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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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2
library/algebra/binary.lean
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/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.binary
Authors: Leonardo de Moura, Jeremy Avigad Authors: Leonardo de Moura, Jeremy Avigad
General properties of binary operations. General properties of binary operations.

2
library/algebra/bundled.lean
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/- /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved. Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.bundled
Authors: Jeremy Avigad Authors: Jeremy Avigad
Bundled structures Bundled structures

2
library/algebra/category/adjoint.lean
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/- /-
Copyright (c) 2014 Floris van Doorn. All rights reserved. Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.adjoint
Author: Floris van Doorn Author: Floris van Doorn
-/ -/

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

2
library/algebra/category/default.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Floris van Doorn. All rights reserved. Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.default
Author: Floris van Doorn Author: Floris van Doorn
-/ -/

2
library/algebra/category/functor.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Floris van Doorn. All rights reserved. Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.functor
Author: Floris van Doorn Author: Floris van Doorn
-/ -/
import .basic import .basic

2
library/algebra/category/limit.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Floris van Doorn. All rights reserved. Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.limit
Author: Floris van Doorn Author: Floris van Doorn
-/ -/

2
library/algebra/category/morphism.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Floris van Doorn. All rights reserved. Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.morphism
Author: Floris van Doorn Author: Floris van Doorn
-/ -/

2
library/algebra/category/natural_transformation.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Floris van Doorn. All rights reserved. Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.natural_transformation
Author: Floris van Doorn Author: Floris van Doorn
-/ -/

2
library/algebra/category/yoneda.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Floris van Doorn. All rights reserved. Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.yoneda
Author: Floris van Doorn Author: Floris van Doorn
-/ -/

2
library/algebra/field.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Robert Lewis. All rights reserved. Copyright (c) 2014 Robert Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.field
Authors: Robert Lewis Authors: Robert Lewis
Structures with multiplicative and additive components, including division rings and fields. Structures with multiplicative and additive components, including division rings and fields.

2
library/algebra/function.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.function
Author: Leonardo de Moura Author: Leonardo de Moura
General operations on functions. General operations on functions.

2
library/algebra/order.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved. Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.order
Author: Jeremy Avigad Author: Jeremy Avigad
Various types of orders. We develop weak orders "≤" and strict orders "<" separately. We also Various types of orders. We develop weak orders "≤" and strict orders "<" separately. We also

2
library/algebra/ordered_field.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Robert Lewis. All rights reserved. Copyright (c) 2014 Robert Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.ordered_field
Authors: Robert Lewis Authors: Robert Lewis
-/ -/

2
library/algebra/ordered_group.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved. Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.ordered_group
Authors: Jeremy Avigad Authors: Jeremy Avigad
Partially ordered additive groups, modeled on Isabelle's library. We could refine the structures, Partially ordered additive groups, modeled on Isabelle's library. We could refine the structures,

2
library/algebra/ordered_ring.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved. Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.ordered_ring
Authors: Jeremy Avigad Authors: Jeremy Avigad
Here an "ordered_ring" is partially ordered ring, which is ordered with respect to both a weak Here an "ordered_ring" is partially ordered ring, which is ordered with respect to both a weak

2
library/algebra/relation.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.relation
Author: Jeremy Avigad Author: Jeremy Avigad
General properties of relations, and classes for equivalence relations and congruences. General properties of relations, and classes for equivalence relations and congruences.

2
library/algebra/ring.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved. Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.ring
Authors: Jeremy Avigad, Leonardo de Moura Authors: Jeremy Avigad, Leonardo de Moura
Structures with multiplicative and additive components, including semirings, rings, and fields. Structures with multiplicative and additive components, including semirings, rings, and fields.

2
library/classical.lean
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/- /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved. Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: classical
Author: Jeremy Avigad Author: Jeremy Avigad
The standard library together with the classical axioms. The standard library together with the classical axioms.

2
library/data/bool.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.bool
Author: Leonardo de Moura Author: Leonardo de Moura
-/ -/

2
library/data/countable.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved. Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.countable
Author: Leonardo de Moura Author: Leonardo de Moura
Define countable types Define countable types

2
library/data/empty.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.empty
Author: Jeremy Avigad, Floris van Doorn Author: Jeremy Avigad, Floris van Doorn
-/ -/
import logic.cast import logic.cast

2
library/data/encodable.lean
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/- /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved. Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.encodable
Author: Leonardo de Moura Author: Leonardo de Moura
Type class for encodable types. Type class for encodable types.

