refactor(library/*): remove 'Module:' lines

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Jeremy Avigad 2015-05-23 20:52:23 +10:00
parent db7bdce451
commit 8bebd104ff
83 changed files with 0 additions and 166 deletions

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.binary
Authors: Leonardo de Moura, Jeremy Avigad
General properties of binary operations.

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/-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.bundled
Authors: Jeremy Avigad
Bundled structures

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/-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.adjoint
Author: Floris van Doorn
-/

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/-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.basic
Author: Floris van Doorn
-/
open eq eq.ops

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/-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.default
Author: Floris van Doorn
-/

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/-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.functor
Author: Floris van Doorn
-/
import .basic

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/-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.limit
Author: Floris van Doorn
-/

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/-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.morphism
Author: Floris van Doorn
-/

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/-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.natural_transformation
Author: Floris van Doorn
-/

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/-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.yoneda
Author: Floris van Doorn
-/

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/-
Copyright (c) 2014 Robert Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.field
Authors: Robert Lewis
Structures with multiplicative and additive components, including division rings and fields.

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.function
Author: Leonardo de Moura
General operations on functions.

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/-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.order
Author: Jeremy Avigad
Various types of orders. We develop weak orders "≤" and strict orders "<" separately. We also

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/-
Copyright (c) 2014 Robert Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.ordered_field
Authors: Robert Lewis
-/

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/-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.ordered_group
Authors: Jeremy Avigad
Partially ordered additive groups, modeled on Isabelle's library. We could refine the structures,

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/-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.ordered_ring
Authors: Jeremy Avigad
Here an "ordered_ring" is partially ordered ring, which is ordered with respect to both a weak

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.relation
Author: Jeremy Avigad
General properties of relations, and classes for equivalence relations and congruences.

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/-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.ring
Authors: Jeremy Avigad, Leonardo de Moura
Structures with multiplicative and additive components, including semirings, rings, and fields.

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/-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: classical
Author: Jeremy Avigad
The standard library together with the classical axioms.

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.bool
Author: Leonardo de Moura
-/

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/-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.countable
Author: Leonardo de Moura
Define countable types

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.empty
Author: Jeremy Avigad, Floris van Doorn
-/
import logic.cast

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/-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.encodable
Author: Leonardo de Moura
Type class for encodable types.

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/-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.examples.depchoice
Author: Leonardo de Moura
-/
import data.encodable

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/-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.examples.unencodable
Author: Leonardo de Moura
Small example showing that (nat → nat) is not encodable.

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.fin
Author: Leonardo de Moura
Finite ordinals.

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.int.default
Author: Jeremy Avigad
-/
import .basic .order .div .power

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/-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.int.div
Author: Jeremy Avigad
Definitions and properties of div, mod, gcd, lcm, coprime, following the SSReflect library.

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/-
Copyright (c) 2015 Leonardo de Moura. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.list.as_type
Authors: Leonardo de Moura
-/
import data.list.basic

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/-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.list.basic
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura
Basic properties of lists.

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.nat.bquant
Author: Leonardo de Moura
Show that "bounded" quantifiers: (∃x, x < n ∧ P x) and (∀x, x < n → P x)

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/-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.nat.choose
Authors: Leonardo de Moura
Choice function for decidable predicates on natural numbers.

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/-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.nat.div
Authors: Jeremy Avigad, Leonardo de Moura
Definitions and properties of div, mod, gcd, lcm, coprime. Much of the development follows

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/-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.nat.pairing
Authors: Leonardo de Moura
Elegant pairing function.

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/-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.nat.sqrt
Authors: Leonardo de Moura
Very simple (sqrt n) function that returns s s.t.

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Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Jeremy Avigad
Module: data.nat.sub
Subtraction on the natural numbers, as well as min, max, and distance.
-/
import .order

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.num
Author: Leonardo de Moura
-/
import data.bool tools.helper_tactics

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.option
Author: Leonardo de Moura
-/

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.prod
Author: Leonardo de Moura, Jeremy Avigad
-/
import logic.eq

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/-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.rat.basic
Author: Jeremy Avigad
The rational numbers as a field generated by the integers, defined as the usual quotient.

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/-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.rat.order
Author: Jeremy Avigad
Adds the ordering, and instantiates the rationals as an ordered field.

