fact stringlengths 6 2.88k | type stringclasses 17
values | library stringclasses 2
values | imports listlengths 0 16 | filename stringclasses 89
values | symbolic_name stringlengths 1 36 | docstring stringclasses 1
value |
|---|---|---|---|---|---|---|
morphism_1aF rF := forall x, f (aF x) = rF (f x). | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | morphism_1 | |
morphism_2aOp rOp := forall x y, f (aOp x y) = rOp (f x) (f y). | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | morphism_2 | |
homomorphism_1(aP rP : _ -> Prop) := forall x, aP x -> rP (f x). | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | homomorphism_1 | |
homomorphism_2(aR rR : _ -> _ -> Prop) :=
forall x y, aR x y -> rR (f x) (f y). | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | homomorphism_2 | |
monomorphism_1(aP rP : _ -> sT) := forall x, rP (f x) = aP x. | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | monomorphism_1 | |
monomorphism_2(aR rR : _ -> _ -> sT) :=
forall x y, rR (f x) (f y) = aR x y. | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | monomorphism_2 | |
injective:= forall x1 x2, f x1 = f x2 -> x1 = x2. | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | injective | |
cancelg := forall x, g (f x) = x. | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | cancel | |
pcancelg := forall x, g (f x) = Some x. | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | pcancel | |
ocancel(g : aT -> option rT) h := forall x, oapp h x (g x) = x. | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | ocancel | |
can_pcang : cancel g -> pcancel (fun y => Some (g y)).
Proof. by move=> fK x; congr (Some _). Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | can_pcan | |
pcan_injg : pcancel g -> injective.
Proof. by move=> fK x y /(congr1 g); rewrite !fK => [[]]. Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | pcan_inj | |
can_injg : cancel g -> injective.
Proof. by move/can_pcan; apply: pcan_inj. Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | can_inj | |
canLRg x y : cancel g -> x = f y -> g x = y.
Proof. by move=> fK ->. Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | canLR | |
canRLg x y : cancel g -> f x = y -> x = g y.
Proof. by move=> fK <-. Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | canRL | |
injective2(rT aT1 aT2 : Type) (f : aT1 -> aT2 -> rT) :=
forall (x1 x2 : aT1) (y1 y2 : aT2), f x1 y1 = f x2 y2 ->
(x1 = x2) * (y1 = y2).
Arguments injective2 [rT aT1 aT2] f. | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | injective2 | |
Some_inj{T : nonPropType} : injective (@Some T).
Proof. by move=> x y []. Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | Some_inj | |
inj_omap{aT rT : Type} (f : aT -> rT) :
injective f -> injective (omap f).
Proof. by move=> injf [?|] [?|] //= [/injf->]. Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | inj_omap | |
omapK{aT rT : Type} (f : aT -> rT) (g : rT -> aT) :
cancel f g -> cancel (omap f) (omap g).
Proof. by move=> fK [?|] //=; rewrite fK. Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | omapK | |
of_voidKT : pcancel (of_void T) [fun _ => None].
Proof. by case. Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | of_voidK | |
esymKT x y : cancel (@esym T x y) (@esym T y x).
Proof. by case: y /. Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | esymK | |
etrans_idT x y (eqxy : x = y :> T) : etrans (erefl x) eqxy = eqxy.
Proof. by case: y / eqxy. Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | etrans_id | |
inj_id: injective (@id A).
Proof. by []. Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | inj_id | |
inj_can_symf' : cancel f f' -> injective f' -> cancel f' f.
Proof. by move=> fK injf' x; apply: injf'. Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | inj_can_sym | |
inj_comp: injective f -> injective h -> injective (f \o h).
Proof. by move=> injf injh x y /injf; apply: injh. Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | inj_comp | |
inj_compr: injective (f \o h) -> injective h.
Proof. by move=> injfh x y /(congr1 f) /injfh. Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | inj_compr | |
can_compf' h' : cancel f f' -> cancel h h' -> cancel (f \o h) (h' \o f').
Proof. by move=> fK hK x; rewrite /= fK hK. Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | can_comp | |
pcan_pcompf' h' :
pcancel f f' -> pcancel h h' -> pcancel (f \o h) (pcomp h' f').