2
library/data/examples/depchoice.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved. Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.examples.depchoice
Author: Leonardo de Moura Author: Leonardo de Moura
-/ -/
import data.encodable import data.encodable

2
library/data/examples/notencodable.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved. Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.examples.unencodable
Author: Leonardo de Moura Author: Leonardo de Moura
Small example showing that (nat → nat) is not encodable. Small example showing that (nat → nat) is not encodable.

2
library/data/fin.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.fin
Author: Leonardo de Moura Author: Leonardo de Moura
Finite ordinals. Finite ordinals.

2
library/data/int/default.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.int.default
Author: Jeremy Avigad Author: Jeremy Avigad
-/ -/
import .basic .order .div .power import .basic .order .div .power

2
library/data/int/div.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved. Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.int.div
Author: Jeremy Avigad Author: Jeremy Avigad
Definitions and properties of div, mod, gcd, lcm, coprime, following the SSReflect library. Definitions and properties of div, mod, gcd, lcm, coprime, following the SSReflect library.

2
library/data/list/as_type.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2015 Leonardo de Moura. All rights reserved. Copyright (c) 2015 Leonardo de Moura. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.list.as_type
Authors: Leonardo de Moura Authors: Leonardo de Moura
-/ -/
import data.list.basic import data.list.basic

2
library/data/list/basic.lean
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/- /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved. Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.list.basic
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura
Basic properties of lists. Basic properties of lists.

2
library/data/nat/bquant.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.nat.bquant
Author: Leonardo de Moura Author: Leonardo de Moura
Show that "bounded" quantifiers: (∃x, x < n ∧ P x) and (∀x, x < n → P x) Show that "bounded" quantifiers: (∃x, x < n ∧ P x) and (∀x, x < n → P x)

2
library/data/nat/choose.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved. Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.nat.choose
Authors: Leonardo de Moura Authors: Leonardo de Moura
Choice function for decidable predicates on natural numbers. Choice function for decidable predicates on natural numbers.

2
library/data/nat/div.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved. Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.nat.div
Authors: Jeremy Avigad, Leonardo de Moura Authors: Jeremy Avigad, Leonardo de Moura
Definitions and properties of div, mod, gcd, lcm, coprime. Much of the development follows Definitions and properties of div, mod, gcd, lcm, coprime. Much of the development follows

2
library/data/nat/pairing.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved. Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.nat.pairing
Authors: Leonardo de Moura Authors: Leonardo de Moura
Elegant pairing function. Elegant pairing function.

2
library/data/nat/sqrt.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved. Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.nat.sqrt
Authors: Leonardo de Moura Authors: Leonardo de Moura
Very simple (sqrt n) function that returns s s.t. Very simple (sqrt n) function that returns s s.t.

2
library/data/nat/sub.lean
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@ -3,8 +3,6 @@ Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Jeremy Avigad Authors: Floris van Doorn, Jeremy Avigad
Module: data.nat.sub
Subtraction on the natural numbers, as well as min, max, and distance. Subtraction on the natural numbers, as well as min, max, and distance.
-/ -/
import .order import .order

2
library/data/num.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.num
Author: Leonardo de Moura Author: Leonardo de Moura
-/ -/
import data.bool tools.helper_tactics import data.bool tools.helper_tactics

2
library/data/option.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.option
Author: Leonardo de Moura Author: Leonardo de Moura
-/ -/

2
library/data/prod.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.prod
Author: Leonardo de Moura, Jeremy Avigad Author: Leonardo de Moura, Jeremy Avigad
-/ -/
import logic.eq import logic.eq

2
library/data/rat/basic.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved. Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.rat.basic
Author: Jeremy Avigad Author: Jeremy Avigad
The rational numbers as a field generated by the integers, defined as the usual quotient. The rational numbers as a field generated by the integers, defined as the usual quotient.

2
library/data/rat/order.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved. Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.rat.order
Author: Jeremy Avigad Author: Jeremy Avigad
Adds the ordering, and instantiates the rationals as an ordered field. Adds the ordering, and instantiates the rationals as an ordered field.

2
library/data/set/classical_inverse.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved. Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.set.function
Author: Jeremy Avigad, Andrew Zipperer Author: Jeremy Avigad, Andrew Zipperer
Using classical logic, defines an inverse function. Using classical logic, defines an inverse function.

