data.nat.choose.boundsMathlib.Data.Nat.Choose.Bounds

This file has been ported!

Changes since the initial port

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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Changes in mathlib3port

mathlib3
mathlib3port
Diff
@@ -3,9 +3,9 @@ Copyright (c) 2021 Yaël Dillies. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Eric Rodriguez
 -/
-import Mathbin.Algebra.GroupPower.Lemmas
-import Mathbin.Algebra.Order.Field.Basic
-import Mathbin.Data.Nat.Choose.Basic
+import Algebra.GroupPower.Lemmas
+import Algebra.Order.Field.Basic
+import Data.Nat.Choose.Basic
 
 #align_import data.nat.choose.bounds from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"
 
Diff
@@ -2,16 +2,13 @@
 Copyright (c) 2021 Yaël Dillies. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Eric Rodriguez
-
-! This file was ported from Lean 3 source module data.nat.choose.bounds
-! leanprover-community/mathlib commit c3291da49cfa65f0d43b094750541c0731edc932
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.GroupPower.Lemmas
 import Mathbin.Algebra.Order.Field.Basic
 import Mathbin.Data.Nat.Choose.Basic
 
+#align_import data.nat.choose.bounds from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"
+
 /-!
 # Inequalities for binomial coefficients
 
Diff
@@ -34,6 +34,7 @@ variable {α : Type _} [LinearOrderedSemifield α]
 
 namespace Nat
 
+#print Nat.choose_le_pow /-
 theorem choose_le_pow (r n : ℕ) : (n.choose r : α) ≤ n ^ r / r ! :=
   by
   rw [le_div_iff']
@@ -42,7 +43,9 @@ theorem choose_le_pow (r n : ℕ) : (n.choose r : α) ≤ n ^ r / r ! :=
     exact n.desc_factorial_le_pow r
   exact_mod_cast r.factorial_pos
 #align nat.choose_le_pow Nat.choose_le_pow
+-/
 
+#print Nat.pow_le_choose /-
 -- horrific casting is due to ℕ-subtraction
 theorem pow_le_choose (r n : ℕ) : ((n + 1 - r : ℕ) ^ r : α) / r ! ≤ n.choose r :=
   by
@@ -52,6 +55,7 @@ theorem pow_le_choose (r n : ℕ) : ((n + 1 - r : ℕ) ^ r : α) / r ! ≤ n.cho
     exact n.pow_sub_le_desc_factorial r
   exact_mod_cast r.factorial_pos
 #align nat.pow_le_choose Nat.pow_le_choose
+-/
 
 end Nat
 
Diff
@@ -28,7 +28,7 @@ bounds `n^r/r^r ≤ n.choose r ≤ e^r n^r/r^r` in the future.
 -/
 
 
-open Nat
+open scoped Nat
 
 variable {α : Type _} [LinearOrderedSemifield α]
 
Diff
@@ -34,12 +34,6 @@ variable {α : Type _} [LinearOrderedSemifield α]
 
 namespace Nat
 
-/- warning: nat.choose_le_pow -> Nat.choose_le_pow is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nat.choose_le_pow Nat.choose_le_powₓ'. -/
 theorem choose_le_pow (r n : ℕ) : (n.choose r : α) ≤ n ^ r / r ! :=
   by
   rw [le_div_iff']
@@ -49,12 +43,6 @@ theorem choose_le_pow (r n : ℕ) : (n.choose r : α) ≤ n ^ r / r ! :=
   exact_mod_cast r.factorial_pos
 #align nat.choose_le_pow Nat.choose_le_pow
 
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-Case conversion may be inaccurate. Consider using '#align nat.pow_le_choose Nat.pow_le_chooseₓ'. -/
 -- horrific casting is due to ℕ-subtraction
 theorem pow_le_choose (r n : ℕ) : ((n + 1 - r : ℕ) ^ r : α) / r ! ≤ n.choose r :=
   by
Diff
@@ -36,7 +36,7 @@ namespace Nat
 
 /- warning: nat.choose_le_pow -> Nat.choose_le_pow is a dubious translation:
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align nat.choose_le_pow Nat.choose_le_powₓ'. -/
@@ -51,7 +51,7 @@ theorem choose_le_pow (r n : ℕ) : (n.choose r : α) ≤ n ^ r / r ! :=
 
