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/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Jeremy Avigad Theory of filters on sets. -/ import order.galois_connection order.zorn import data.set.finite open lattice set universes u v w x y open_locale classic...
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/- Copyright (c) 2019 Johan Commelin All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import order.filter.lift import topology.opens import topology.algebra.ring open topological_space open_locale topological_space set_option old_structure_cmd true /...
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/- Copyright (c) 2020 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import data.fintype.card tactic.omega /-! # Compositions A composition of an integer `n` is a decomposition `n = i₀ + ... + i_{k-1}` of `n` into a sum of pos...
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/- Copyright (c) 2020 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Daniel Selsam -/ import Binport.Basic import Binport.Rules import Binport.ParseExport import Binport.ProcessActionItem import Binport.Path import Lean import Std.Data.HashMap i...
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import ..imperative_DSL.environment open lang.axisOrientation def axisOrientationEval : lang.axisOrientation.orientationExpr → environment.env → orientation.AxisOrientation 3 | (lang.axisOrientation.orientationExpr.lit V) i := V | (lang.axisOrientation.orientationExpr.var v) i := i.ax.or v
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/- Copyright (c) 2019 Neil Strickland. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Neil Strickland Sums of finite geometric series -/ import algebra.big_operators algebra.commute universe u variable {α : Type u} open finset /-- Sum of the finite geometric serie...
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/- Copyright (c) 2020 Kevin Lacker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Lacker -/ import data.nat.digits /-! # IMO 1962 Q1 Find the smallest natural number $n$ which has the following properties: (a) Its decimal representation has 6 as the last dig...
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import solutions.world2_multiplication import mynat.le /- Here's what you get from the import: 1) The following data: * a binary relation called mynat.le, and notation a ≤ b for this relation. The definition is: a ≤ b ↔ ∃ c : mynat, b = a + c 2) The following axiom: * `le_def (a b : mynat) : a ≤ b ↔ ∃ (c : m...
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/- Copyright (c) 2020 Kevin Buzzard. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Buzzard, Calle Sönne -/ import topology.category.CompHaus import topology.connected import topology.subset_properties import topology.locally_constant.basic import category_theor...
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/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov -/ import tactic.linarith import tactic.tfae import algebra.archimedean import algebra.group.pi import algebra.ordered_ring 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 init.relation Authors: Leonardo de Moura -/ prelude import init.logic -- TODO(Leo): remove duplication between this file and algebra/relation.lean -- We need some of the followi...
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/- Copyright (c) 2019 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon, Keeley Hoek, Floris van Doorn -/ import data.list.defs /-! # Definitions for `string` This file defines a bunch of functions for the `string` datatype. -/ namespace string...
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/- This file develops the memory model that is used in the dynamic semantics of all the languages used in the compiler. It defines a type [mem] of memory states, the following 4 basic operations over memory states, and their properties: - [load]: read a memory chunk at a given address; - [store]: store a memory ...
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/- Copyright (c) 2014 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura -/ prelude import init.reserved_notation namespace bool definition cond {A : Type} (b : bool) (t e : A) := bool.rec_on b e t definition bor (a b : boo...
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/- Copyright (c) 2022 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jujian Zhang -/ import group_theory.subgroup.pointwise import group_theory.group_action.pi import group_theory.quotient_group import algebra.group.pi /-! # Divisible Group and rootable ...
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/- Author: E.W.Ayers © 2019 -/ import .engine .policy import algebra.group_power import tactic.ring /- The `equate` tactic. -/ namespace robot meta def equate_user_attr : user_attribute rule_table unit := { name := `equate , descr := "add the given lemma to equate's rule-table." , cache_cfg := { mk_cache := rul...
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import types.eq types.pi hit.colimit types.nat.hott homotopy.sphere --open unit pi equiv sum open eq quotient sphere sphere.ops nat seq_colim is_trunc sum pointed -- /- HELPER LEMMAS -/ -- definition inv_con_con_eq_of_eq_con_con_inv {A : Type} {a₁ a₂ b₁ b₂ : A} {p : a₁ = b₁} -- {q : a₁ = a₂} {r : a₂ = b₂} {s ...