Proof. by move=> fK hK x; rewrite /pcomp fK /= hK. Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | pcan_pcomp | |
ocan_comp[fo : B -> option A] [ho : C -> option B]
[f' : A -> B] [h' : B -> C] :
ocancel fo f' -> ocancel ho h' -> ocancel (obind fo \o ho) (h' \o f').
Proof.
move=> fK hK c /=; rewrite -[RHS]hK/=; case hcE : (ho c) => [b|]//=.
by rewrite -[b in RHS]fK; case: (fo b) => //=; have := hK c; rewrite hcE.
Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | ocan_comp | |
eq_inj: injective f -> f =1 g -> injective g.
Proof. by move=> injf eqfg x y; rewrite -2!eqfg; apply: injf. Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | eq_inj | |
eq_canf' g' : cancel f f' -> f =1 g -> f' =1 g' -> cancel g g'.
Proof. by move=> fK eqfg eqfg' x; rewrite -eqfg -eqfg'. Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | eq_can | |
inj_can_eqf' : cancel f f' -> injective f' -> cancel g f' -> f =1 g.
Proof. by move=> fK injf' gK x; apply: injf'; rewrite fK. Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | inj_can_eq | |
bijective: Prop := Bijective g of cancel f g & cancel g f.
Hypothesis bijf : bijective. | Variant | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | bijective | |
bij_inj: injective f.
Proof. by case: bijf => g fK _; apply: can_inj fK. Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | bij_inj | |
bij_can_symf' : cancel f' f <-> cancel f f'.
Proof.
split=> fK; first exact: inj_can_sym fK bij_inj.
by case: bijf => h _ hK x; rewrite -[x]hK fK.
Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | bij_can_sym | |
bij_can_eqf' f'' : cancel f f' -> cancel f f'' -> f' =1 f''.
Proof.
by move=> fK fK'; apply: (inj_can_eq _ bij_inj); apply/bij_can_sym.
Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | bij_can_eq | |
eq_bij: bijective f -> forall g, f =1 g -> bijective g.
Proof. by case=> f' fK f'K g eqfg; exists f'; eapply eq_can; eauto. Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | eq_bij | |
bij_comp: bijective f -> bijective h -> bijective (f \o h).
Proof.
by move=> [f' fK f'K] [h' hK h'K]; exists (h' \o f'); apply: can_comp; auto.
Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | bij_comp | |
bij_can_bij: bijective f -> forall f', cancel f f' -> bijective f'.
Proof. by move=> bijf; exists f; first by apply/(bij_can_sym bijf). Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | bij_can_bij | |
involutive:= cancel f f.
Hypothesis Hf : involutive. | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | involutive | |
inv_inj: injective f. Proof. exact: can_inj Hf. Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | inv_inj | |
inv_bij: bijective f. Proof. by exists f. Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | inv_bij | |
left_inversee inv op := forall x, op (inv x) x = e. | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | left_inverse | |
right_inversee inv op := forall x, op x (inv x) = e. | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | right_inverse | |
left_injectiveop := forall x, injective (op^~ x). | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | left_injective | |
right_injectiveop := forall y, injective (op y). | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | right_injective | |
right_ide op := forall x, op x e = x. | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | right_id | |
left_zeroz op := forall x, op z x = z. | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | left_zero | |
right_commutativeop := forall x y z, op (op x y) z = op (op x z) y. | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | right_commutative | |
left_distributiveop add :=
forall x y z, op (add x y) z = add (op x z) (op y z). | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | left_distributive | |
right_loopinv op := forall y, cancel (op^~ y) (op^~ (inv y)). | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | right_loop | |
rev_right_loopinv op := forall y, cancel (op^~ (inv y)) (op^~ y). | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | rev_right_loop | |
left_ide op := forall x, op e x = x. | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | left_id | |
right_zeroz op := forall x, op x z = z. | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | right_zero | |
left_commutativeop := forall x y z, op x (op y z) = op y (op x z). | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | left_commutative | |
right_distributiveop add :=
forall x y z, op x (add y z) = add (op x y) (op x z). | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | right_distributive | |
left_loopinv op := forall x, cancel (op x) (op (inv x)). | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | left_loop | |
rev_left_loopinv op := forall x, cancel (op (inv x)) (op x). | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | rev_left_loop | |
self_inversee op := forall x, op x x = e. | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | self_inverse | |
commutativeop := forall x y, op x y = op y x. | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | commutative | |
idempotent_opop := forall x, op x x = x. | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | idempotent_op | |
associativeop := forall x y z, op x (op y z) = op (op x y) z. | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | associative | |
interchangeop1 op2 :=
forall x y z t, op1 (op2 x y) (op2 z t) = op2 (op1 x z) (op1 y t). | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | interchange | |
idempotent_fun(U : Type) (f : U -> U) := f \o f =1 f. | Definition | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | idempotent_fun | |
inr_inj{A B} : injective (@inr A B). Proof. by move=> ? ? []. Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | inr_inj | |
inl_inj{A B} : injective (@inl A B). Proof. by move=> ? ? []. Qed. | Lemma | Corelib | [
"Require Import ssreflect"
] | Corelib/ssr/ssrfun.v | inl_inj | |
compat_Reflexive:
forall {A} {R : relation A},
RelationClasses.Reflexive R ->
ssrclasses.Reflexive R | 12.