2
library/data/set/default.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved. Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.set.default
Author: Jeremy Avigad Author: Jeremy Avigad
-/ -/
import .basic .function .map import .basic .function .map

2
library/data/set/function.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved. Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.set.function
Author: Jeremy Avigad, Andrew Zipperer, Haitao Zhang Author: Jeremy Avigad, Andrew Zipperer, Haitao Zhang
Functions between subsets of finite types. Functions between subsets of finite types.

2
library/data/set/map.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved. Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.set.map
Author: Jeremy Avigad, Andrew Zipperer Author: Jeremy Avigad, Andrew Zipperer
Functions between subsets of finite types, bundled with the domain and range. Functions between subsets of finite types, bundled with the domain and range.

2
library/data/sigma.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.sigma
Author: Leonardo de Moura, Jeremy Avigad, Floris van Doorn Author: Leonardo de Moura, Jeremy Avigad, Floris van Doorn
Sigma types, aka dependent sum. Sigma types, aka dependent sum.

2
library/data/squash.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved. Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.squash
Author: Leonardo de Moura Author: Leonardo de Moura
Define squash type (aka propositional truncation) using quotients. Define squash type (aka propositional truncation) using quotients.

2
library/data/stream.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved. Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.stream
Author: Leonardo de Moura Author: Leonardo de Moura
-/ -/
import data.nat import data.nat

2
library/data/string.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.string
Author: Leonardo de Moura Author: Leonardo de Moura
-/ -/
import data.bool import data.bool

2
library/data/subtype.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.subtype
Author: Leonardo de Moura, Jeremy Avigad Author: Leonardo de Moura, Jeremy Avigad
-/ -/

2
library/data/sum.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.sum
Authors: Leonardo de Moura, Jeremy Avigad Authors: Leonardo de Moura, Jeremy Avigad
The sum type, aka disjoint union. The sum type, aka disjoint union.

2
library/data/unit.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.unit
Author: Leonardo de Moura Author: Leonardo de Moura
-/ -/
import logic.eq import logic.eq

2
library/data/uprod.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved. Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.uprod
Author: Leonardo de Moura Author: Leonardo de Moura
Unordered pairs Unordered pairs

2
library/data/vector.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Floris van Doorn. All rights reserved. Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.vector
Author: Floris van Doorn, Leonardo de Moura Author: Floris van Doorn, Leonardo de Moura
-/ -/
import data.nat data.list data.fin import data.nat data.list data.fin

2
library/init/datatypes.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: init.datatypes
Authors: Leonardo de Moura Authors: Leonardo de Moura
Basic datatypes Basic datatypes

2
library/init/default.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: init.default
Authors: Leonardo de Moura Authors: Leonardo de Moura
-/ -/
prelude prelude

2
library/init/funext.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved. Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: init.funext
Author: Jeremy Avigad Author: Jeremy Avigad
Extensional equality for functions, and a proof of function extensionality from quotients. Extensional equality for functions, and a proof of function extensionality from quotients.

2
library/init/logic.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: init.logic
Authors: Leonardo de Moura, Jeremy Avigad, Floris van Doorn Authors: Leonardo de Moura, Jeremy Avigad, Floris van Doorn
-/ -/
prelude prelude

2
library/init/measurable.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: init.measurable
Authors: Leonardo de Moura Authors: Leonardo de Moura
Types with a nat-valued complexity measure. Types with a nat-valued complexity measure.

2
library/init/nat.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: init.nat
Authors: Floris van Doorn, Leonardo de Moura Authors: Floris van Doorn, Leonardo de Moura
-/ -/
prelude prelude

2
library/init/num.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: init.num
Authors: Leonardo de Moura Authors: Leonardo de Moura
-/ -/

2
library/init/priority.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: init.priority
Authors: Leonardo de Moura Authors: Leonardo de Moura
-/ -/
prelude prelude

2
library/init/prod.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: init.prod
Author: Leonardo de Moura, Jeremy Avigad Author: Leonardo de Moura, Jeremy Avigad
-/ -/
prelude prelude

2
library/init/quot.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved. Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: init.quot
Author: Leonardo de Moura Author: Leonardo de Moura
Quotient types. Quotient types.