 /- warning: nat.pow_le_choose -> Nat.pow_le_choose is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedSemifield.{u1} α] (r : Nat) (n : Nat), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (GroupWithZero.toDivInvMonoid.{u1} α (DivisionSemiring.toGroupWithZero.{u1} α (Semifield.toDivisionSemiring.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α _inst_1)))))) (HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (Semifield.toDivisionSemiring.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α _inst_1))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u1} Nat α (CoeTCₓ.coe.{1, succ u1} Nat α (Nat.castCoe.{u1} α (AddMonoidWithOne.toNatCast.{u1} α (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} α (NonAssocSemiring.toAddCommMonoidWithOne.{u1} α (Semiring.toNonAssocSemiring.{u1} α (DivisionSemiring.toSemiring.{u1} α (Semifield.toDivisionSemiring.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α _inst_1)))))))))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) r)) r) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u1} Nat α (CoeTCₓ.coe.{1, succ u1} Nat α (Nat.castCoe.{u1} α (AddMonoidWithOne.toNatCast.{u1} α (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} α (NonAssocSemiring.toAddCommMonoidWithOne.{u1} α (Semiring.toNonAssocSemiring.{u1} α (DivisionSemiring.toSemiring.{u1} α (Semifield.toDivisionSemiring.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α _inst_1)))))))))) (Nat.factorial r))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u1} Nat α (CoeTCₓ.coe.{1, succ u1} Nat α (Nat.castCoe.{u1} α (AddMonoidWithOne.toNatCast.{u1} α (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} α (NonAssocSemiring.toAddCommMonoidWithOne.{u1} α (Semiring.toNonAssocSemiring.{u1} α (DivisionSemiring.toSemiring.{u1} α (Semifield.toDivisionSemiring.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α _inst_1)))))))))) (Nat.choose n r))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedSemifield.{u1} α] (r : Nat) (n : Nat), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (GroupWithZero.toDivInvMonoid.{u1} α (DivisionSemiring.toGroupWithZero.{u1} α (Semifield.toDivisionSemiring.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α _inst_1)))))) (HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (Semiring.toMonoidWithZero.{u1} α (DivisionSemiring.toSemiring.{u1} α (Semifield.toDivisionSemiring.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α _inst_1))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u1} Nat α (CoeTCₓ.coe.{1, succ u1} Nat α (Nat.castCoe.{u1} α (AddMonoidWithOne.toNatCast.{u1} α (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} α (NonAssocSemiring.toAddCommMonoidWithOne.{u1} α (Semiring.toNonAssocSemiring.{u1} α (DivisionSemiring.toSemiring.{u1} α (Semifield.toDivisionSemiring.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α _inst_1)))))))))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) r)) r) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u1} Nat α (CoeTCₓ.coe.{1, succ u1} Nat α (Nat.castCoe.{u1} α (AddMonoidWithOne.toNatCast.{u1} α (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} α (NonAssocSemiring.toAddCommMonoidWithOne.{u1} α (Semiring.toNonAssocSemiring.{u1} α (DivisionSemiring.toSemiring.{u1} α (Semifield.toDivisionSemiring.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α _inst_1)))))))))) (Nat.factorial r))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat α (HasLiftT.mk.{1, succ u1} Nat α (CoeTCₓ.coe.{1, succ u1} Nat α (Nat.castCoe.{u1} α (AddMonoidWithOne.toNatCast.{u1} α (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} α (NonAssocSemiring.toAddCommMonoidWithOne.{u1} α (Semiring.toNonAssocSemiring.{u1} α (DivisionSemiring.toSemiring.{u1} α (Semifield.toDivisionSemiring.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α _inst_1)))))))))) (Nat.choose n r))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedSemifield.{u1} α] (r : Nat) (n : Nat), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedSemiring.toPartialOrder.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedSemifield.toDiv.{u1} α _inst_1)) (Nat.cast.{u1} α (Semiring.toNatCast.{u1} α (DivisionSemiring.toSemiring.{u1} α (Semifield.toDivisionSemiring.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α _inst_1)))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) r) r)) (Nat.cast.{u1} α (Semiring.toNatCast.{u1} α (DivisionSemiring.toSemiring.{u1} α (Semifield.toDivisionSemiring.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α _inst_1)))) (Nat.factorial r))) (Nat.cast.{u1} α (Semiring.toNatCast.{u1} α (DivisionSemiring.toSemiring.{u1} α (Semifield.toDivisionSemiring.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α _inst_1)))) (Nat.choose n r))
 Case conversion may be inaccurate. Consider using '#align nat.pow_le_choose Nat.pow_le_chooseₓ'. -/

Changes in mathlib4

mathlib3
mathlib4
chore: Move zpow lemmas (#9720)

These lemmas can be proved much earlier with little to no change to their proofs.