Proof. now trivial. Qed. | Instance | Corelib | [
"Require Import ssrclasses",
"Require Import ssrunder",
"Require Import RelationClasses",
"Require Import Relation_Definitions"
] | Corelib/ssr/ssrsetoid.v | compat_Reflexive | |
Under_rel:
forall (A : Type) (eqA : A -> A -> Prop), A -> A -> Prop. | Parameter | Corelib | [
"Require Import ssrclasses"
] | Corelib/ssr/ssrunder.v | Under_rel | |
Under_rel_from_rel:
forall (A : Type) (eqA : A -> A -> Prop) (x y : A),
@Under_rel A eqA x y -> eqA x y. | Parameter | Corelib | [
"Require Import ssrclasses"
] | Corelib/ssr/ssrunder.v | Under_rel_from_rel | |
Under_relE:
forall (A : Type) (eqA : A -> A -> Prop),
@Under_rel A eqA = eqA. | Parameter | Corelib | [
"Require Import ssrclasses"
] | Corelib/ssr/ssrunder.v | Under_relE | |
Over_rel:
forall (A : Type) (eqA : A -> A -> Prop), A -> A -> Prop. | Parameter | Corelib | [
"Require Import ssrclasses"
] | Corelib/ssr/ssrunder.v | Over_rel | |
over_rel:
forall (A : Type) (eqA : A -> A -> Prop) (x y : A),
@Under_rel A eqA x y = @Over_rel A eqA x y. | Parameter | Corelib | [
"Require Import ssrclasses"
] | Corelib/ssr/ssrunder.v | over_rel | |
over_rel_done:
forall (A : Type) (eqA : A -> A -> Prop) (EeqA : Reflexive eqA) (x : A),
@Over_rel A eqA x x. | Parameter | Corelib | [
"Require Import ssrclasses"
] | Corelib/ssr/ssrunder.v | over_rel_done | |
under_rel_done:
forall (A : Type) (eqA : A -> A -> Prop) (EeqA : Reflexive eqA) (x : A),
@Under_rel A eqA x x. | Parameter | Corelib | [
"Require Import ssrclasses"
] | Corelib/ssr/ssrunder.v | under_rel_done | |
Under_rel(A : Type) (eqA : A -> A -> Prop) :=
eqA. | Definition | Corelib | [
"Require Import ssrclasses"
] | Corelib/ssr/ssrunder.v | Under_rel | |
Under_rel_from_rel:
forall (A : Type) (eqA : A -> A -> Prop) (x y : A),
@Under_rel A eqA x y -> eqA x y.
Proof. now trivial. Qed. | Lemma | Corelib | [
"Require Import ssrclasses"
] | Corelib/ssr/ssrunder.v | Under_rel_from_rel | |
Under_relE(A : Type) (eqA : A -> A -> Prop) :
@Under_rel A eqA = eqA.
