I'll break down this Lean code line by line:
elab tk:"#trans_imports" stx:(str)? : command => do#trans_importstk:"#trans_imports" specifies the syntax for invoking this commandstx:(str)? means the command optionally takes a string argument: command => indicates this is a command-level elaboratordo starts a do-block for sequential imperative-style operations
Q: In Lean 4, how do I write a tactic that adds a fixed list of lemmas to a simp call?
A: Here is one way to write a tactic in Lean 4 that adds a fixed list of lemmas to a simp call:
import tactic
-- List of lemmas we want to add
def my_simp_lemmas : list name := [`foo, `bar, `baz]
| import Mathlib.Data.Polynomial.Eval | |
| open scoped Polynomial | |
| open Polynomial (C X) | |
| variable {R} [Semiring R] (p q : R[X]) | |
| class Polynomial.ComputableRepr where | |
| coeff : ℕ → R | |
| degreeBound : ℕ |
| 2023-11-22T02:15:59.7794991Z error: > LEAN_PATH=./.lake/packages/std/.lake/build/lib:./.lake/packages/Qq/.lake/build/lib:./.lake/packages/aesop/.lake/build/lib:./.lake/packages/proofwidgets/.lake/build/lib:./.lake/packages/Cli/.lake/build/lib:./.lake/build/lib LD_LIBRARY_PATH=./.lake/build/lib /home/lean/.elan/toolchains/leanprover--lean4---v4.3.0-rc2/bin/lean -Dpp.unicode.fun=true -Dpp.proofs.withType=false -DautoImplicit=false -DrelaxedAutoImplicit=false ./././Mathlib/CategoryTheory/Sites/Grothendieck.lean -R ././. -o ./.lake/build/lib/Mathlib/CategoryTheory/Sites/Grothendieck.olean -i ./.lake/build/lib/Mathlib/CategoryTheory/Sites/Grothendieck.ilean -c ./.lake/build/ir/Mathlib/CategoryTheory/Sites/Grothendieck.c | |
| 2023-11-22T02:15:59.7802783Z error: stdout: | |
| 2023-11-22T02:15:59.7805141Z ##[error]./././Mathlib/CategoryTheory/Sites/Grothendieck.lean:309:66: error: application type mismatch | |
| 2023-11-22T02:15:59.7806652Z completeLatticeOfInf | |
| 2023-11-22T02:15:59.7806982Z (WithTop | |
| 2023-11-22T02:15:59.8263195Z |
| import Mathlib.Topology.Covering | |
| import Mathlib.Topology.Instances.AddCircle | |
| open Topology | |
| variable {E X A : Type*} [TopologicalSpace E] [TopologicalSpace X] [TopologicalSpace A] | |
| /- Note: WeaklyLocallyCompact + T2 actually implies LocallyCompact. -/ | |
| @[to_additive] lemma coveringMulAction_of_properlyDiscontinuousSMul {Γ T} | |
| [TopologicalSpace T] [SMul Γ T] (cont : ∀ g : Γ, Continuous (fun t : T ↦ g • t)) |
| /- | |
| Copyright (c) 2023 Junyan Xu. All rights reserved. | |
| Released under Apache 2.0 license as described in the file LICENSE. | |
| Authors: Junyan Xu | |
| -/ | |
| import Mathlib.Topology.Covering | |
| import Mathlib.Topology.Homotopy.Path | |
| import Mathlib.Topology.UnitInterval | |
| /-! |
| Before adding instance `covariantClass_le_of_lt`: | |
| [Elab.command] [1.263200s] set_option profiler true in | |
| @[simp] | |
| theorem le_sub_one_iff {n : ℕ} {k : Fin (n + 1)} : k ≤ k - 1 ↔ k = 0 := | |
| by | |
| cases n | |
| · simp [fin_one_eq_zero k] | |
| rw [← lt_sub_one_iff, le_iff_lt_or_eq, lt_sub_one_iff, or_iff_left_iff_imp, eq_comm, sub_eq_iff_eq_add] | |
| simp ▼ |
| HPC cluster node with Intel(R) Xeon(R) CPU E7-8860 v4 @ 2.20GHz or AMD EPYC 7543 32-Core Processor: | |
| both the original (float64) and the float32 versions always yield 0.0 | |
| blas_info: | |
| libraries = ['cblas', 'blas', 'cblas', 'blas'] | |
| library_dirs = ['/usr/local/Anaconda/envs/py3.9/lib'] | |
| include_dirs = ['/usr/local/Anaconda/envs/py3.9/include'] | |
| language = c | |
| define_macros = [('HAVE_CBLAS', None)] | |
| blas_opt_info: | |
| define_macros = [('NO_ATLAS_INFO', 1), ('HAVE_CBLAS', None)] |
| import Mathlib.Algebra.Squarefree | |
| -- For definition of decomposition monoid and relative primeness, cf. https://link.springer.com/article/10.1007/s00233-019-10022-3 | |
| -- Discussion about the correct general definition of coprimality: https://leanprover.zulipchat.com/#narrow/stream/116395-maths/topic/IsCoprime.20is.20.40.5Bsimp.5D.3F | |
| -- GCD monoids are decomposition monoids: https://leanprover-community.github.io/mathlib4_docs/Mathlib/Algebra/GCDMonoid/Basic.html#exists_dvd_and_dvd_of_dvd_mul | |
| class DecompositionMonoid (R) [Semigroup R] : Prop where | |
| exists_dvd_and_dvd_of_dvd_mul : ∀ m n k : R, k ∣ m * n → ∃ d₁ d₂, d₁ ∣ m ∧ d₂ ∣ n ∧ k = d₁ * d₂ | |
| theorem exists_dvd_and_dvd_of_dvd_mul' {R} [Semigroup R] [DecompositionMonoid R] {m n k : R} |