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import mynat.add namespace mynat /- add_zero (a : mynat) := a + 0 = a add_succ (a b : mynat) := a + succ(b) = succ(a + b) -/ lemma add_succ_zero (a : mynat) : a + succ(0) = succ(a) := begin [nat_num_game] rw add_succ, rw add_zero, refl, end end mynat
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/- Copyright (c) 2020 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.PrePort import Mathlib.Lean3Lib.init.default import Mathlib.order.conditionally_complete_lattice import Mathlib.PostPort universes u namespace Mathl...
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/- Copyright (c) 2019 Seul Baek. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Seul Baek -/ import data.nat.basic open list universes u v w variables {α : Type u} {β : Type v} {γ : Type w} namespace list namespace func variables {a : α} variables {as as1 as2 as3 :...
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prelude -- Porting Vladimir's file to Lean notation `assume` binders `,` r:(scoped f, f) := r notation `take` binders `,` r:(scoped f, f) := r inductive empty : Type inductive unit : Type := tt : unit definition tt := @unit.tt inductive nat : Type := O : nat, S : nat → nat inductive paths {A : Type} (a : A) : A → T...
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import .classical_geometry import .classical_time import .classical_velocity
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run_cmd mk_simp_attr `fol meta def simp_fol := `[simp only with fol]
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/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl Theory of topological spaces. -/ import algebra.lattice.filter open set filter lattice universes u v w structure topological_space (α : Type u) := (open' : set ...
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/- Copyright (c) 2014 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Amelia Livingston, Yury Kudryashov, Neil Strickland -/ import algebra.divisibility import data.set.basic /-! # Properties and homomo...
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/- Copyright (c) 2018 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Author: Sebastian Ullrich, Leonardo de Moura Message Type used by the Lean frontend -/ import Lean.Data.Position import Lean.Data.OpenDecl import Lean.MetavarContext import Lean.Environ...
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/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Mario Carneiro -/ import data.set.disjointed import data.set.countable import data.indicator_function import data.equiv.encodable.lattice import order.filter.basic /-!...
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/- Copyright (c) 2018 Robert Y. Lewis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robert Y. Lewis, Chris Hughes -/ import algebra.associated import algebra.big_operators.basic import ring_theory.valuation.basic /-! # Multiplicity of a divisor For a commutative mo...
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/- Copyright (c) 2014 Robert Lewis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robert Lewis, Leonardo de Moura, Mario Carneiro, Floris van Doorn -/ import algebra.ordered_ring import algebra.field /-! ### Linear ordered fields A linear ordered field is a field ...
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/- Copyright (c) 2020 Alena Gusakov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alena Gusakov, Arthur Paulino, Kyle Miller -/ import combinatorics.simple_graph.degree_sum import combinatorics.simple_graph.subgraph /-! # Matchings A *matching* for a simple graph i...
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reserve prefix `#where`:max open lean.parser tactic open interactive namespace command.where meta def sanitize_prefix (pfx : name) : name → name | name.anonymous := name.anonymous | (name.mk_string s p) := if p.get_prefix.get_prefix = name.anonymous then name.mk_string s pfx else name.mk_string s name.anonymous ...
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example : {(0,1)} = (singleton (0, 1) : set (ℕ × ℕ)) := rfl example : {(0,1)} = [(0,1)] := rfl
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/- Copyright (c) 2020 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import algebra.group.opposite import group_theory.group_action.defs /-! # Scalar actions on and by `Mᵐᵒᵖ` This file defines the actions on the opposite type `has_smul R M...
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def Foo := List Nat def test (x : Nat) : Foo := [x, x+1, x+2] #eval test 4 #check fun (x y : Foo) => x == y -- Error deriving instance BEq, Repr for Foo #eval test 4 #check fun (x y : Foo) => x == y def Boo := List (String × String) deriving BEq, Repr, DecidableEq def mkBoo (s : String) : Boo := [(s, s)] ...
