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prelude import init.meta.interactive namespace unbundled class broken₁ (A : Type*) := (f : A → A) open broken₁ class broken₂ (A : Type*) (a : out_param $ A) [broken₁ A] := (f_eq : ∀ x, f x = a) open broken₂ -- Even if the goal doesn't contain an instance of `broken₂`, the parameter `a` -- to `f_eq` should still be ...
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inductive V (α : Bool → Type) : Bool → Type | mk₁ {b} : α true → V α b | mk₂ : V α false → V α false def V.map {α β} (f : (b : Bool) → α b → β b) : {b : Bool} → V α b → V β b | _, mk₁ x => mk₁ (f true x) | _, mk₂ e => mk₂ (e.map f)
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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, Chris Hughes -/ import ring_theory.coprime import ring_theory.ideal.basic /-! # Lemmas about Euclidean domains Various about Euclidean domains are proved; all of them...
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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 Defines bounded lattice type class hierarchy. Includes the Prop and fun instances. -/ import order.lattice import data.option.basic import tactic.pi_instances set_opt...
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/- Copyright (c) 2018 Violeta Hernández Palacios, Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Violeta Hernández Palacios, Mario Carneiro -/ import set_theory.ordinal.arithmetic /-! # Fixed points of normal functions We prove various statements abo...
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/- Copyright (c) 2018 Andreas Swerdlow. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Author: Andreas Swerdlow -/ import algebra.module ring_theory.maps /-! # Sesquilinear form This file defines a bilinear form over a module. The definition requires a ring antiautomorphism...
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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 -/ import algebra.group_with_zero.power import algebra.big_operators.order import algebra.big_operators.ring import algebra.big_operators.intervals /-! # Partial sum...
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/- Copyright (c) 2018 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Author: Simon Hudon Lemmas about traversing collections. Inspired by: The Essence of the Iterator Pattern Jeremy Gibbons and Bruno César dos Santos Oliveira In Journal of Functional...
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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, Mario Carneiro -/ import data.list.basic data.pnat data.array.lemmas universes u v w /-- `bucket_array α β` is the underlying data type for `hash_map α β`, ...
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/- Copyright (c) 2021 Kevin Buzzard. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Author : Kevin Buzzard -/ import tactic -- imports all the Lean tactics /-! # Logic in Lean, example sheet 5 : "iff" (`↔`) We learn about how to manipulate `P ↔ Q` in Lean. ## Tactics You'...
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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.logic init.monad init.alternative open decidable universe variables u v attribute [instance] definition option_is_inhabited (A : Type ...
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definition Prop : Type.{1} := Type.{0} inductive or (A B : Prop) : Prop := intro_left : A → or A B, intro_right : B → or A B check or check or.intro_left check or.rec
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inductive Expr | Var : UInt32 → Expr | Val : UInt32 → Expr | Add : Expr → Expr → Expr open Expr def dec (n : UInt32) : UInt32 := if n = 0 then 0 else n-1 def mkExpr : UInt32 → UInt32 → Expr | n, v => if n = 0 then Val v else Add (mkExpr (n-1) (v+1)) (mkExpr (n-1) (dec v)) def eval : Expr → UInt32 | Var x => 0 | V...
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import data.set open set classical variable {X : Type} variables A B C D : set X -- Here is a short, though laconic, Lean proof of Proposition 0.1. example : A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) := eq_of_subset_of_subset (take x, suppose x ∈ A ∪ (B ∩ C), or.elim this (suppose x ∈ A, and.intro (or.inl this...
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/- Copyright (c) 2021 Yury G. Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury G. Kudryashov -/ import geometry.manifold.algebra.structures import geometry.manifold.bump_function import topology.metric_space.partition_of_unity import topology.shrinking_l...
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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, Robert Y. Lewis -/ import algebra.invertible import data.mv_polynomial.variables import data.mv_polynomial.comm_ring import data.mv_polynomial.expand import data.zmod....
