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fact
string | imports
string | filename
string | symbolic_name
string | __index_level_0__
int64 |
|---|---|---|---|---|
Definition annot {A B} (a : A) (b : B) : A := a.
|
Coq.Program.Tactics Coq.Arith.PeanoNat List FunctionalExtensionality
|
coq-community-autosubst/Autosubst_Basics
|
coq-community-autosubst
| 0 |
Definition id {A} (x : A) := x.
|
Coq.Program.Tactics Coq.Arith.PeanoNat List FunctionalExtensionality
|
coq-community-autosubst/Autosubst_Basics
|
coq-community-autosubst
| 1 |
Definition var := nat.
|
Coq.Program.Tactics Coq.Arith.PeanoNat List FunctionalExtensionality
|
coq-community-autosubst/Autosubst_Basics
|
coq-community-autosubst
| 2 |
Definition iterate := fix iterate {A} (f : A -> A) n a := match n with | 0 => a | S n' => f(iterate f n' a) end.
|
Coq.Program.Tactics Coq.Arith.PeanoNat List FunctionalExtensionality
|
coq-community-autosubst/Autosubst_Basics
|
coq-community-autosubst
| 3 |
Definition funcomp {A B C : Type} (f : A -> B) (g : B -> C) x := g(f(x)).
|
Coq.Program.Tactics Coq.Arith.PeanoNat List FunctionalExtensionality
|
coq-community-autosubst/Autosubst_Basics
|
coq-community-autosubst
| 4 |
Definition scons {X : Type} (s : X) (sigma : var -> X) (x : var) : X := match x with S y => sigma y | _ => s end.
|
Coq.Program.Tactics Coq.Arith.PeanoNat List FunctionalExtensionality
|
coq-community-autosubst/Autosubst_Basics
|
coq-community-autosubst
| 5 |
Definition lift (x y : var) : var := plus x y.
|
Coq.Program.Tactics Coq.Arith.PeanoNat List FunctionalExtensionality
|
coq-community-autosubst/Autosubst_Basics
|
coq-community-autosubst
| 6 |
Variable (A B C : Type).
|
Autosubst_Basics Autosubst_MMap
|
coq-community-autosubst/Autosubst_MMapInstances
|
coq-community-autosubst
| 7 |
Variable (MMap_A_B : MMap A B).
|
Autosubst_Basics Autosubst_MMap
|
coq-community-autosubst/Autosubst_MMapInstances
|
coq-community-autosubst
| 8 |
Variable (MMap_A_C : MMap A C).
|
Autosubst_Basics Autosubst_MMap
|
coq-community-autosubst/Autosubst_MMapInstances
|
coq-community-autosubst
| 9 |
Variable (MMapLemmas_A_B : MMapLemmas A B).
|
Autosubst_Basics Autosubst_MMap
|
coq-community-autosubst/Autosubst_MMapInstances
|
coq-community-autosubst
| 10 |
Variable (MMapLemmas_A_C : MMapLemmas A C).
|
Autosubst_Basics Autosubst_MMap
|
coq-community-autosubst/Autosubst_MMapInstances
|
coq-community-autosubst
| 11 |
Variable (MMapExt_A_B : MMapExt A B).
|
Autosubst_Basics Autosubst_MMap
|
coq-community-autosubst/Autosubst_MMapInstances
|
coq-community-autosubst
| 12 |
Variable (MMapExt_A_C : MMapExt A C).
|
Autosubst_Basics Autosubst_MMap
|
coq-community-autosubst/Autosubst_MMapInstances
|
coq-community-autosubst
| 13 |
Definition _bind (T1 : Type) (T2 : Type) (n : nat) := T2.
|
Autosubst_Basics Autosubst_MMap
|
coq-community-autosubst/Autosubst_Classes
|
coq-community-autosubst
| 14 |
Definition scomp {A} `{Subst A} (f : var -> A) (g : var -> A) : var -> A := f >>> subst g.
