.NumOcc",
"list.Permut"
] | examples/insertion_sort_list.mlw | list_le | |
le = le | predicate | examples | [
"int.Int",
"ref.Ref",
"ref.Refint",
"array.Array",
"array.IntArraySorted",
"array.ArrayPermut",
"int.Int",
"ref.Ref",
"ref.Refint",
"array.Array",
"array.ArrayPermut",
"int.Int",
"ref.Ref",
"ref.Refint",
"map.Map",
"array.Array",
"array.ArrayPermut",
"predicate",
"int.Int",
"ref.Ref",
"ref.Refint",
"map.Map",
"array.Array",
"array.ArrayPermut"
] | examples/insertion_sort_naive.mlw | le | |
sorted(a : array elt) = M.sorted_sub a.elts 0 a.length | predicate | examples | [
"int.Int",
"ref.Ref",
"ref.Refint",
"array.Array",
"array.IntArraySorted",
"array.ArrayPermut",
"int.Int",
"ref.Ref",
"ref.Refint",
"array.Array",
"array.ArrayPermut",
"int.Int",
"ref.Ref",
"ref.Refint",
"map.Map",
"array.Array",
"array.ArrayPermut",
"predicate",
"int.Int",
"ref.Ref",
"ref.Refint",
"map.Map",
"array.Array",
"array.ArrayPermut"
] | examples/insertion_sort_naive.mlw | sorted | |
is_permutation_inverse : forall a b: array int. length a = length b -> | lemma | examples | [
"int.Int",
"int.NumOf",
"ref.Ref",
"array.Array",
"array.Array",
"InverseInPlace"
] | examples/inverse_in_place.mlw | is_permutation_inverse | |
is_permutation(a: array int) = forall i. 0 <= i < length a -> | predicate | examples | [
"int.Int",
"int.NumOf",
"ref.Ref",
"array.Array",
"array.Array",
"InverseInPlace"
] | examples/inverse_in_place.mlw | is_permutation | |
sqr_non_neg : forall x:int. sqr x >= 0 | lemma | examples | [
"int.Int",
"int.Int",
"ref.Refint",
"Square",
"int.Int",
"mach.int.Int",
"ref.Ref",
"Square"
] | examples/isqrt.mlw | sqr_non_neg | |
sqr_increasing : forall x y:int. 0 <= x <= y -> sqr x <= sqr y | lemma | examples | [
"int.Int",
"int.Int",
"ref.Refint",
"Square",
"int.Int",
"mach.int.Int",
"ref.Ref",
"Square"
] | examples/isqrt.mlw | sqr_increasing | |
sqr_sum : forall x y : int. sqr(x+y) = sqr x + 2*x*y + sqr y | lemma | examples | [
"int.Int",
"int.Int",
"ref.Refint",
"Square",
"int.Int",
"mach.int.Int",
"ref.Ref",
"Square"
] | examples/isqrt.mlw | sqr_sum | |
sqr(x:int) : int | function | examples | [
"int.Int",
"int.Int",
"ref.Refint",
"Square",
"int.Int",
"mach.int.Int",
"ref.Ref",
"Square"
] | examples/isqrt.mlw | sqr | |
isqrt_spec(x res:int) = res >= 0 /\ sqr res <= x < sqr (res + 1) | predicate | examples | [
"int.Int",
"int.Int",
"ref.Refint",
"Square",
"int.Int",
"mach.int.Int",
"ref.Ref",
"Square"
] | examples/isqrt.mlw | isqrt_spec | |
sqr_add2 : forall x y. | lemma | examples | [
"of",
"ref.Ref",
"bv.BV16",
"ref.Ref",
"bv.BV32",
"ref.Ref",
"bv.BV64"
] | examples/isqrt_von_neumann.mlw | sqr_add2 | |
sqr_add2 : forall x y. | lemma | examples | [
"of",
"ref.Ref",
"bv.BV16",
"ref.Ref",
"bv.BV32",
"ref.Ref",
"bv.BV64"
] | examples/isqrt_von_neumann.mlw | sqr_add2 | |
sqr_add2 : forall x y. | lemma | examples | [
"of",
"ref.Ref",
"bv.BV16",
"ref.Ref",
"bv.BV32",
"ref.Ref",
"bv.BV64"
] | examples/isqrt_von_neumann.mlw | sqr_add2 | |
sqr(x:t) : t | function | examples | [
"of",
"ref.Ref",
"bv.BV16",
"ref.Ref",
"bv.BV32",
"ref.Ref",
"bv.BV64"
] | examples/isqrt_von_neumann.mlw | sqr | |
succ(x:t) : t | function | examples | [
"of",
"ref.Ref",
"bv.BV16",
"ref.Ref",
"bv.BV32",
"ref.Ref",
"bv.BV64"
] | examples/isqrt_von_neumann.mlw | succ | |
pred(x:t) : t | function | examples | [
"of",
"ref.Ref",
"bv.BV16",
"ref.Ref",
"bv.BV32",
"ref.Ref",
"bv.BV64"
] | examples/isqrt_von_neumann.mlw | pred | |
pow2(n:t) : t | function | examples | [