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/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Author: Mario Carneiro The partial recursive functions are defined similarly to the primitive recursive functions, but now all functions are partial, implemented using the `roption` monad, and...
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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.list.prod_sigma import tactic.omega.clause import tactic.omega.nat.form /-! # DNF transformation -/ namespace omega namespace nat open_locale omega.nat @[simp] ...
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/- Copyright (c) 2021 Kevin Buzzard. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Buzzard, Ines Wright, Joachim Breitner -/ import group_theory.quotient_group import group_theory.solvable import group_theory.p_group import group_theory.sylow import data.nat.fa...
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/- Copyright (c) 2020 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Dupuis, Yaël Dillies -/ import algebra.order.smul /-! # Ordered module In this file we provide lemmas about `ordered_smul` that hold once a module structure is present. ##...
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/- Copyright (c) 2021 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import measure_theory.measure.complex_lebesgue import measure_theory.integral.divergence_theorem import measure_theory.integral.circle_integral import analysis.calc...
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example (p q : Prop) : p ∧ q → q ∧ p := begin intro h, cases h with hp hq, constructor, exact hq, exact hp end
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/- Copyright (c) 2020 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen, Devon Tuma -/ import ring_theory.polynomial.basic import ring_theory.non_zero_divisors section scale_roots variables {A K R S : Type*} [integral_domain A] [field K] [comm_...
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/- Copyright (c) 2020 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta, E. W. Ayers -/ import category_theory.over import category_theory.limits.shapes.finite_limits import category_theory.yoneda import order.complete_lattice import data.set.l...
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/- Copyright (c) 2021 Aaron Anderson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson -/ import group_theory.perm.fin import tactic.interval_cases /-! # Alternating Groups The alternating group on a finite type `α` is the subgroup of the permutation gr...
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-- modded induction', cases', rw' -- *TODO* -- waiting for simon PR for symmetry' import tactic.interactive run_cmd mk_simp_attr `leakage open lean open lean.parser local postfix `?`:9001 := optional local postfix *:9001 := many namespace tactic namespace interactive open interactive interactive.types expr privat...
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/- Copyright (c) 2021 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import analysis.calculus.deriv import analysis.analytic.basic import analysis.calculus.cont_diff /-! # Frechet derivatives of analytic functions. A function expre...
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/- Copyright (c) 2014 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Yaël Dillies, Patrick Stevens -/ import algebra.order.field import data.nat.cast /-! # Cast of naturals into fields This file concerns the canonical homomorphism `ℕ →...
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namespace nat check induction_on -- ERROR check rec_on -- ERROR check nat.induction_on check less_than_or_equal.rec_on -- OK check nat.less_than_or_equal.rec_on namespace le check rec_on -- ERROR check less_than_or_equal.rec_on end le end nat
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/- Copyright (c) 2021 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import analysis.normed_space.finite_dimension import analysis.calculus.affine_map import analysis.convex.combination import linear_algebra.affine_space.basis /-! # Bases i...
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mutual inductive AList (α β : Type u) | nil | cons (a : α) (t : BList α β) inductive BList (α β : Type u) | cons (b : β) (t : AList α β) end #print AList.nil.sizeOf_spec #print AList.cons.sizeOf_spec #print BList.cons.sizeOf_spec mutual inductive Foo (α : Type u) | mk (cs : AList (Foo α) (Boo α...
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/- Copyright (c) 2016 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura, Jannis Limperg -/ import Mathlib.PrePort import Mathlib.Lean3Lib.init.meta.tactic import Mathlib.Lean3Lib.init.meta.type_context import Mathlib.Lean3Lib.init....
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import .lovelib import init.data.char.basic namespace Day1 def search_helper : ℕ → ℕ → list ℕ → list (ℕ × ℕ) | needle a (b :: bs) := if a + b = needle then (a, b) :: search_helper needle a bs else search_helper needle a bs | _ _ [] := [] def search : ℕ → list ℕ → list (ℕ × ℕ) | needle (n :: ns) := sear...
