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

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This commit is contained in:
Jeremy Avigad 2015-05-23 20:52:58 +10:00
parent 8bebd104ff
commit 33214f0895
81 changed files with 0 additions and 162 deletions
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2
hott/algebra/binary.hlean
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/-
Copyright (c) 2014-15 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.

2
hott/algebra/category/adjoint.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.precategory.adjoint
Authors: Floris van Doorn
-/

2
hott/algebra/category/category.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2014 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.category
Author: Jakob von Raumer
-/

2
hott/algebra/category/constructions/comma.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.constructions.comma
Authors: Floris van Doorn, Jakob von Raumer
Comma category

2
hott/algebra/category/constructions/default.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.constructions.default
Authors: Floris van Doorn
-/

2
hott/algebra/category/constructions/functor.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.constructions.functor
Authors: Floris van Doorn, Jakob von Raumer
Functor precategory and category

2
hott/algebra/category/constructions/hset.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.constructions.hset
Authors: Floris van Doorn, Jakob von Raumer
Category of hsets

2
hott/algebra/category/constructions/opposite.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.constructions.opposite
Authors: Floris van Doorn, Jakob von Raumer
Opposite precategory and (TODO) category

2
hott/algebra/category/constructions/product.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.constructions.product
Authors: Floris van Doorn, Jakob von Raumer
Functor product precategory and (TODO) category

2
hott/algebra/category/default.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.default
Authors: Floris van Doorn
-/

2
hott/algebra/category/functor.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.functor
Authors: Floris van Doorn, Jakob von Raumer
-/

2
hott/algebra/category/groupoid.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2014 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.groupoid
Author: Jakob von Raumer
Ported from Coq HoTT

2
hott/algebra/category/iso.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.iso
Author: Floris van Doorn, Jakob von Raumer
-/

2
hott/algebra/category/nat_trans.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.nat_trans
Author: Floris van Doorn, Jakob von Raumer
-/
import .functor .iso

2
hott/algebra/category/precategory.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.precategory
Authors: Floris van Doorn
-/
import types.trunc types.pi arity

2
hott/algebra/category/strict.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.strict
Authors: Floris van Doorn, Jakob von Raumer
-/

2
hott/algebra/category/yoneda.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.category.yoneda
Authors: Floris van Doorn
-/

2
hott/algebra/field.hlean
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@ -1,8 +1,6 @@
/-
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.

2
hott/algebra/fundamental_group.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.fundamental_group
Authors: Floris van Doorn
fundamental group of a pointed space

2
hott/algebra/group.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: algebra.group
Authors: Jeremy Avigad, Leonardo de Moura
Various multiplicative and additive structures.

2
hott/algebra/hott.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: types.algebra.hott
Author: Floris van Doorn
Theorems about algebra specific to HoTT

2
hott/algebra/order.hlean
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@ -1,8 +1,6 @@
/-
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

2
hott/algebra/ordered_group.hlean
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@ -1,8 +1,6 @@
/-
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,

2
hott/algebra/ordered_ring.hlean
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@ -1,8 +1,6 @@
/-
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

2
hott/algebra/relation.hlean
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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: algebra.relation
Author: Jeremy Avigad
General properties of relations, and classes for equivalence relations and congruences.

2
hott/algebra/ring.hlean
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@ -1,8 +1,6 @@
/-
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.

2
hott/arity.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.path
Author: Floris van Doorn
Theorems about functions with multiple arguments

2
hott/core.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: core
Authors: Floris van Doorn
The core of the HoTT library

2
hott/cubical/pathover.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: cubical.pathover
Author: Floris van Doorn
Theorems about pathovers

2
hott/cubical/square.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: cubical.square
Author: Floris van Doorn
Theorems about square

2
hott/hit/circle.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: hit.circle
Authors: Floris van Doorn
Declaration of the circle

2
hott/hit/coeq.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: hit.coeq
Authors: Floris van Doorn
Declaration of the coequalizer

2
hott/hit/colimit.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: hit.colimit
Authors: Floris van Doorn
Definition of general colimits and sequential colimits.

2
hott/hit/cylinder.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: hit.cylinder
Authors: Floris van Doorn
Declaration of mapping cylinders

2
hott/hit/pushout.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: hit.pushout
Authors: Floris van Doorn
Declaration of the pushout

2
hott/hit/quotient.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: hit.quotient
Authors: Floris van Doorn
Declaration of set-quotients

2
hott/hit/sphere.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: hit.circle
Authors: Floris van Doorn
Declaration of the n-spheres

2
hott/hit/suspension.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: hit.suspension
Authors: Floris van Doorn
Declaration of suspension

2
hott/hit/trunc.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: hit.trunc
Authors: Floris van Doorn
n-truncation of types.