2
library/init/reserved_notation.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: init.reserved_notation
Authors: Leonardo de Moura, Jeremy Avigad Authors: Leonardo de Moura, Jeremy Avigad
-/ -/
prelude prelude

2
library/init/sigma.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: init.sigma
Author: Leonardo de Moura, Jeremy Avigad, Floris van Doorn Author: Leonardo de Moura, Jeremy Avigad, Floris van Doorn
-/ -/
prelude prelude

2
library/init/tactic.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: init.tactic
Author: Leonardo de Moura Author: Leonardo de Moura
This is just a trick to embed the 'tactic language' as a Lean This is just a trick to embed the 'tactic language' as a Lean

2
library/init/wf.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: init.wf
Author: Leonardo de Moura Author: Leonardo de Moura
-/ -/
prelude prelude

2
library/logic/axioms/classical.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: logic.axioms.classical
Author: Jeremy Avigad Author: Jeremy Avigad
-/ -/
import logic.axioms.prop_complete logic.axioms.hilbert import logic.axioms.prop_complete logic.axioms.hilbert

2
library/logic/axioms/em.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved. Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: logic.axioms.funext
Author: Leonardo de Moura Author: Leonardo de Moura
Excluded middle Excluded middle

2
library/logic/axioms/hilbert.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: logic.axioms.hilbert
Authors: Leonardo de Moura, Jeremy Avigad Authors: Leonardo de Moura, Jeremy Avigad
Follows Coq.Logic.ClassicalEpsilon (but our definition of "inhabited" is the constructive one). Follows Coq.Logic.ClassicalEpsilon (but our definition of "inhabited" is the constructive one).

2
library/logic/axioms/prop_complete.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: logic.axioms.classical
Author: Leonardo de Moura Author: Leonardo de Moura
-/ -/
import logic.connectives logic.quantifiers logic.cast algebra.relation import logic.connectives logic.quantifiers logic.cast algebra.relation

2
library/logic/axioms/prop_decidable.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: logic.axioms.prop_decidable
Author: Leonardo de Moura Author: Leonardo de Moura
Excluded middle + Hilbert implies every proposition is decidable. Excluded middle + Hilbert implies every proposition is decidable.

2
library/logic/cast.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: cast.lean
Author: Leonardo de Moura Author: Leonardo de Moura
Casts and heterogeneous equality. See also init.datatypes and init.logic. Casts and heterogeneous equality. See also init.datatypes and init.logic.

2
library/logic/default.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: logic.default
Author: Jeremy Avigad Author: Jeremy Avigad
-/ -/
import logic.eq logic.connectives logic.cast import logic.eq logic.connectives logic.cast

2
library/logic/eq.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: logic.eq
Authors: Leonardo de Moura, Jeremy Avigad, Floris van Doorn Authors: Leonardo de Moura, Jeremy Avigad, Floris van Doorn
Additional declarations/theorems about equality. See also init.datatypes and init.logic. Additional declarations/theorems about equality. See also init.datatypes and init.logic.

2
library/logic/examples/instances_test.lean
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/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: logic.examples.instances_test
Author: Jeremy Avigad Author: Jeremy Avigad
Illustrates substitution and congruence with iff. Illustrates substitution and congruence with iff.

2
library/logic/identities.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: logic.identities
Authors: Jeremy Avigad, Leonardo de Moura Authors: Jeremy Avigad, Leonardo de Moura
Useful logical identities. Since we are not using propositional extensionality, some of the Useful logical identities. Since we are not using propositional extensionality, some of the

2
library/logic/instances.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: logic.instances
Author: Jeremy Avigad Author: Jeremy Avigad
Class instances for iff and eq. Class instances for iff and eq.

2
library/logic/quantifiers.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: logic.quantifiers
Authors: Leonardo de Moura, Jeremy Avigad Authors: Leonardo de Moura, Jeremy Avigad
Universal and existential quantifiers. See also init.logic. Universal and existential quantifiers. See also init.logic.

2
library/standard.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: standard
Authors: Leonardo de Moura, Jeremy Avigad Authors: Leonardo de Moura, Jeremy Avigad
The constructive core of Lean's library. The constructive core of Lean's library.

2
tests/lean/run/finbug.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.fin
Author: Leonardo de Moura Author: Leonardo de Moura
Finite ordinals. Finite ordinals.

2
tests/lean/run/finbug2.lean
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@ -1,8 +1,6 @@
/- /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved. Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE. Released under Apache 2.0 license as described in the file LICENSE.
Module: data.fin
Author: Leonardo de Moura Author: Leonardo de Moura
Finite ordinals. Finite ordinals.