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/- Copyright (c) 2018 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Johannes Hölzl -/ import analysis.normed.field.basic import analysis.normed.group.infinite_sum import data.matrix.basic import topology.sequences /-! # Normed spaces ...
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/- Copyright (c) 2019 Gabriel Ebner. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Gabriel Ebner, Marc Huisinga -/ import Lean.Data.Json.Basic namespace Lean universes u class FromJson (α : Type u) where fromJson? : Json → Except String α export FromJson (fromJ...
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/- Copyright (c) 2022 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne, Kexing Ying -/ import measure_theory.function.conditional_expectation.indicator /-! # Conditional expectation of real-valued functions This file proves some results reg...
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/- Copyright (c) 2021 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import category_theory.limits.shapes.pullbacks import ring_theory.tensor_product import algebra.category.Ring.limits import algebra.category.Ring.colimits import category_t...
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/- Copyright 2020 Grayson Burton License available in the LICENSE file. -/ import data.set.basic tactic private lemma {u} set_ins_comm {α : Type u} (x y : α) : ({x, y} : set α) = {y, x} := by simp [set.insert_def, or.comm] /-- A strict betweenness relation. -/ class {u} has_betweenness (α : Type u) : Type u :=...
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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: Leonardo de Moura -/ import Lean.Meta.Tactic.Rewrite import Lean.Meta.Tactic.Split import Lean.Elab.PreDefinition.Basic import Lean.Elab.PreDefinition.Eqns namespace Lean.Elab....
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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 Theory of Cauchy filters in uniform spaces. Complete uniform spaces. Totally bounded subsets. -/ import topology.uniform_space.basic open filter topol...
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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 -/ prelude import init.data.nat universes u w structure array (α : Type u) (n : nat) := (data : fin n → α) def mk_array {α} (n) (v : α) : array α n := {data ...
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-- Theorems/Exercises from "Logical Investigations, with the Nuprl Proof Assistant" -- by Robert L. Constable and Anne Trostle -- http://www.nuprl.org/MathLibrary/LogicalInvestigations/ import logic -- 2. The Minimal Implicational Calculus theorem thm1 {A B : Prop} : A → B → A := assume Ha Hb, Ha theorem thm2 {A B C ...
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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: Shing Tak Lam -/ import Mathlib.PrePort import Mathlib.Lean3Lib.init.default import Mathlib.data.mv_polynomial.variables import Mathlib.algebra.module.basic import Mathlib.tactic.ring ...
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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, Kenny Lau, Scott Morrison -/ import data.list.chain import data.list.nodup import data.list.of_fn import data.list.zip /-! # Ranges of naturals as lists This file sho...
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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 -/ import data.seq.seq import data.dlist universes u v w /- coinductive wseq (α : Type u) : Type u | nil : wseq α | cons : α → wseq α → wseq α | think : wseq α → ...
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import logic import set_theory.zfc namespace Set -- We have ext axiom. (Set.ext) -- Set.eq_empty proves there is only one empty set (using extensionality). -- We have pairing axiom. (Set.mem_pair) theorem pair_commutative {x y : Set} : ({x, y} : Set) = {y, x} := begin apply Set.ext, intro z, simp [Set.mem_pair]...
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/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Johannes Hölzl, Scott Morrison, Jens Wagemaker -/ import data.polynomial.field_division /-! # Theory of univariate polynomials -/ noncomputable theory local attribute [...
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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 algebra.indicator_function import data.equiv.encodable.lattice import data.set.countable import order.disjointed import order.filter.basic impo...
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/- Copyright (c) 2017 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Author: Mario Carneiro -/ import data.finset.lattice import data.multiset.sort /-! # Construct a sorted list from a finset. -/ namespace finset open multiset nat variables {α β : Type*} /-!...