|
Autosubst_Basics Autosubst_MMap
|
coq-community-autosubst/Autosubst_Classes
|
coq-community-autosubst
| 15 |
Definition hcomp {A B} `{HSubst A B} (f : var -> B) (g : var -> A) : var -> B := f >>> hsubst g.
|
Autosubst_Basics Autosubst_MMap
|
coq-community-autosubst/Autosubst_Classes
|
coq-community-autosubst
| 16 |
Definition ren {T} `{Ids T} (xi : var -> var) : var -> T := xi >>> ids.
|
Autosubst_Basics Autosubst_MMap
|
coq-community-autosubst/Autosubst_Classes
|
coq-community-autosubst
| 17 |
Definition up {T} `{Ids T} `{Rename T} (sigma : var -> T) : var -> T := ids 0 .: sigma >>> rename (+1).
|
Autosubst_Basics Autosubst_MMap
|
coq-community-autosubst/Autosubst_Classes
|
coq-community-autosubst
| 18 |
Definition upren (xi : var -> var) : (var -> var) := 0 .: xi >>> S.
|
Autosubst_Basics Autosubst_MMap
|
coq-community-autosubst/Autosubst_Classes
|
coq-community-autosubst
| 19 |
Axiom Pigeon_In_Hole : nat -> nat -> Prop.
|
List
|
fbesson-itauto/benchmark/pigeon_hole
|
fbesson-itauto
| 20 |
Definition cons_option {A: Type} (e: option A) (l: list A) := match e with | None => l | Some v => v:: l end.
|
List
|
fbesson-itauto/benchmark/pigeon_hole
|
fbesson-itauto
| 21 |
Fixpoint map_n (F: nat -> option Prop) (n: nat) := cons_option (F n) (match n with | O => nil | S n' => map_n F n' end).
|
List
|
fbesson-itauto/benchmark/pigeon_hole
|
fbesson-itauto
| 22 |
Fixpoint or_list (l: list Prop) := match l with | nil => False | e::nil => e | e::l => e \/ or_list l end.
|
List
|
fbesson-itauto/benchmark/pigeon_hole
|
fbesson-itauto
| 23 |
Fixpoint and_list (l: list Prop) := match l with | nil => True | e::nil => e | e::l => e /\ and_list l end.
|
List
|
fbesson-itauto/benchmark/pigeon_hole
|
fbesson-itauto
| 24 |
Definition big_or (n:nat) (F: nat -> option Prop) := or_list (map_n F n).
|
List
|
fbesson-itauto/benchmark/pigeon_hole
|
fbesson-itauto
| 25 |
Definition big_and (n:nat) (F: nat -> option Prop) := and_list (map_n F n).
|
List
|
fbesson-itauto/benchmark/pigeon_hole
|
fbesson-itauto
| 26 |
Fixpoint pigeon_in_hole (b:nat) (n:nat) : Prop := (big_or n (fun n => Some (Pigeon_In_Hole b n)) /\ match b with | O => True | S b' => pigeon_in_hole b' n end).
|
List
|
fbesson-itauto/benchmark/pigeon_hole
|
fbesson-itauto
| 27 |
Fixpoint forall_2 (P : nat -> nat -> option Prop) (i:nat) (j:nat) := big_and j (P i) /\ match i with | O => True | S i' => forall_2 P i' j end.
|
List
|
fbesson-itauto/benchmark/pigeon_hole
|
fbesson-itauto
| 28 |
Definition at_most_one_pigeon_per_hole (dis:bool) (b:nat) (k:nat) := let F i j := if dis then (not (Pigeon_In_Hole i k) \/ not (Pigeon_In_Hole j k)) else (Pigeon_In_Hole i k -> Pigeon_In_Hole j k -> False) in Some (forall_2 (fun i j => if Nat.ltb i j then Some (F i j) else None) b b).
|
List
|
fbesson-itauto/benchmark/pigeon_hole
|
fbesson-itauto
| 29 |
Definition at_most_one_pigeon (dis: bool) (b:nat) (n:nat) := big_and n (at_most_one_pigeon_per_hole dis b).