"of",
"ref.Ref",
"bv.BV16",
"ref.Ref",
"bv.BV32",
"ref.Ref",
"bv.BV64"
] | examples/isqrt_von_neumann.mlw | pow2 | |
sqr(x:t) : t | function | examples | [
"of",
"ref.Ref",
"bv.BV16",
"ref.Ref",
"bv.BV32",
"ref.Ref",
"bv.BV64"
] | examples/isqrt_von_neumann.mlw | sqr | |
succ(x:t) : t | function | examples | [
"of",
"ref.Ref",
"bv.BV16",
"ref.Ref",
"bv.BV32",
"ref.Ref",
"bv.BV64"
] | examples/isqrt_von_neumann.mlw | succ | |
pred(x:t) : t | function | examples | [
"of",
"ref.Ref",
"bv.BV16",
"ref.Ref",
"bv.BV32",
"ref.Ref",
"bv.BV64"
] | examples/isqrt_von_neumann.mlw | pred | |
pow2(n:t) : t | function | examples | [
"of",
"ref.Ref",
"bv.BV16",
"ref.Ref",
"bv.BV32",
"ref.Ref",
"bv.BV64"
] | examples/isqrt_von_neumann.mlw | pow2 | |
sqr(x:t) : t | function | examples | [
"of",
"ref.Ref",
"bv.BV16",
"ref.Ref",
"bv.BV32",
"ref.Ref",
"bv.BV64"
] | examples/isqrt_von_neumann.mlw | sqr | |
succ(x:t) : t | function | examples | [
"of",
"ref.Ref",
"bv.BV16",
"ref.Ref",
"bv.BV32",
"ref.Ref",
"bv.BV64"
] | examples/isqrt_von_neumann.mlw | succ | |
pred(x:t) : t | function | examples | [
"of",
"ref.Ref",
"bv.BV16",
"ref.Ref",
"bv.BV32",
"ref.Ref",
"bv.BV64"
] | examples/isqrt_von_neumann.mlw | pred | |
pow2(n:t) : t | function | examples | [
"of",
"ref.Ref",
"bv.BV16",
"ref.Ref",
"bv.BV32",
"ref.Ref",
"bv.BV64"
] | examples/isqrt_von_neumann.mlw | pow2 | |
rel = le, axiom . | predicate | examples | [
"int.Int",
"array.Array",
"array.ArraySwap",
"array.ArrayPermut"
] | examples/i_cant_believe_it_can_sort.mlw | rel | |
le = le, axiom . | predicate | examples | [
"int.Int",
"array.Array",
"array.ArraySwap",
"array.ArrayPermut"
] | examples/i_cant_believe_it_can_sort.mlw | le | |
ht(t: tree) : int | function | examples | [
"int.Int",
"int.MinMax"
] | examples/just_join.mlw | ht | |
height(t: tree) : int | function | examples | [
"int.Int",
"int.MinMax"
] | examples/just_join.mlw | height | |
rel = lt, axiom . | predicate | examples | [
"int.Int",
"int.MinMax"
] | examples/just_join.mlw | rel | |
wf(t: tree) = match t with | predicate | examples | [
"int.Int",
"int.MinMax"
] | examples/just_join.mlw | wf | |
bst(t: tree) = match t with | predicate | examples | [
"int.Int",
"int.MinMax"
] | examples/just_join.mlw | bst | |
avl(t: tree) = match t with | predicate | examples | [
"int.Int",
"int.MinMax"
] | examples/just_join.mlw | avl | |
le_refl : forall x. x <= x | lemma | examples | [
"int.Int",
"int.Int",
"int.Int",
"set.Set"
] | examples/kleene_algebra.mlw | le_refl | |
le_antisym : forall x y. x <= y -> y <= x -> x = y | lemma | examples | [
"int.Int",
"int.Int",
"int.Int",
"set.Set"
] | examples/kleene_algebra.mlw | le_antisym | |
le_trans : forall x y z. x <= y -> y <= z -> x <= z | lemma | examples | [
"int.Int",
"int.Int",
"int.Int",
"set.Set"
] | examples/kleene_algebra.mlw | le_trans | |
zero_le : forall x. zero <= x | lemma | examples | [
"int.Int",
"int.Int",
"int.Int",
"set.Set"
] | examples/kleene_algebra.mlw | zero_le | |
le_compat_add : forall x y z. x <= y -> x + z <= y + z | lemma | examples | [
"int.Int",
"int.Int",
"int.Int",
"set.Set"
] | examples/kleene_algebra.mlw | le_compat_add | |
le_add : forall x y. x <= x + y | lemma | examples | [
"int.Int",
"int.Int",
"int.Int",
"set.Set"
] | examples/kleene_algebra.mlw | le_add | |
le_add_le : forall x y z. x <= z -> y <= z -> x + y <= z | lemma | examples | [
"int.Int",
"int.Int",
"int.Int",
"set.Set"
] | examples/kleene_algebra.mlw | le_add_le | |