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/- Copyright (c) 2022 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Gabriel Ebner -/ import Lean.Elab.Deriving.Basic namespace Lean.Elab open Command Std Parser Term private def deriveTypeNameInstance (declNames : Array Name) : CommandElabM B...
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/- Copyright (c) 2021 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser, Kevin Buzzard -/ import algebra.direct_sum.module import tactic.fin_cases /-! # Not all complementary decompositions of a module over a semiring make up a direct sum This ...
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/- Copyright (c) 2019 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Yury Kudryashov -/ import analysis.calculus.local_extr import analysis.convex.topology /-! # The mean value inequality and equalities In this file we prove the ...
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-- Authors: Floris van Doorn /- The "dependent" smash product. Given A : Type* and B : A → Type* it is the cofiber of A ∨ B pt → Σ(a : A), B a However, we define it (equivalently) as the pushout of 2 ← A + B pt → Σ(a : A), B a. -/ import .smash_adjoint ..pointed_binary open bool pointed eq equiv is_equiv sum bool ...
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/- Copyright (c) 2020 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne, Sébastien Gouëzel -/ import analysis.normed_space.indicator_function import analysis.normed.group.hom import measure_theory.function.ess_sup import measure_theory.function....
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/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Author: Yury Kudryashov -/ import algebra.invertible import linear_algebra.affine_space.affine_equiv /-! # Midpoint of a segment ## Main definitions * `midpoint R x y`: midpoint of the segm...
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/- Copyright (c) 2017 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura -/ import Std.Data.RBMap namespace Std universes u v w def RBTree (α : Type u) (lt : α → α → Bool) : Type u := RBMap α Unit lt instance : Inhabited (RBTree...
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-- Copyright (c) 2018 Scott Morrison. All rights reserved. -- Released under Apache 2.0 license as described in the file LICENSE. -- Authors: Scott Morrison, Reid Barton, Mario Carneiro import category_theory.limits.shape open category_theory namespace category_theory.limits universes u v w variables {C : Type u} ...
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/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl Infinite sum over a topological monoid This sum is known as unconditionally convergent, as it sums to the same value under all possible permutations. For Euclidean spa...
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/- Copyright (c) 2020 Marc Huisinga. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Marc Huisinga, Wojciech Nawrocki -/ import Init.Control import Init.System.IO import Std.Data.RBTree import Lean.Data.Json /-! Implementation of JSON-RPC 2.0 (https://www.jsonrpc.org/...
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/- Copyright (c) 2021 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import topology.instances.real import order.filter.archimedean /-! # Convergence of subadditive sequences A subadditive sequence `u : ℕ → ℝ` is a sequence sat...
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/- Copyright (c) 2017 Scott Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Scott Morrison -/ import Mathlib.PrePort import Mathlib.Lean3Lib.init.default import Mathlib.category_theory.limits.limits import Mathlib.category_theory.concrete_category.basic import...
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/- Copyright (c) 2021 Lu-Ming Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Author: Lu-Ming Zhang. -/ import field_theory.finite.basic import group_theory.quotient_group import monoid_hom import set_finset_fintype /-! # Finite fields This file supplements...
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/- Copyright (c) 2014 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Mario Carneiro -/ import data.set.basic open function /-! # Basic definitions about `≤` and `<` ## Definitions ### Predicates on functions - `monotone f`: a function ...
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-- Copyright (c) 2018 Michael Jendrusch. All rights reserved. import category_theory.category import category_theory.functor import category_theory.products import category_theory.natural_isomorphism import ..monoidal_category import ..braided_monoidal_category open category_theory open tactic universes u v namespace...
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import morphism.Reynold_operator import sub_module import homothetic import Projection.test_linear_algebra open Reynold universes u v w w' variables {G : Type u} [group G][fintype G] {R : Type v}[comm_ring R] variables {M : Type w}[add_comm_group M] [module R M] ( ρ : group_representation G R M) (W : submodule R...
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/- Copyright (c) 2017 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura -/ import Mathlib.PrePort import Mathlib.Lean3Lib.init.data.unsigned.basic import Mathlib.Lean3Lib.init.data.fin.ops namespace Mathlib namespace unsigned d...
