# The Coq Standard Library

Here is a short description of the Coq standard library, which is distributed with the system. It provides a set of modules directly available through the `Require` command.

The standard library is composed of the following subdirectories:

Init: The core library
  Datatypes, DatatypesSyntax, Logic, LogicSyntax, Logic_Type, Logic_TypeSyntax, Peano, Prelude, SpecifSyntax, Specif, Wf
Logic: Classical logic and dependent equality
  Berardi, Classical_Pred_Set, Classical_Pred_Type, Classical_Prop, Classical_Type, Classical, Decidable, Elimdep, Eqdep_dec, Eqdep, JMeq
Arith: Basic Peano arithmetic
  Arith, Between, Compare_dec, Compare, Div2, Div, EqNat, Euclid, Even, Gt, Le, Lt, Max, Minus, Min, Mult, Peano_dec, Plus, Wf_nat
ZArith: Binary integers (those used by the `Omega` decision tactic)
  auxiliary, fast_integer, Wf_Z, zarith_aux, ZArith_dec, ZArith, Zcomplements, Zhints, Zlogarithm, Zmisc, Zpower, Zdiv, Zsyntax
Reals: Formalization of real numbers
  DiscrR, Ranalysis, Raxioms, Rbase, Rbasic_fun, Rdefinitions, Rderiv, Reals, Rfunctions, Rgeom, R_Ifp, Rlimit, Rseries, Rsigma, R_sqr, Rsyntax, Rtrigo_fun, Rtrigo, SplitAbsolu, SplitRmult, TypeSyntax
Bool: Booleans (basic functions and results)
  BoolEq, Bool, DecBool, IfProp, Sumbool, Zerob
Lists : Monomorphic and polymorphic lists, Streams (infinite sequences)
  ListSet, List, PolyListSyntax, PolyList, Streams, TheoryList
Sets: Sets (classical, constructive, finite, infinite, powerset, etc.)
  Classical_sets, Constructive_sets, Cpo, Ensembles, Finite_sets_facts, Finite_sets, Image, Infinite_sets, Integers, Multiset, Partial_Order, Permut, Powerset_Classical_facts, Powerset_facts, Powerset, Relations_1_facts, Relations_1, Relations_2_facts, Relations_2, Relations_3_facts, Relations_3, Uniset
Relations: Relations (definitions and basic results)
  Newman, Operators_Properties, Relation_Definitions, Relation_Operators, Relations, Rstar
Wellfounded: Well founded Relations
  Disjoint_Union, Inclusion, Inverse_Image, Lexicographic_Exponentiation, Lexicographic_Product, Transitive_Closure, Union, Wellfounded, Well_Ordering
Sorting: Axiomatizations of sorts
  Heap, Permutation, Sorting
Setoids:
  Setoid
IntMap: Finite sets/maps as trees indexed by adresses
  Adalloc, Addec, Addr, Adist, Allmaps, Fset, Lsort, Mapaxioms, Mapcanon, Mapcard, Mapc, Mapfold, Mapiter, Maplists, Mapsubset, Map

Global Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (3685 entries)
Tactic Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (10 entries)
Axiom Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (106 entries)
Lemma Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (2574 entries)
Constructor Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (184 entries)
Inductive Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (118 entries)
Definition Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (527 entries)
Module Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (166 entries)

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