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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.types.prod Author: Leonardo de Moura, Jeremy Avigad -/ prelude import ..wf ..num definition pair := @prod.mk namespace prod notation A * B := prod A B notation A × ...
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set_option pp.universes true check @not inductive list (A : Type) : Type := | nil {} : list A | cons : A → list A → list A namespace list open lift theorem nil_ne_cons {A : Type} (a : A) (v : list A) : nil ≠ cons a v := λ H, down (list.no_confusion H) theorem cons.inj₁ {A : Type} (a₁ a₂ : A) (v₁ v₂ : list...
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/- Copyright (c) 2021 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import analysis.normed_space.continuous_affine_map import analysis.calculus.cont_diff /-! # Smooth affine maps This file contains results about smoothness of affine maps....
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example (h : False) : False := by fail_if_success simp (config := { failIfUnchanged := true }) cases h example (h : (a :: [b]).length = 3) : False := by fail_if_success simp (config := { failIfUnchanged := true }) only at h simp (config := { failIfUnchanged := false }) only at h simp (config := { fai...
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/- Author: E.W.Ayers -/ meta def hello_override := `hello_override.name @[vm_override hello_override] -- this means that the VM should replace the definition of `hello` with `hello_override` when evaluating. meta def hello := `hello.name #print hello -- should use `hello #eval hello ...
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def all (p : Nat → Prop) : Prop := ∀x, p x example {p : Nat → Prop} (h : all p) : p 0 := h 0
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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 order.preorder_hom import category_theory.concrete_category import algebra.punit_instances /-! # Category of preorders -/ open category_theory /-- The categ...
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/- Copyright (c) 2020 The Xena project. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Author: Kevin Buzzard Thanks: Imperial College London, leanprover-community The complex numbers, modelled as R^2 in the obvious way. -/ import complex.basic -- tutorial level /-! # Level 1...
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/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Author: Chris Hughes -/ import data.int.modeq data.int.gcd data.fintype data.pnat.basic open nat nat.modeq int def zmod (n : ℕ+) := fin n namespace zmod instance (n : ℕ+) : has_neg (zmod n) :...
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/- Copyright (c) 2019 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import algebra.ordered_pi import order.well_founded import algebra.order_functions /-! # Lexicographic order on Pi types This file defines the lexicographic relation fo...
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/- Copyright (c) 2021 Eric Rodriguez. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Rodriguez -/ import logic.embedding /-! # Equivalences on embeddings This file shows some advanced equivalences on embeddings, useful for constructing larger embeddings from sma...
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/- Copyright (c) 2019 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Sébastien Gouëzel, Yury Kudryashov -/ import analysis.calculus.tangent_cone import analysis.normed_space.units import analysis.asymptotic_equivalent /-! # The Fréchet de...
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-- TODO construct limits from products and equalizers
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import Lean new_frontend open Lean #eval (mkFVar `a).hasFVar #eval (mkApp (mkConst `foo) (mkFVar `a)).hasFVar #eval (mkApp (mkConst `foo) (mkConst `a)).hasFVar #eval (mkMVar `a).hasMVar #eval (mkApp (mkConst `foo) (mkMVar `a)).hasMVar #eval (mkApp (mkConst `foo) (mkConst `a)).hasMVar
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/- Copyright (c) 2022 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Shing Tak Lam, Frédéric Dupuis -/ import algebra.star.basic import group_theory.submonoid.membership /-! # Unitary elements of a star monoid This file defines `unitary R`, where `R`...
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/- Copyright (c) 2020 Yury Kudryashov All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Moritz Doll -/ import linear_algebra.basic import linear_algebra.prod /-! # Partially defined linear maps A `linear_pmap R E F` or `E →ₗ.[R] F` is a linear map from ...
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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, Yury Kudryashov -/ import category_theory.types import category_theory.epi_mono /-! # Concrete categories A concrete catego...