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import analysis.topology.topological_structures import ring_theory.subring import ring_theory.ideal_operations universe u variables {A : Type u} [comm_ring A] [topological_space A] [topological_ring A] instance subring_has_zero (R : Type u) [comm_ring R] (S : set R) [HS : is_subring S] : has_zero S := ⟨⟨0, is_add_su...
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/- Copyright (c) 2017 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Author: Mario Carneiro Coinductive formalization of unbounded computations. -/ import data.stream logic.relator tactic.basic universes u v w /- coinductive computation (α : Type u) : T...
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def f1 (x : Nat × Nat) : Nat := match x with | { fst := x, snd := y } => x - y #eval f1 (20, 15) def g1 (h : Nat × Nat × Nat → Nat) : Nat := h (1, 2, 3) def f2 (w : Nat) : Nat := g1 fun (x, y, z) => x + y + z + w #eval f2 10 def g2 (h : Nat × Nat → Nat × Nat → Nat) : Nat := h (1, 2) (20, 40) def f3 (a : Nat) : ...
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/- Copyright (c) 2019 Jean Lo. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jean Lo, Yaël Dillies, Moritz Doll -/ import analysis.locally_convex.basic import data.real.pointwise import data.real.sqrt import topology.algebra.filter_basis import topology.algebra.module...
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/- Copyright (c) 2021 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import analysis.normed.group.basic import topology.algebra.group_completion import topology.metric_space.completion /-! # Completion of a normed group > THIS FILE I...
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/- Copyright (c) 2019 Scott Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Scott Morrison, Markus Himmel -/ import category_theory.limits.shapes.equalizers import category_theory.limits.shapes.pullbacks import category_theory.limits.shapes.strong_epi /-! # C...
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import system.io leanpkg.git leanpkg.main def io.cmd' (args : io.process.spawn_args) : io unit := leanpkg.exec_cmd args -- do child ← io.proc.spawn args, -- exitv ← io.proc.wait child, -- when (exitv ≠ 0) $ io.fail $ "process exited with status " ++ repr exitv, -- return () open io io.proc io.fs def git_checko...
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/- Copyright (c) 2016 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Author: Leonardo de Moura -/ prelude import init.data.string.basic init.data.bool.basic init.data.subtype.basic import init.data.unsigned init.data.prod init.data.sum.basic open sum subt...
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/- Copyright (c) 2019 Scott Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Scott Morrison -/ import algebra.category.Group.preadditive import group_theory.quotient_group import category_theory.limits.concrete_category import category_theory.limits.shapes.kern...
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/- Copyright (c) 2021 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura -/ import Lean.Meta.MatchUtil import Lean.Meta.Tactic.Assumption import Lean.Meta.Tactic.Cases namespace Lean.Meta def elimEmptyInductive (mvarId : MVarId) (...
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/- Copyright (c) 2022 Aaron Anderson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson -/ import model_theory.semantics /-! # Ordered First-Ordered Structures This file defines ordered first-order languages and structures, as well as their theories. ## M...
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import standard example (A : Type) : A → A := begin intro a, exact a end example (A : Type) : ∀ x : A, x = x := begin intro x, exact eq.refl x end
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-- Math 2001 Teamwork 4 (Optional) -- You may submit individual solutions to this assignment for extra credit. -- You may work on a team, but you must submit your own tw4-lastname.lean file if you want it to be graded and counted. -- Due Date: Fri 3 May 2019 -- Below you will be asked to prove some facts about natu...
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/- Copyright (c) 2020 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import data.fintype.card import data.finset.sort import algebra.big_operators.order /-! # Compositions A composition of a natural number `n` is a decompositio...
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/- Copyright (c) 2017 Scott Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Scott Morrison, Mario Carneiro -/ import topology.category.Top.basic import category_theory.limits.types import category_theory.limits.preserves.basic open topological...
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/- Copyright (c) 2015 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn homotopy groups of a pointed space -/ import .trunc_group .hott types.trunc open nat eq pointed trunc is_trunc algebra namespace eq definition phomotopy_group...