add_le : forall x y z. x + y <= z -> x <= z | lemma | examples | [
"int.Int",
"int.Int",
"int.Int",
"set.Set"
] | examples/kleene_algebra.mlw | add_le | |
le_compat_add_left : forall x y z. x <= y -> z * x <= z * y | lemma | examples | [
"int.Int",
"int.Int",
"int.Int",
"set.Set"
] | examples/kleene_algebra.mlw | le_compat_add_left | |
le_compat_add_right : forall x y z. x <= y -> x * z <= y * z | lemma | examples | [
"int.Int",
"int.Int",
"int.Int",
"set.Set"
] | examples/kleene_algebra.mlw | le_compat_add_right | |
one_le_star : forall x. one <= !x | lemma | examples | [
"int.Int",
"int.Int",
"int.Int",
"set.Set"
] | examples/kleene_algebra.mlw | one_le_star | |
mul_var_le_star : forall x. x * !x <= !x | lemma | examples | [
"int.Int",
"int.Int",
"int.Int",
"set.Set"
] | examples/kleene_algebra.mlw | mul_var_le_star | |
var_mul_le_star : forall x. !x * x <= !x | lemma | examples | [
"int.Int",
"int.Int",
"int.Int",
"set.Set"
] | examples/kleene_algebra.mlw | var_mul_le_star | |
power_le_star : forall i x. i >= 0 -> x ^ i <= !x | lemma | examples | [
"int.Int",
"int.Int",
"int.Int",
"set.Set"
] | examples/kleene_algebra.mlw | power_le_star | |
star_mul_star : forall x. !x * !x = !x | lemma | examples | [
"int.Int",
"int.Int",
"int.Int",
"set.Set"
] | examples/kleene_algebra.mlw | star_mul_star | |
star_star : forall x. !(!x) = !x | lemma | examples | [
"int.Int",
"int.Int",
"int.Int",
"set.Set"
] | examples/kleene_algebra.mlw | star_star | |
star_unfold_left : forall x. one + x * !x = !x | lemma | examples | [
"int.Int",
"int.Int",
"int.Int",
"set.Set"
] | examples/kleene_algebra.mlw | star_unfold_left | |
star_unfold_right : forall x. one + !x * x = !x | lemma | examples | [
"int.Int",
"int.Int",
"int.Int",
"set.Set"
] | examples/kleene_algebra.mlw | star_unfold_right | |
star_le : forall x y. x <= y -> !x <= !y | lemma | examples | [
"int.Int",
"int.Int",
"int.Int",
"set.Set"
] | examples/kleene_algebra.mlw | star_le | |
le_star_left_right : forall x y z. z * x <= y * z -> z * !x <= !y * z | lemma | examples | [
"int.Int",
"int.Int",
"int.Int",
"set.Set"
] | examples/kleene_algebra.mlw | le_star_left_right | |
le_star_right_left : forall x y z. x * z <= z * y -> !x * z <= z * !y | lemma | examples | [
"int.Int",
"int.Int",
"int.Int",
"set.Set"
] | examples/kleene_algebra.mlw | le_star_right_left | |
slide_left : forall x y. !(x + y) = !x * !(y * !x) | lemma | examples | [
"int.Int",
"int.Int",
"int.Int",
"set.Set"
] | examples/kleene_algebra.mlw | slide_left | |
slide_right : forall x y. !(x + y) = !(!x * y) * !x | lemma | examples | [
"int.Int",
"int.Int",
"int.Int",
"set.Set"
] | examples/kleene_algebra.mlw | slide_right | |
sum_pow_left : forall x a b. | lemma | examples | [
"int.Int",
"int.Int",
"int.Int",
"set.Set"
] | examples/kleene_algebra.mlw | sum_pow_left | |
mul_sum_pow : forall x a b. | lemma | examples | [
"int.Int",
"int.Int",
"int.Int",
"set.Set"
] | examples/kleene_algebra.mlw | mul_sum_pow | |
sum_pow_le_star : forall x a b. | lemma | examples | [
"int.Int",
"int.Int",
"int.Int",
"set.Set"
] | examples/kleene_algebra.mlw | sum_pow_le_star | |
Conway_equality : forall x n. | lemma | examples | [
"int.Int",
"int.Int",
"int.Int",
"set.Set"
] | examples/kleene_algebra.mlw | Conway_equality | |
zero_def : forall x. not mem x zero | lemma | examples | [
"int.Int",
"int.Int",
"int.Int",
"set.Set"
] | examples/kleene_algebra.mlw | zero_def |
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