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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.System.IO import Init.Data.Int universes u /- Basic random number generator support based on the one available on the Haskell library -...
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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, Yury Kudryashov -/ import measure_theory.constructions.pi import measure_theory.measure.stieltjes import linear_algebra.matrix.transvection import dynamics.ergodic.meas...
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/- Copyright (c) 2022 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller -/ import set_theory.cardinal.finite /-! # Cardinality of finite types The cardinality of a finite type `α` is given by `nat.card α`. This function has the "junk value" of ...
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-- 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 inductive nat : Type := | O : nat | S : nat → nat inductive paths {A : Type} (a : A) : A → Type := | idpath : paths a a ...
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/- Copyright (c) 2018 Sean Leather. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sean Leather, Mario Carneiro Association lists. -/ import data.list.sigma universes u v w open list /-- `alist α β` is a key-value map stored as a linked list. It is a wrapper aroun...
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/- Copyright (c) 2019 Reid Barton. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Reid Barton -/ import topology.Top.adjunctions import category_theory.epi_mono universe u open category_theory open Top namespace Top lemma epi_iff_surjective {X Y : Top.{u}} (f : X ⟶...
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/- Copyright (c) 2021 Arthur Paulino. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Arthur Paulino, Kyle Miller -/ import combinatorics.simple_graph.clique import data.nat.lattice import data.setoid.partition import order.antichain /-! # Graph Coloring > THIS FILE ...
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import algebra.category.CommRing.basic import algebra.category.CommRing.adjunctions import algebra.category.CommRing.limits import algebra.category.CommRing.colimits
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/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Author: Johannes Hölzl, Kenny Lau -/ import Mathlib.PrePort import Mathlib.Lean3Lib.init.default import Mathlib.data.dfinsupp import Mathlib.linear_algebra.basic import Mathlib.PostPort universes u...
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/- Copyright (c) 2020 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying -/ import group_theory.submonoid /-! # Subgroups This file defines multiplicative and additive subgroups as an extension of submonoids, in a bundled form (unbundled subgroup...
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variable vec : Nat → Type variable concat {n m : Nat} (v : vec n) (w : vec m) : vec (n + m) infixl 65 ; : concat axiom concat_assoc {n1 n2 n3 : Nat} (v1 : vec n1) (v2 : vec n2) (v3 : vec n3) : (v1 ; v2) ; v3 = cast (to_heq (congr2 vec (symm (Nat::add_assoc n1 n2 n3)))) ...
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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.fin.vec_notation import logic.equiv.defs /-! # Equivalences for `fin n` -/ universes u variables {m n : ℕ} /-- Equivalence between `fin 0` and `empty`. -/ def f...
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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 -/ import Lean.Elab.Binders import Lean.Elab.SyntheticMVars namespace Lean.Elab.Command structure Scope where header : String opts : Opti...
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/- Copyright (c) 2019 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Author: Simon Hudon -/ import control.traversable.basic import tactic.simpa open interactive interactive.types lean.parser private meta def loc.to_string_aux : option name → string | none := "⊢"...
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/- Copyright (c) 2017 Gabriel Ebner. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Gabriel Ebner -/ import .clause_ops .prover_state open tactic monad namespace super meta def prove_using_assumption : tactic unit := do tgt ← target, ass ← mk_local_def `h tgt, exact ...
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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 -/ import analysis.calculus.cont_diff import geometry.manifold.charted_space /-! # Smooth manifolds (possibly with boundary or corners) A smooth manifold is a ma...
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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: Johan Commelin, Scott Morrison, Adam Topaz -/ import topology.sheaves.sheaf_of_functions import topology.sheaves.stalks import topology.local_homeomorph import topology.sheaves.sheaf_c...
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/- Copyright (c) 2019 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Sébastien Gouëzel, Yury Kudryashov -/ import analysis.calculus.tangent_cone import analysis.normed_space.units import analysis.asymptotics.asymptotic_equivalent import an...