Part of #9411

Diff
@@ -4,6 +4,8 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Eric Rodriguez
 -/
 import Mathlib.Algebra.Order.Field.Basic
+import Mathlib.Algebra.Order.Ring.CharZero
+import Mathlib.Data.Nat.Cast.Order
 import Mathlib.Data.Nat.Choose.Basic
 import Mathlib.Algebra.Order.Ring.CharZero
 import Mathlib.Data.Nat.Cast.Order
fix: shake the import tree (#9749)

cherry-picked from #9347

Co-Authored-By: @digama0

Diff
@@ -3,9 +3,10 @@ Copyright (c) 2021 Yaël Dillies. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Eric Rodriguez
 -/
-import Mathlib.Algebra.GroupPower.Lemmas
 import Mathlib.Algebra.Order.Field.Basic
 import Mathlib.Data.Nat.Choose.Basic
+import Mathlib.Algebra.Order.Ring.CharZero
+import Mathlib.Data.Nat.Cast.Order
 
 #align_import data.nat.choose.bounds from "leanprover-community/mathlib"@"550b58538991c8977703fdeb7c9d51a5aa27df11"
 
chore: replace exact_mod_cast tactic with mod_cast elaborator where possible (#8404)

We still have the exact_mod_cast tactic, used in a few places, which somehow (?) works a little bit harder to prevent the expected type influencing the elaboration of the term. I would like to get to the bottom of this, and it will be easier once the only usages of exact_mod_cast are the ones that don't work using the term elaborator by itself.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

Diff
@@ -33,7 +33,7 @@ theorem choose_le_pow (r n : ℕ) : (n.choose r : α) ≤ (n ^ r : α) / r ! :=
   · norm_cast
     rw [← Nat.descFactorial_eq_factorial_mul_choose]
     exact n.descFactorial_le_pow r
-  exact_mod_cast r.factorial_pos
+  exact mod_cast r.factorial_pos
 #align nat.choose_le_pow Nat.choose_le_pow
 
 -- horrific casting is due to ℕ-subtraction
@@ -42,7 +42,7 @@ theorem pow_le_choose (r n : ℕ) : ((n + 1 - r : ℕ) ^ r : α) / r ! ≤ n.cho
   · norm_cast
     rw [← Nat.descFactorial_eq_factorial_mul_choose]
     exact n.pow_sub_le_descFactorial r
-  exact_mod_cast r.factorial_pos
+  exact mod_cast r.factorial_pos
 #align nat.pow_le_choose Nat.pow_le_choose
 
 end Nat
chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

Diff
@@ -24,7 +24,7 @@ bounds `n^r/r^r ≤ n.choose r ≤ e^r n^r/r^r` in the future.
 
 open Nat
 
-variable {α : Type _} [LinearOrderedSemifield α]
+variable {α : Type*} [LinearOrderedSemifield α]
 
 namespace Nat
 
chore: script to replace headers with #align_import statements (#5979)

Open in Gitpod

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

Diff
@@ -2,16 +2,13 @@
 Copyright (c) 2021 Yaël Dillies. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Eric Rodriguez
-
-! This file was ported from Lean 3 source module data.nat.choose.bounds
-! leanprover-community/mathlib commit 550b58538991c8977703fdeb7c9d51a5aa27df11
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.GroupPower.Lemmas
 import Mathlib.Algebra.Order.Field.Basic
 import Mathlib.Data.Nat.Choose.Basic
 
+#align_import data.nat.choose.bounds from "leanprover-community/mathlib"@"550b58538991c8977703fdeb7c9d51a5aa27df11"
+
 /-!
 # Inequalities for binomial coefficients
 
chore: cleanup whitespace (#5988)

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

Diff
@@ -31,7 +31,7 @@ variable {α : Type _} [LinearOrderedSemifield α]
 
 namespace Nat
 
-theorem choose_le_pow (r n : ℕ) : (n.choose r : α)  ≤ (n ^ r : α) / r ! := by
+theorem choose_le_pow (r n : ℕ) : (n.choose r : α) ≤ (n ^ r : α) / r ! := by
   rw [le_div_iff']
   · norm_cast
     rw [← Nat.descFactorial_eq_factorial_mul_choose]
feat: port data.nat.choose.bounds (#1139)

Port of data.nat.choose.bounds

based on 550b5853

Co-authored-by: Antoine Labelle <antoinelab01@gmail.com>

Dependencies 3 + 140

141 files ported (97.9%)
57123 lines ported (98.2%)
Show graph

The unported dependencies are