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/- UVa CS2102/Sullivan, Spring 2020, Homework #2 This homework assignment is due by noon on Tuesday, Feb 4. Submit your result through the HW#2 tab under the Assignments category on Collab. Do so by uploading a completed version of this file. The goal of this assignment is to develop and evaluate your ability to wr...
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namespace fol_08 variable A : Type variable f : A → A variable P : A → Prop variable h : ∀ x, P x → P (f x) include h theorem fol_08 : ∀ y, P y → P (f (f y)) := assume y (h1: P y), have h2: P y → P (f y), from h y, have h3: P (f y), from h2 h1, have h4: P (f y) → P (f (f y)), from h (f y), show P (f (f y)), from h4...
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/- Copyright (c) 2021 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying -/ import measure_theory.measure.measure_space import analysis.complex.basic /-! # Vector valued measures This file defines vector valued measures, which are σ-additive fun...
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/- Copyright (c) 2020 Scott Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import linear_algebra.exterior_algebra.basic import linear_algebra.clifford_algebra /-! Tests that the ring instances for `free_algebra` and derived quotient types act...
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/- Copyright (c) 2019 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Fabian Glöckle -/ import linear_algebra.tensor_product import linear_algebra.finite_dimensional import tactic.apply_fun noncomputable theory /-! # Dual vector spaces ...
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/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Yury Kudryashov -/ import algebra.algebra.basic import linear_algebra.tensor_product import algebra.iterate_hom /-! # Facts about algebras involving bilinear maps and tensor pro...
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/- Copyright (c) 2015 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Author: Floris van Doorn Basic theorems about pathovers -/ import .path .equiv universes u v l hott_theory namespace hott open hott.equiv hott.is_equiv function variables {A : Type _} {A'...
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/- Copyright (c) 2014 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad Here an "ordered_ring" is partially ordered ring, which is ordered with respect to both a weak order and an associated strict order. Our numeric structures (int, rat, and...
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/- Copyright (c) 2020 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn -/ import Mathlib.PrePort import Mathlib.Lean3Lib.init.default import Mathlib.measure_theory.measure_space import Mathlib.measure_theory.borel_space import Mathlib.t...
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/- ;; A. Bear and Big Brother Problem ;; https://codeforces.com/problemset/problem/791/A (loop for x = 4 then (* x 3) for y = 9 then (* y 2) until (> x y) collect (cons x y)) Theorem? A) exists p in CL | p: range(1,10) x range(1,10) -> nat and for any a, b in range(1,10) x range(1,10) it holds tha...
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/- Copyright (c) 2020 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import algebra.associated import algebra.big_operators.basic /-! # Prime elements in rings > THIS FILE IS SYNCHRONIZED WITH MATHLIB4. > Any changes to this file require ...
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/- Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Metric spaces. Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel Many definitions and theorems expected on metric spaces are already introduced o...
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/- Copyright (c) 2020 Aaron Anderson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson -/ import data.matrix.basic import algebra.char_p /-! # Matrices in prime characteristic -/ open matrix variables {n : Type*} [fintype n] {R : Type*} [ring R] instance...
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def foo (a : nat) (b : nat) := b def g (a : nat) := foo (1000000000000 + 1) a def f (a : nat) := foo (1 + 1000000000000) a lemma foo_lemma (a b : nat) : foo b a = foo (1 + 1000000000000) a := rfl lemma f_fold_lemma (a : nat) : foo (1 + 1000000000000) a = f a := rfl lemma ex (a : nat) (p : nat → Prop) (h : p (f a)) :...
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/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import data.finset.fold import data.multiset.lattice import order.order_dual import order.complete_lattice /-! # Lattice operations on finsets -/ variables {α β γ :...
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/- Copyright (c) 2019 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura -/ prelude import Init.Lean.Compiler.IR.CompilerM namespace Lean namespace IR namespace Checker structure CheckerContext := (env : Environment) (localCtx : ...
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-- Copyright (c) 2017 Scott Morrison. All rights reserved. -- Released under Apache 2.0 license as described in the file LICENSE. -- Authors: Scott Morrison import category_theory.products.bifunctors import category_theory.equivalence -- FIXME why do we need this here? @[obviously] meta def obviously_2 := tactic.tidy...