|
List
|
fbesson-itauto/benchmark/pigeon_hole
|
fbesson-itauto
| 30 |
Definition pigeon_hole (dis: bool) (b:nat) (n:nat) := pigeon_in_hole b n /\ at_most_one_pigeon dis b n.
|
List
|
fbesson-itauto/benchmark/pigeon_hole
|
fbesson-itauto
| 31 |
Axiom width: Z.
|
Lia ZArith Cdcl.Itauto
|
fbesson-itauto/issues/issue_9
|
fbesson-itauto
| 32 |
Fixpoint compile(program: nat): list Z := match program with | S n => Z.of_nat n :: compile n | O => nil end.
|
ZArith List Cdcl.Itauto
|
fbesson-itauto/issues/issue_2
|
fbesson-itauto
| 33 |
Axiom F: list Z -> list Z.
|
ZArith List Cdcl.Itauto
|
fbesson-itauto/issues/issue_2
|
fbesson-itauto
| 34 |
Axiom X : Type.
|
ZArith List Cdcl.Itauto
|
fbesson-itauto/issues/issue_2
|
fbesson-itauto
| 35 |
Axiom x : X.
|
ZArith List Cdcl.Itauto
|
fbesson-itauto/issues/issue_2
|
fbesson-itauto
| 36 |
Axiom opaque_compile: nat -> list Z.
|
ZArith List Cdcl.Itauto
|
fbesson-itauto/issues/issue_2
|
fbesson-itauto
| 37 |
Variables A B : Set.
|
Cdcl.Itauto List ZArith Lia
|
fbesson-itauto/issues/issue_cc
|
fbesson-itauto
| 39 |
Variable P : A -> bool.
|
Cdcl.Itauto List ZArith Lia
|
fbesson-itauto/issues/issue_cc
|
fbesson-itauto
| 40 |
Variable R : A -> B -> Prop.
|
Cdcl.Itauto List ZArith Lia
|
fbesson-itauto/issues/issue_cc
|
fbesson-itauto
| 41 |
Definition Q (b : B) (r : A) := P r = true -> R r b.
|
Cdcl.Itauto List ZArith Lia
|
fbesson-itauto/issues/issue_cc
|
fbesson-itauto
| 42 |
Variable F : nat -> Prop.
|
Lia ZArith Cdcl.Itauto
|
fbesson-itauto/issues/issue_12
|
fbesson-itauto
| 43 |
Fixpoint orn (n : nat) := match n with | O => F 0 | S m => F n \/ orn m end.
|
Lia ZArith Cdcl.Itauto
|
fbesson-itauto/issues/issue_12
|
fbesson-itauto
| 44 |
Axiom Fbad : forall n, F n -> False.
|
Lia ZArith Cdcl.Itauto
|
fbesson-itauto/issues/issue_12
|
fbesson-itauto
| 45 |
Definition Register := Z.
|
Lia ZArith Cdcl.Itauto
|
fbesson-itauto/issues/issue_8
|
fbesson-itauto
| 46 |
Record ok (n: nat) := { getOk1: n <= 10 }.
|
Cdcl.Itauto Lia
|
fbesson-itauto/issues/issue_3
|
fbesson-itauto
| 47 |
Record ok' := { getP: Prop; getOk': getP }.
|
Cdcl.Itauto Lia
|
fbesson-itauto/issues/issue_3
|
fbesson-itauto
| 48 |
Definition block (A: Prop) := A.
|
Cdcl.Itauto
|
fbesson-itauto/issues/cnf
|
fbesson-itauto
| 49 |
Axiom word: Type.
|
Lia ZArith Cdcl.Itauto
|
fbesson-itauto/issues/issue_10
|
fbesson-itauto
| 51 |
Axiom w2z : word -> Z.
|
Lia ZArith Cdcl.Itauto
|
fbesson-itauto/issues/issue_10
|
fbesson-itauto
| 52 |
Axiom z2w : Z -> word.
|
Lia ZArith Cdcl.Itauto
|
fbesson-itauto/issues/issue_10
|
fbesson-itauto
| 53 |
Axiom stmt: Type.
