combinatorics.derangements.exponential
⟷
Mathlib.Combinatorics.Derangements.Exponential
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -46,7 +46,7 @@ theorem numDerangements_tendsto_inv_e :
rw [Real.exp_eq_exp_ℝ]
exact NormedSpace.expSeries_div_hasSum_exp ℝ (-1 : ℝ)
intro n
- rw [← Int.cast_ofNat, numDerangements_sum]
+ rw [← Int.cast_natCast, numDerangements_sum]
push_cast
rw [Finset.sum_div]
-- get down to individual terms
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -44,7 +44,7 @@ theorem numDerangements_tendsto_inv_e :
-- there's no specific lemma for ℝ that ∑ x^k/k! sums to exp(x), but it's
-- true in more general fields, so use that lemma
rw [Real.exp_eq_exp_ℝ]
- exact expSeries_div_hasSum_exp ℝ (-1 : ℝ)
+ exact NormedSpace.expSeries_div_hasSum_exp ℝ (-1 : ℝ)
intro n
rw [← Int.cast_ofNat, numDerangements_sum]
push_cast
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,9 +3,9 @@ Copyright (c) 2021 Henry Swanson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Henry Swanson, Patrick Massot
-/
-import Mathbin.Analysis.SpecialFunctions.Exponential
-import Mathbin.Combinatorics.Derangements.Finite
-import Mathbin.Order.Filter.Basic
+import Analysis.SpecialFunctions.Exponential
+import Combinatorics.Derangements.Finite
+import Order.Filter.Basic
#align_import combinatorics.derangements.exponential from "leanprover-community/mathlib"@"c20927220ef87bb4962ba08bf6da2ce3cf50a6dd"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,16 +2,13 @@
Copyright (c) 2021 Henry Swanson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Henry Swanson, Patrick Massot
-
-! This file was ported from Lean 3 source module combinatorics.derangements.exponential
-! leanprover-community/mathlib commit c20927220ef87bb4962ba08bf6da2ce3cf50a6dd
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Analysis.SpecialFunctions.Exponential
import Mathbin.Combinatorics.Derangements.Finite
import Mathbin.Order.Filter.Basic
+#align_import combinatorics.derangements.exponential from "leanprover-community/mathlib"@"c20927220ef87bb4962ba08bf6da2ce3cf50a6dd"
+
/-!
# Derangement exponential series
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -29,6 +29,7 @@ open scoped BigOperators
open scoped Topology
+#print numDerangements_tendsto_inv_e /-
theorem numDerangements_tendsto_inv_e :
Tendsto (fun n => (numDerangements n : ℝ) / n.factorial) atTop (𝓝 (Real.exp (-1))) :=
by
@@ -60,4 +61,5 @@ theorem numDerangements_tendsto_inv_e :
field_simp [Nat.factorial_ne_zero]
ring
#align num_derangements_tendsto_inv_e numDerangements_tendsto_inv_e
+-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Henry Swanson, Patrick Massot
! This file was ported from Lean 3 source module combinatorics.derangements.exponential
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit c20927220ef87bb4962ba08bf6da2ce3cf50a6dd
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -15,6 +15,9 @@ import Mathbin.Order.Filter.Basic
/-!
# Derangement exponential series
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
This file proves that the probability of a permutation on n elements being a derangement is 1/e.
The specific lemma is `num_derangements_tendsto_inv_e`.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297
@@ -43,7 +43,7 @@ theorem numDerangements_tendsto_inv_e :
-- there's no specific lemma for ℝ that ∑ x^k/k! sums to exp(x), but it's
-- true in more general fields, so use that lemma
rw [Real.exp_eq_exp_ℝ]
- exact exp_series_div_hasSum_exp ℝ (-1 : ℝ)
+ exact expSeries_div_hasSum_exp ℝ (-1 : ℝ)
intro n
rw [← Int.cast_ofNat, numDerangements_sum]
push_cast
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -22,9 +22,9 @@ The specific lemma is `num_derangements_tendsto_inv_e`.
open Filter
-open BigOperators
+open scoped BigOperators
-open Topology
+open scoped Topology
theorem numDerangements_tendsto_inv_e :
Tendsto (fun n => (numDerangements n : ℝ) / n.factorial) atTop (𝓝 (Real.exp (-1))) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
OfNat
and Nat.cast
lemmas (#11861)
This renames
Int.cast_ofNat
to Int.cast_natCast
Int.int_cast_ofNat
to Int.cast_ofNat
I think the history here is that this lemma was previously about Int.ofNat
, before we globally fixed the simp-normal form to be Nat.cast
.
Since the Int.cast_ofNat
name is repurposed, it can't be deprecated. Int.int_cast_ofNat
is such a wonky name that it was probably never used.
@@ -41,7 +41,7 @@ theorem numDerangements_tendsto_inv_e :
rw [Real.exp_eq_exp_ℝ]
exact expSeries_div_hasSum_exp ℝ (-1 : ℝ)
intro n
- rw [← Int.cast_ofNat, numDerangements_sum]
+ rw [← Int.cast_natCast, numDerangements_sum]
push_cast
rw [Finset.sum_div]
-- get down to individual terms
@@ -17,7 +17,7 @@ The specific lemma is `numDerangements_tendsto_inv_e`.
-/
-open Filter
+open Filter NormedSpace
open scoped BigOperators
@@ -2,16 +2,13 @@
Copyright (c) 2021 Henry Swanson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Henry Swanson, Patrick Massot
-
-! This file was ported from Lean 3 source module combinatorics.derangements.exponential
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Analysis.SpecialFunctions.Exponential
import Mathlib.Combinatorics.Derangements.Finite
import Mathlib.Order.Filter.Basic
+#align_import combinatorics.derangements.exponential from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
/-!
# Derangement exponential series
The unported dependencies are
algebra.order.module
init.core
linear_algebra.free_module.finite.rank
algebra.order.monoid.cancel.defs
algebra.abs
algebra.group_power.lemmas
init.data.list.basic
linear_algebra.free_module.rank
algebra.order.monoid.cancel.basic
init.data.list.default
topology.subset_properties
init.logic
The following 1 dependencies have changed in mathlib3 since they were ported, which may complicate porting this file