Proof. now trivial. Qed. | Lemma | Corelib | [
"Require Import ssrclasses"
] | Corelib/ssr/ssrunder.v | Under_relE | |
Over_rel:= Under_rel. | Definition | Corelib | [
"Require Import ssrclasses"
] | Corelib/ssr/ssrunder.v | Over_rel | |
over_rel:
forall (A : Type) (eqA : A -> A -> Prop) (x y : A),
@Under_rel A eqA x y = @Over_rel A eqA x y.
Proof. now trivial. Qed. | Lemma | Corelib | [
"Require Import ssrclasses"
] | Corelib/ssr/ssrunder.v | over_rel | |
over_rel_done:
forall (A : Type) (eqA : A -> A -> Prop) (EeqA : Reflexive eqA) (x : A),
@Over_rel A eqA x x.
Proof. now unfold Over_rel. Qed. | Lemma | Corelib | [
"Require Import ssrclasses"
] | Corelib/ssr/ssrunder.v | over_rel_done | |
under_rel_done:
forall (A : Type) (eqA : A -> A -> Prop) (EeqA : Reflexive eqA) (x : A),
@Under_rel A eqA x x.
Proof. now trivial. Qed. | Lemma | Corelib | [
"Require Import ssrclasses"
] | Corelib/ssr/ssrunder.v | under_rel_done | |
char63:= int.
Primitive string := #string_type.
Primitive max_length : int := #string_max_length.
Primitive make : int -> char63 -> string := #string_make.
Primitive length : string -> int := #string_length.
Primitive get : string -> int -> char63 := #string_get.
Primitive sub : string -> int -> int -> string := ... | Definition | Corelib | [
"Require Import PrimInt63"
] | Corelib/Strings/PrimString.v | char63 | |
eqb(s1 s2 : string) := match compare s1 s2 with
| Eq => true
| Lt | Gt => false
end.
Register eqb as strings.pstring.eqb. | Definition | Corelib | [
"Require Import PrimInt63"
] | Corelib/Strings/PrimString.v | eqb | |
string_wrapper:= wrap_string {string_wrap : string}. | Record | Corelib | [
"Require Import PrimInt63"
] | Corelib/Strings/PrimString.v | string_wrapper | |
id_string(s : string) : string := s.
Register string as strings.pstring.type.
Register string_wrapper as strings.pstring.string_wrapper.
Register wrap_string as strings.pstring.wrap_string.
Declare Scope pstring_scope.
Delimit Scope pstring_scope with pstring.
Bind Scope pstring_scope with string.
String... | Definition | Corelib | [
"Require Import PrimInt63"
] | Corelib/Strings/PrimString.v | id_string | |
char63_wrapper:= wrap_char63 { char63_wrap : char63 }. | Record | Corelib | [
"Require Import PrimInt63"
] | Corelib/Strings/PrimString.v | char63_wrapper | |
char63_wrap: char63_wrapper >-> char63. | Coercion | Corelib | [
"Require Import PrimInt63"
] | Corelib/Strings/PrimString.v | char63_wrap | |
parse(s : string) : option char63_wrapper :=
if PrimInt63.eqb (length s) 1%uint63 then Some (wrap_char63 (get s 0)) else None. | Definition | Corelib | [
"Require Import PrimInt63"
] | Corelib/Strings/PrimString.v | parse | |
print(i : char63_wrapper) : option string :=
if PrimInt63.ltb i.(char63_wrap) 256%uint63 then Some (make 1 i.(char63_wrap)) else None.
Declare Scope char63_scope.
Delimit Scope char63_scope with char63.
Bind Scope char63_scope with char63.