|
Cdcl.Itauto Uint63 Bool ZArith Lia Coq.Lists.List Coq.ZArith.ZArith Coq.micromega.Lia
|
fbesson-itauto/test-suite/arith
|
fbesson-itauto
| 55 |
Axiom stackalloc_size: stmt -> Z.
|
Cdcl.Itauto Uint63 Bool ZArith Lia Coq.Lists.List Coq.ZArith.ZArith Coq.micromega.Lia
|
fbesson-itauto/test-suite/arith
|
fbesson-itauto
| 56 |
Axiom bytes_per_word: Z.
|
Cdcl.Itauto Uint63 Bool ZArith Lia Coq.Lists.List Coq.ZArith.ZArith Coq.micromega.Lia
|
fbesson-itauto/test-suite/arith
|
fbesson-itauto
| 57 |
Axiom list_union: forall {A: Type}, (A -> A -> bool) -> list A -> list A -> list A.
|
Cdcl.Itauto Uint63 Bool ZArith Lia Coq.Lists.List Coq.ZArith.ZArith Coq.micromega.Lia
|
fbesson-itauto/test-suite/arith
|
fbesson-itauto
| 58 |
Axiom modVars_as_list: (Z -> Z -> bool) -> stmt -> list Z.
|
Cdcl.Itauto Uint63 Bool ZArith Lia Coq.Lists.List Coq.ZArith.ZArith Coq.micromega.Lia
|
fbesson-itauto/test-suite/arith
|
fbesson-itauto
| 59 |
Axiom of_Z: Z -> word.
|
Cdcl.Itauto Uint63 Bool ZArith Lia Coq.Lists.List Coq.ZArith.ZArith Coq.micromega.Lia
|
fbesson-itauto/test-suite/arith
|
fbesson-itauto
| 60 |
Variable f : nat -> nat.
|
ZArith List Lia ZifyClasses Cdcl.NOlia
|
fbesson-itauto/test-suite/no_test_lia
|
fbesson-itauto
| 61 |
Axiom f : nat -> nat.
|
ZArith List Lia ZifyClasses Cdcl.NOlia
|
fbesson-itauto/test-suite/no_test_lia
|
fbesson-itauto
| 62 |
Variable f : R -> R.
|
ZArith List Lra ZifyClasses ZArith Cdcl.NOlra Reals
|
fbesson-itauto/test-suite/no_test_lra
|
fbesson-itauto
| 63 |
Axiom f : R -> R.
|
ZArith List Lra ZifyClasses ZArith Cdcl.NOlra Reals
|
fbesson-itauto/test-suite/no_test_lra
|
fbesson-itauto
| 64 |
Definition zero := 0%uint63.
|
Bool ZifyClasses ZifyUint63 ZArith Lia Cdcl.PatriciaR
|
fbesson-itauto/theories/KeyInt
|
fbesson-itauto
| 65 |
Definition one := 1%uint63.
|
Bool ZifyClasses ZifyUint63 ZArith Lia Cdcl.PatriciaR
|
fbesson-itauto/theories/KeyInt
|
fbesson-itauto
| 66 |
Definition int_of_nat (n:nat) := Uint63.of_Z (Z.of_nat n).
|
Bool ZifyClasses ZifyUint63 ZArith Lia Cdcl.PatriciaR
|
fbesson-itauto/theories/KeyInt
|
fbesson-itauto
| 67 |
Definition testbit (i:Uint63.int) (n:nat) := if 63 <=? n then false else Uint63.bit i (int_of_nat n).
|
Bool ZifyClasses ZifyUint63 ZArith Lia Cdcl.PatriciaR
|
fbesson-itauto/theories/KeyInt
|
fbesson-itauto
| 68 |
Definition interp:= (fun i => (Uint63.sub i one)).
|
Bool ZifyClasses ZifyUint63 ZArith Lia Cdcl.PatriciaR
|
fbesson-itauto/theories/KeyInt
|
fbesson-itauto
| 69 |
Definition is_mask := (fun (m: Uint63.int) (n: nat) => forall p, testbit m p = true <-> n = p).