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/- Copyright (c) 2021 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura -/ import Lean.Meta.Match.MatchPatternAttr import Lean.Elab.Arg import Lean.Elab.MatchAltView namespace Lean.Elab.Term open Meta inductive PatternVar where ...
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/- Copyright (c) 2020 Yury G. Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury G. Kudryashov -/ import linear_algebra.affine_space.affine_map import algebra.invertible /-! # Affine equivalences In this file we define `affine_equiv k P₁ P₂` (notation: `...
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open tactic set_option pp.binder_types true set_option pp.implicit true set_option pp.notation false example (a : nat) : true := by do mk_const `add >>= eta_expand >>= trace, mk_const `nat.succ >>= eta_expand >>= trace, to_expr `(add a) >>= eta_expand >>= trace, to_expr `(λ x : nat, add x) >>= eta_expand >>= ...
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import data.examples.vector open nat vector variable {A : Type} definition foo : Π {n : nat}, vector A n → nat | foo nil := 0 | foo (a :: b :: v) := 0 set_option pp.implicit false definition foo : Π {n : nat}, vector A n → nat | foo nil := 0 | foo (a :: b :: v) := 0
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/- Copyright (c) 2020 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn, Robert Y. Lewis, Gabriel Ebner -/ import tactic.lint.basic /-! # Linters about type classes This file defines several linters checking the correct usage of type c...
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open tactic meta def simp_at' (h : expr) (extra_lemmas : list expr := []) (cfg : simp_config := {}) : tactic unit := do when (expr.is_local_constant h = ff) (fail "tactic simp_at failed, the given expression is not a hypothesis"), htype ← infer_type h, S ← simp_lemmas.mk_default, S ← S.append extra_le...
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/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau -/ import data.opposite import algebra.field import algebra.group.commute import group_theory.group_action.defs import data.equiv.mul_add /-! # Algebraic operations on `αᵒᵖ` Thi...
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/- Copyright (c) 2020 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn, Robert Y. Lewis, Gabriel Ebner -/ import tactic.lint.basic /-! # Linter frontend and commands This file defines the linter commands which spot common mistakes in ...
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/- Copyright (c) 2018 Scott Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Scott Morrison, Johannes Hölzl, Reid Barton, Sean Leather Bundled types. -/ import tactic.doc_commands /-! `bundled c` provides a uniform structure for bundling a type equipped with ...
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/- Copyright (c) 2019 Jean Lo. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jean Lo, Bhavik Mehta, Yaël Dillies -/ import analysis.normed_space.basic /-! # Local convexity This file defines absorbent and balanced sets. An absorbent set is one that "surrounds" the ...
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import topo import inst.exec.propagate import inst.network.prec open reactor open reactor.ports -- Cf. inst/primitives.lean variables {υ : Type*} [decidable_eq υ] namespace inst namespace network namespace graph -- Runs a reaction in a network graph and propagates all of its affected output ports. noncomputable ...
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/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Jeremy Avigad -/ import data.set.finite import order.copy import order.zorn import tactic.monotonicity /-! # Theory of filters on sets ## Main definitions * `filter`...
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/- -/mnl6sc@virginia.edu https://github.com/mlarusso/CS-2120.git npj5kr@virginia.edu https://github.com/njeyasingh/CS-2120.git fpg2kv@virginia.edu https://github.com/franklin-glance/cs2120f21.git /- EQUALITY -/ /- #1 Suppose that x, y, z, and w are arbitrary objects of some type, T; and suppose further that we know (...
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/- Copyright (c) 2021 Christopher Hoskin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christopher Hoskin -/ import algebra.lie.of_associative /-! # Jordan rings > THIS FILE IS SYNCHRONIZED WITH MATHLIB4. > Any changes to this file require a corresponding PR to mat...
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/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Johannes Hölzl -/ import data.list.basic universes u v w z open nat function variables {α : Type u} {β : Type v} {γ : Type w} {δ : Type z} namespace list /- forall₂...