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/- Copyright (c) 2022 Henrik Böving. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Henrik Böving -/ import Lean.Compiler.LCNF.PassManager import Lean.Compiler.LCNF.PrettyPrinter namespace Lean.Compiler.LCNF partial def Code.containsConst (constName : Name) (code : C...
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import tactic import tactic.linarith import tactic.norm_num import data.sigma.fst import category.basic universes u structure ref (α : Type u) : Type u := (addr : ℕ) def value := Σ α : Type u, α namespace intl inductive st (α : Type u) : Type.{u+1} | pure (x : α) : st | new_ref {β : Type u} : β → (ref β → st) → s...
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inductive List (T : Sort*) : Sort* | nil {} : List | cons : T → List → List namespace explicit inductive {u₁ u₂} ftree (A : Type u₁) (B : Type u₂) : Type (max 1 u₁ u₂) | leafa : A → ftree | leafb : B → ftree | node : (A → ftree) → (B → ftree) → ftree end explicit namespace implicit inductive ftree (A : Type) (B...
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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 category_theory.limits.shapes.terminal import category_theory.limits.shapes.binary_products import category_theory.limits.shapes.products import category_theor...
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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: Johan Commelin, Scott Morrison, Adam Topaz -/ import topology.sheaves.sheaf_of_functions import topology.sheaves.stalks /-! # Functions satisfying a local predicate form a sheaf. At ...
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open tactic smt_tactic list expr /- The replace tactic above is very naive since it recomputes the size of every subterm without using any cache. This produces a quadratic behavior. The profiler will report the bottleneck at size. We can address this performance bottleneck by using a cache. -/ structure rsimp'_cfg :=...
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variables p q : Prop check ¬(p → q) check ¬p → q check (¬p) → q check ¬(p → q) check p ↔ q check ¬(p ↔ q) check ¬p ↔ q check (¬p) ↔ q check (p → q) ↔ q check p → (q ↔ q)
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constants a b : ℤ constant f : ℤ → ℤ constant g : ℤ → ℤ → ℤ --#check λ x : ℤ, g (f (g a x)) (g x b) --#check λ x, g (f (g a x)) (g x b) constant Trool : Type constants Trool.true Trool.false Trool.maybe : Trool
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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: Floris van Doorn, Leonardo de Moura -/ prelude import Init.SimpLemmas universe u namespace Nat @[specialize] def foldAux {α : Type u} (f : Nat → α → α) (s : Nat) : Nat → α → α...
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import system.io open list vm_eval pp ([["aaa", "bbb", "ccc", "dddd", "eeeeee", "ffffff"], ["aaa", "bbb", "ccc", "dddd", "eeeeee", "ffffff"], ["aaa", "bbb", "ccc", "dddd", "eeeeee", "ffffff"], ["aaa", "bbb", "ccc", "dddd", "eeeeee", "ffffff"]], [(10:nat), 20, 30])
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/- Copyright (c) 2017 Simon Hudon All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon, Mario Carneiro -/ import data.rat.cast data.rat.meta_defs tactic.doc_commands /-! # `norm_num` Evaluating arithmetic expressions including *, +, -, ^, ≤ -/ universes u v w ...
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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: Leonardo de Moura -/ import Lean.Parser.Module namespace Lean namespace ParseImports structure State where imports : Array Import := #[] pos : String.Pos := 0 error?...
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/- Copyright (c) 2022 María Inés de Frutos-Fernández. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: María Inés de Frutos-Fernández -/ import ring_theory.dedekind_domain.ideal /-! # Factorization of ideals of Dedekind domains > THIS FILE IS SYNCHRONIZED WITH MATHLIB4....
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/- Copyright (c) 2019 Alexander Bentkamp. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alexander Bentkamp, Yury Kudriashov, Yaël Dillies -/ import data.complex.module import data.set.intervals.image_preimage import linear_algebra.affine_space.affine_map import order....