|
Bool ZifyClasses ZifyUint63 ZArith Lia Cdcl.PatriciaR
|
fbesson-itauto/theories/KeyInt
|
fbesson-itauto
| 70 |
Variable P : nat -> bool.
|
Bool ZifyClasses ZifyUint63 ZArith Lia Cdcl.PatriciaR
|
fbesson-itauto/theories/KeyInt
|
fbesson-itauto
| 71 |
Fixpoint forall_n (n:nat) : bool := match n with | O => P O | S n' => P n && forall_n n' end.
|
Bool ZifyClasses ZifyUint63 ZArith Lia Cdcl.PatriciaR
|
fbesson-itauto/theories/KeyInt
|
fbesson-itauto
| 72 |
Variable P : nat -> nat -> bool.
|
Bool ZifyClasses ZifyUint63 ZArith Lia Cdcl.PatriciaR
|
fbesson-itauto/theories/KeyInt
|
fbesson-itauto
| 73 |
Fixpoint forall_2n (n:nat) (m:nat) := match n with | O => forall_n (P O) m | S n' => forall_n (P n) m && forall_2n n' m end.
|
Bool ZifyClasses ZifyUint63 ZArith Lia Cdcl.PatriciaR
|
fbesson-itauto/theories/KeyInt
|
fbesson-itauto
| 74 |
Definition mask_spec : forall m n, is_mask m n -> if 63 <=? n then False else m = Uint63.lsl one (int_of_nat n).
|
Bool ZifyClasses ZifyUint63 ZArith Lia Cdcl.PatriciaR
|
fbesson-itauto/theories/KeyInt
|
fbesson-itauto
| 75 |
Definition ones (n:int) := ((1 << n) - 1)%uint63.
|
Bool ZifyClasses ZifyUint63 ZArith Lia Cdcl.PatriciaR
|
fbesson-itauto/theories/KeyInt
|
fbesson-itauto
| 76 |
Definition split_m (i: int) (m: int) := ( (i land ((ones digits) << m)) lor ((i land (ones m))))%uint63.
|
Bool ZifyClasses ZifyUint63 ZArith Lia Cdcl.PatriciaR
|
fbesson-itauto/theories/KeyInt
|
fbesson-itauto
| 77 |
Definition is_set (k:int) (m:nat) := (forall p, (p < m)%nat -> testbit k p = false) /\ testbit k m = true.
|
Bool ZifyClasses ZifyUint63 ZArith Lia Cdcl.PatriciaR
|
fbesson-itauto/theories/KeyInt
|
fbesson-itauto
| 78 |
Definition is_set_int (k:int) (m:int) := (forall p, (p <? m = true)%uint63 -> bit k p = false) /\ bit k m = true.
|
Bool ZifyClasses ZifyUint63 ZArith Lia Cdcl.PatriciaR
|
fbesson-itauto/theories/KeyInt
|
fbesson-itauto
| 79 |
Definition nat_of_int (i:int) := Z.to_nat (to_Z i).
|
Bool ZifyClasses ZifyUint63 ZArith Lia Cdcl.PatriciaR
|
fbesson-itauto/theories/KeyInt
|
fbesson-itauto
| 80 |
Definition not_int (x : int) := (- x - 1)%uint63.
|
Bool ZifyClasses ZifyUint63 ZArith Lia Cdcl.PatriciaR
|
fbesson-itauto/theories/KeyInt
|
fbesson-itauto
| 81 |
Definition bit_excl (x y: int) := (forall n : int, bit x n = true -> bit y n = true -> False).
|
Bool ZifyClasses ZifyUint63 ZArith Lia Cdcl.PatriciaR
|
fbesson-itauto/theories/KeyInt
|
fbesson-itauto
| 82 |
Definition lowest_bit (x: int) := (x land (opp x))%uint63.
|
Bool ZifyClasses ZifyUint63 ZArith Lia Cdcl.PatriciaR
|
fbesson-itauto/theories/KeyInt
|
fbesson-itauto
| 83 |
Fixpoint find_lowest (n: nat) (k: int) (p: nat) := match p with | O => n | S q => if testbit k (n - p)%nat then (n - p)%nat else find_lowest n k q end.