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/-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.set.function
Author: Jeremy Avigad, Andrew Zipperer
Using classical logic, defines an inverse function.

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/-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.set.default
Author: Jeremy Avigad
-/
import .basic .function .map

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/-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.set.function
Author: Jeremy Avigad, Andrew Zipperer, Haitao Zhang
Functions between subsets of finite types.

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/-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.set.map
Author: Jeremy Avigad, Andrew Zipperer
Functions between subsets of finite types, bundled with the domain and range.

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.sigma
Author: Leonardo de Moura, Jeremy Avigad, Floris van Doorn
Sigma types, aka dependent sum.

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/-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.squash
Author: Leonardo de Moura
Define squash type (aka propositional truncation) using quotients.

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/-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.stream
Author: Leonardo de Moura
-/
import data.nat

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.string
Author: Leonardo de Moura
-/
import data.bool

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.subtype
Author: Leonardo de Moura, Jeremy Avigad
-/

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.sum
Authors: Leonardo de Moura, Jeremy Avigad
The sum type, aka disjoint union.

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.unit
Author: Leonardo de Moura
-/
import logic.eq

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/-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.uprod
Author: Leonardo de Moura
Unordered pairs

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/-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.vector
Author: Floris van Doorn, Leonardo de Moura
-/
import data.nat data.list data.fin

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.datatypes
Authors: Leonardo de Moura
Basic datatypes

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.default
Authors: Leonardo de Moura
-/
prelude

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/-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.funext
Author: Jeremy Avigad
Extensional equality for functions, and a proof of function extensionality from quotients.

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.logic
Authors: Leonardo de Moura, Jeremy Avigad, Floris van Doorn
-/
prelude

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.measurable
Authors: Leonardo de Moura
Types with a nat-valued complexity measure.

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.nat
Authors: Floris van Doorn, Leonardo de Moura
-/
prelude

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.num
Authors: Leonardo de Moura
-/

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.priority
Authors: Leonardo de Moura
-/
prelude

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.prod
Author: Leonardo de Moura, Jeremy Avigad
-/
prelude

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/-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.quot
Author: Leonardo de Moura
Quotient types.

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.reserved_notation
Authors: Leonardo de Moura, Jeremy Avigad
-/
prelude

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.sigma
Author: Leonardo de Moura, Jeremy Avigad, Floris van Doorn
-/
prelude

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.tactic
Author: Leonardo de Moura
This is just a trick to embed the 'tactic language' as a Lean

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.wf
Author: Leonardo de Moura
-/
prelude

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: logic.axioms.classical
Author: Jeremy Avigad
-/
import logic.axioms.prop_complete logic.axioms.hilbert

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/-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: logic.axioms.funext
Author: Leonardo de Moura
Excluded middle

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: logic.axioms.hilbert
Authors: Leonardo de Moura, Jeremy Avigad
Follows Coq.Logic.ClassicalEpsilon (but our definition of "inhabited" is the constructive one).

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: logic.axioms.classical
Author: Leonardo de Moura
-/
import logic.connectives logic.quantifiers logic.cast algebra.relation

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: logic.axioms.prop_decidable
Author: Leonardo de Moura
Excluded middle + Hilbert implies every proposition is decidable.

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: cast.lean
Author: Leonardo de Moura
Casts and heterogeneous equality. See also init.datatypes and init.logic.

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: logic.default
Author: Jeremy Avigad
-/
import logic.eq logic.connectives logic.cast

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: logic.eq
Authors: Leonardo de Moura, Jeremy Avigad, Floris van Doorn
Additional declarations/theorems about equality. See also init.datatypes and init.logic.

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: logic.examples.instances_test
Author: Jeremy Avigad
Illustrates substitution and congruence with iff.

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: logic.identities
Authors: Jeremy Avigad, Leonardo de Moura
Useful logical identities. Since we are not using propositional extensionality, some of the

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: logic.instances
Author: Jeremy Avigad
Class instances for iff and eq.

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: logic.quantifiers
Authors: Leonardo de Moura, Jeremy Avigad
Universal and existential quantifiers. See also init.logic.

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: standard
Authors: Leonardo de Moura, Jeremy Avigad
The constructive core of Lean's library.

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/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.fin
Author: Leonardo de Moura
Finite ordinals.

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@ -1,8 +1,6 @@
/-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.fin
Author: Leonardo de Moura
Finite ordinals.