2
hott/hit/type_quotient.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: hit.type_quotient
Authors: Floris van Doorn
Type quotients (quotient without truncation)

2
hott/init/bool.hlean
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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: init.bool
Authors: Leonardo de Moura
-/

2
hott/init/datatypes.hlean
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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: init.datatypes
Authors: Leonardo de Moura, Jakob von Raumer
Basic datatypes

2
hott/init/default.hlean
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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: init.default
Authors: Leonardo de Moura, Jakob von Raumer
-/

2
hott/init/equiv.hlean
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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: init.equiv
Author: Jeremy Avigad, Jakob von Raumer
Ported from Coq HoTT

2
hott/init/function.hlean
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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: init.function
Author: Leonardo de Moura
General operations on functions.

2
hott/init/funext.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2014 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.funext
Authors: Jakob von Raumer
Ported from Coq HoTT

2
hott/init/hit.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.hit
Authors: Floris van Doorn
Declaration of the primitive hits in Lean

2
hott/init/logic.hlean
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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: init.logic
Authors: Leonardo de Moura
-/

2
hott/init/nat.hlean
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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: init.nat
Authors: Floris van Doorn, Leonardo de Moura
-/
prelude

2
hott/init/num.hlean
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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: init.num
Authors: Leonardo de Moura
-/

2
hott/init/path.hlean
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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: init.path
Authors: Jeremy Avigad, Jakob von Raumer, Floris van Doorn
Ported from Coq HoTT

2
hott/init/priority.hlean
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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: init.priority
Authors: Leonardo de Moura
-/

2
hott/init/relation.hlean
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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: init.relation
Authors: Leonardo de Moura
-/

2
hott/init/reserved_notation.hlean
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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: init.reserved_notation
Authors: Leonardo de Moura
-/
prelude

2
hott/init/tactic.hlean
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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: init.tactic
Author: Leonardo de Moura
This is just a trick to embed the 'tactic language' as a Lean

2
hott/init/trunc.hlean
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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: init.trunc
Authors: Jeremy Avigad, Floris van Doorn
Definition of is_trunc (n-truncatedness)

2
hott/init/types.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2014-2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.types
Authors: Leonardo de Moura, Jeremy Avigad, Floris van Doorn, Jakob von Raumer
-/

2
hott/init/ua.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2014 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.ua
Author: Jakob von Raumer
Ported from Coq HoTT

2
hott/init/util.hlean
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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: init.util
Author: Leonardo de Moura
Auxiliary definitions used by automation

2
hott/init/wf.hlean
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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: init.wf
Author: Leonardo de Moura
-/

2
hott/types/W.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: types.W
Author: Floris van Doorn
Theorems about W-types (well-founded trees)

2
hott/types/arrow.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: types.arrow
Author: Floris van Doorn
Ported from Coq HoTT

2
hott/types/bool.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: types.bool
Authors: Floris van Doorn
Theorems about the booleans

2
hott/types/default.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: types.default
Authors: Floris van Doorn
-/

2
hott/types/eq.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: types.eq
Author: Floris van Doorn
Ported from Coq HoTT

2
hott/types/equiv.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: types.equiv
Author: Floris van Doorn
Ported from Coq HoTT

2
hott/types/fiber.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: types.fiber
Author: Floris van Doorn
Ported from Coq HoTT

2
hott/types/function.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: types.function
Author: Floris van Doorn
Ported from Coq HoTT

2
hott/types/hprop_trunc.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: types.hprop_trunc
Authors: Jakob von Raumer, Floris van Doorn
Proof of the theorem that (is_trunc n A) is a mere proposition

2
hott/types/int/basic.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: types.int.basic
Authors: Floris van Doorn, Jeremy Avigad
The integers, with addition, multiplication, and subtraction. The representation of the integers is

2
hott/types/int/default.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: types.int.default
Authors: Floris van Doorn
-/

2
hott/types/int/hott.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: types.int.hott
Author: Floris van Doorn
Theorems about the integers specific to HoTT

2
hott/types/nat/basic.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: types.nat.basic
(Ported from standard library file data.nat.basic on May 02, 2015)
Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad

2
hott/types/nat/default.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: types.nat.default
Authors: Floris van Doorn
-/

2
hott/types/nat/order.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: types.nat.order
Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad
The order relation on the natural numbers.

2
hott/types/nat/sub.hlean
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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.
Authors: Floris van Doorn, Jeremy Avigad
Module: data.nat.sub
Subtraction on the natural numbers, as well as min, max, and distance.
Ported from standard library

2
hott/types/pi.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2014-15 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: types.pi
Author: Floris van Doorn
Ported from Coq HoTT

2
hott/types/pointed.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2014 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: types.pointed
Authors: Jakob von Raumer, Floris van Doorn
Ported from Coq HoTT

2
hott/types/prod.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2014 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: types.prod
Author: Floris van Doorn
Ported from Coq HoTT

2
hott/types/sigma.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2014-15 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: types.sigma
Author: Floris van Doorn
Ported from Coq HoTT

2
hott/types/trunc.hlean
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@ -1,8 +1,6 @@
/-
Copyright (c) 2015 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: types.trunc
Authors: Floris van Doorn
Properties of is_trunc and trunctype