|
Bool ZifyClasses ZifyUint63 ZArith Lia Cdcl.PatriciaR
|
fbesson-itauto/theories/KeyInt
|
fbesson-itauto
| 84 |
Definition digits := Some 63%nat.
|
Bool ZifyClasses ZifyUint63 ZArith Lia Cdcl.PatriciaR
|
fbesson-itauto/theories/KeyInt
|
fbesson-itauto
| 85 |
Record RarithThy : Type.
|
Cdcl.Itauto ZifyClasses Lra Reals
|
fbesson-itauto/theories/NOlra
|
fbesson-itauto
| 86 |
Axiom t: Type.
|
Lia Cdcl.Coqlib
|
fbesson-itauto/theories/Patricia
|
fbesson-itauto
| 87 |
Axiom zero: t.
|
Lia Cdcl.Coqlib
|
fbesson-itauto/theories/Patricia
|
fbesson-itauto
| 88 |
Axiom eqb: t -> t -> bool.
|
Lia Cdcl.Coqlib
|
fbesson-itauto/theories/Patricia
|
fbesson-itauto
| 89 |
Axiom testbit: t -> nat -> bool.
|
Lia Cdcl.Coqlib
|
fbesson-itauto/theories/Patricia
|
fbesson-itauto
| 90 |
Axiom interp: t -> t.
|
Lia Cdcl.Coqlib
|
fbesson-itauto/theories/Patricia
|
fbesson-itauto
| 91 |
Axiom land: t -> t -> t.
|
Lia Cdcl.Coqlib
|
fbesson-itauto/theories/Patricia
|
fbesson-itauto
| 92 |
Axiom lxor: t -> t -> t.
|
Lia Cdcl.Coqlib
|
fbesson-itauto/theories/Patricia
|
fbesson-itauto
| 93 |
Axiom lopp: t -> t.
|
Lia Cdcl.Coqlib
|
fbesson-itauto/theories/Patricia
|
fbesson-itauto
| 94 |
Axiom ltb: t -> t -> bool.
|
Lia Cdcl.Coqlib
|
fbesson-itauto/theories/Patricia
|
fbesson-itauto
| 95 |
Definition is_mask (m: t) (n: nat) := forall p, testbit m p = true <-> n = p.
|
Lia Cdcl.Coqlib
|
fbesson-itauto/theories/Patricia
|
fbesson-itauto
| 96 |
Axiom zero_spec: forall n, testbit zero n = false.
|
Lia Cdcl.Coqlib
|
fbesson-itauto/theories/Patricia
|
fbesson-itauto
| 97 |
Axiom eqb_spec : forall k1 k2, eqb k1 k2 = true <-> k1 = k2.
|
Lia Cdcl.Coqlib
|
fbesson-itauto/theories/Patricia
|
fbesson-itauto
| 98 |
Axiom testbit_spec: forall k1 k2, (forall n, testbit k1 n = testbit k2 n) -> k1 = k2.
|
Lia Cdcl.Coqlib
|
fbesson-itauto/theories/Patricia
|
fbesson-itauto
| 99 |
Axiom interp_spec: forall m n, is_mask m n -> forall p, testbit (interp m) p = true <-> (p < n)%nat.
|
Lia Cdcl.Coqlib
|
fbesson-itauto/theories/Patricia
|
fbesson-itauto
| 100 |
Axiom land_spec: forall n k1 k2, testbit (land k1 k2) n = testbit k1 n && testbit k2 n.
|
Lia Cdcl.Coqlib
|
fbesson-itauto/theories/Patricia
|
fbesson-itauto
| 101 |
Axiom lxor_spec: forall n k1 k2, testbit (lxor k1 k2) n = xorb (testbit k1 n) (testbit k2 n).
|
Lia Cdcl.Coqlib
|
fbesson-itauto/theories/Patricia
|
fbesson-itauto
| 102 |
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