String Notation char63_wrapper parse print : char63_scope. | Definition | Corelib | [
"Require Import PrimInt63"
] | Corelib/Strings/PrimString.v | print | |
char63_valid(c : char63) :=
PrimInt63.land c 255%uint63 = c. | Definition | Corelib | [
"From Corelib Require Import BinNums PosDef IntDef ListDef",
"From Corelib Require Export PrimInt63 Uint63Axioms",
"From Corelib Require Export PrimString"
] | Corelib/Strings/PrimStringAxioms.v | char63_valid | |
to_list(s : string) : list char63 :=
ListDef.map (fun i => get s (of_nat i)) (ListDef.seq 0 (to_nat (length s))). | Definition | Corelib | [
"From Corelib Require Import BinNums PosDef IntDef ListDef",
"From Corelib Require Export PrimInt63 Uint63Axioms",
"From Corelib Require Export PrimString"
] | Corelib/Strings/PrimStringAxioms.v | to_list | |
of_list(cs : list char63) : string :=
match cs with
| nil => ""%pstring
| cons c cs => cat (make 1 c) (of_list cs)
end. | Fixpoint | Corelib | [
"From Corelib Require Import BinNums PosDef IntDef ListDef",
"From Corelib Require Export PrimInt63 Uint63Axioms",
"From Corelib Require Export PrimString"
] | Corelib/Strings/PrimStringAxioms.v | of_list | |
of_to_list:
forall (s : string),
of_list (to_list s) = s. | Axiom | Corelib | [
"From Corelib Require Import BinNums PosDef IntDef ListDef",
"From Corelib Require Export PrimInt63 Uint63Axioms",
"From Corelib Require Export PrimString"
] | Corelib/Strings/PrimStringAxioms.v | of_to_list | |
to_list_length:
forall (s : string),
Datatypes.length (to_list s) <= to_nat max_length. | Axiom | Corelib | [
"From Corelib Require Import BinNums PosDef IntDef ListDef",
"From Corelib Require Export PrimInt63 Uint63Axioms",
"From Corelib Require Export PrimString"
] | Corelib/Strings/PrimStringAxioms.v | to_list_length | |
to_list_char63_valid:
forall (s : string),
ListDef.Forall char63_valid (to_list s). | Axiom | Corelib | [
"From Corelib Require Import BinNums PosDef IntDef ListDef",
"From Corelib Require Export PrimInt63 Uint63Axioms",
"From Corelib Require Export PrimString"
] | Corelib/Strings/PrimStringAxioms.v | to_list_char63_valid | |
length_spec:
forall (s : string),
to_nat (length s) = Datatypes.length (to_list s). | Axiom | Corelib | [
"From Corelib Require Import BinNums PosDef IntDef ListDef",
"From Corelib Require Export PrimInt63 Uint63Axioms",
"From Corelib Require Export PrimString"
] | Corelib/Strings/PrimStringAxioms.v | length_spec | |
get_spec:
forall (s : string) (i : int),
get s i = ListDef.nth (to_nat i) (to_list s) 0%uint63. | Axiom | Corelib | [
"From Corelib Require Import BinNums PosDef IntDef ListDef",
"From Corelib Require Export PrimInt63 Uint63Axioms",
"From Corelib Require Export PrimString"
] | Corelib/Strings/PrimStringAxioms.v | get_spec | |
make_spec:
forall (i : int) (c : char63),
to_list (make i c) =
ListDef.repeat (PrimInt63.land c 255%uint63)
(Nat.min (to_nat i) (to_nat max_length)). | Axiom | Corelib | [
"From Corelib Require Import BinNums PosDef IntDef ListDef",
"From Corelib Require Export PrimInt63 Uint63Axioms",
"From Corelib Require Export PrimString"
] | Corelib/Strings/PrimStringAxioms.v | make_spec | |
sub_spec:
forall (s : string) (off len : int),
to_list (sub s off len) =
ListDef.firstn (to_nat len) (ListDef.skipn (to_nat off) (to_list s)). | Axiom | Corelib | [
"From Corelib Require Import BinNums PosDef IntDef ListDef",
"From Corelib Require Export PrimInt63 Uint63Axioms",
"From Corelib Require Export PrimString"
] | Corelib/Strings/PrimStringAxioms.v | sub_spec | |
cat_spec:
forall (s1 s2 : string),
to_list (cat s1 s2) =
ListDef.firstn (to_nat max_length) (to_list s1 ++ to_list s2).
Abbreviation char63_compare := PrimInt63.compare (only parsing). | Axiom | Corelib | [
"From Corelib Require Import BinNums PosDef IntDef ListDef",
"From Corelib Require Export PrimInt63 Uint63Axioms",
"From Corelib Require Export PrimString"
] | Corelib/Strings/PrimStringAxioms.v | cat_spec |
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