imo.imo2021_q1 ⟷ Archive.Imo.Imo2021Q1

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -134,7 +134,7 @@ theorem exists_triplet_summing_to_squares (n : ℕ) (hn : 100 ≤ n) :
     all_goals norm_num
 #align imo2021_q1.exists_triplet_summing_to_squares Imo2021Q1.exists_triplet_summing_to_squares
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (a b «expr ∈ » B) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (a b «expr ∈ » B) -/
 -- Since it will be more convenient to work with sets later on, we will translate the above claim
 -- to state that there always exists a set B ⊆ [n, 2n] of cardinality at least 3, such that each
 -- pair of pairwise unequal elements of B sums to a perfect square.
@@ -169,9 +169,9 @@ end imo2021_q1
 
 open imo2021_q1
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (A «expr ⊆ » finset.Icc[finset.Icc] n «expr * »(2, n)) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (a b «expr ∈ » A) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (a b «expr ∈ » «expr \ »(finset.Icc[finset.Icc] n «expr * »(2, n), A)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (A «expr ⊆ » finset.Icc[finset.Icc] n «expr * »(2, n)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (a b «expr ∈ » A) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (a b «expr ∈ » «expr \ »(finset.Icc[finset.Icc] n «expr * »(2, n), A)) -/
 theorem imo2021_q1 :
     ∀ n : ℕ,
       100 ≤ n →
@@ -191,7 +191,7 @@ theorem imo2021_q1 :
     simpa only [Finset.mem_Icc] using h₂ c hcB
   have hB' : 2 * 1 < (B ∩ (Finset.Icc n (2 * n) \ A) ∪ B ∩ A).card :=
     by
-    rw [← Finset.inter_distrib_left, Finset.sdiff_union_self_eq_union,
+    rw [← Finset.inter_union_distrib_left, Finset.sdiff_union_self_eq_union,
       finset.union_eq_left_iff_subset.mpr hA, (Finset.inter_eq_left_iff_subset _ _).mpr hBsub]
     exact nat.succ_le_iff.mp hB
   -- Since B has cardinality greater or equal to 3, there must exist a subset C ⊆ B such that

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -54,16 +54,16 @@ theorem lower_bound (n l : ℕ) (hl : 2 + sqrt (4 + 2 * n) ≤ 2 * l) : n + 4 *
   by
   suffices 2 * ((n : ℝ) + 4 * l) - 8 * l + 4 ≤ 2 * (2 * l * l) - 8 * l + 4
     by
-    simp only [mul_le_mul_left, sub_le_sub_iff_right, add_le_add_iff_right, zero_lt_two] at this 
+    simp only [mul_le_mul_left, sub_le_sub_iff_right, add_le_add_iff_right, zero_lt_two] at this
     exact_mod_cast this
-  rw [← le_sub_iff_add_le', sqrt_le_iff, pow_two] at hl 
+  rw [← le_sub_iff_add_le', sqrt_le_iff, pow_two] at hl
   convert hl.2 using 1 <;> ring
 #align imo2021_q1.lower_bound Imo2021Q1.lower_bound
 
 theorem upper_bound (n l : ℕ) (hl : (l : ℝ) ≤ sqrt (1 + n) - 1) : 2 * l * l + 4 * l ≤ 2 * n :=
   by
   have h1 : ∀ n : ℕ, 0 ≤ 1 + (n : ℝ) := by intro n; exact_mod_cast Nat.zero_le (1 + n)
-  rw [le_sub_iff_add_le', le_sqrt (h1 l) (h1 n), pow_two] at hl 
+  rw [le_sub_iff_add_le', le_sqrt (h1 l) (h1 n), pow_two] at hl
   rw [← add_le_add_iff_right 2, ← @Nat.cast_le ℝ]
   simp only [Nat.cast_bit0, Nat.cast_add, Nat.cast_one, Nat.cast_mul]
   convert (mul_le_mul_left zero_lt_two).mpr hl using 1 <;> ring
@@ -154,7 +154,7 @@ theorem exists_finset_3_le_card_with_pairs_summing_to_squares (n : ℕ) (hn : 10
       push_neg
       exact ⟨⟨hab.ne, (hab.trans hbc).Ne⟩, hbc.ne⟩
   · intro x hx y hy hxy
-    simp only [Finset.mem_insert, Finset.mem_singleton] at hx hy 
+    simp only [Finset.mem_insert, Finset.mem_singleton] at hx hy
     rcases hx with (rfl | rfl | rfl) <;> rcases hy with (rfl | rfl | rfl)
     all_goals
       first
@@ -198,9 +198,9 @@ theorem imo2021_q1 :
   -- for any A ⊆ [n, 2n], either C ⊆ A or C ⊆ [n, 2n] \ A and C has cardinality greater
   -- or equal to 2.
   obtain ⟨C, hC, hCA⟩ := Finset.exists_subset_or_subset_of_two_mul_lt_card hB'
-  rw [Finset.one_lt_card] at hC 
+  rw [Finset.one_lt_card] at hC
   rcases hC with ⟨a, ha, b, hb, hab⟩
-  simp only [Finset.subset_iff, Finset.mem_inter] at hCA 
+  simp only [Finset.subset_iff, Finset.mem_inter] at hCA
   -- Now we split into the two cases C ⊆ [n, 2n] \ A and C ⊆ A, which can be dealt with identically.
       cases hCA <;>
       [right; left] <;>

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -74,7 +74,7 @@ theorem radical_inequality {n : ℕ} (h : 107 ≤ n) : sqrt (4 + 2 * n) ≤ 2 *
   have h1n : 0 ≤ 1 + (n : ℝ) := by norm_cast; exact Nat.zero_le _
   rw [sqrt_le_iff]
   constructor
-  · simp only [sub_nonneg, zero_le_mul_left, zero_lt_two, le_sqrt zero_lt_three.le h1n]
+  · simp only [sub_nonneg, mul_nonneg_iff_of_pos_left, zero_lt_two, le_sqrt zero_lt_three.le h1n]
     norm_cast; linarith only [h]
   ring
   rw [pow_two, ← sqrt_mul h1n, sqrt_mul_self h1n]

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -3,12 +3,12 @@ Copyright (c) 2021 Mantas Bakšys. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mantas Bakšys
 -/
-import Mathbin.Data.Real.Sqrt
-import Mathbin.Tactic.IntervalCases
+import Data.Real.Sqrt
+import Tactic.IntervalCases
 import Mathbin.Tactic.Linarith.Default
-import Mathbin.Tactic.NormCast
-import Mathbin.Tactic.NormNum
-import Mathbin.Tactic.RingExp
+import Tactic.NormCast
+import Tactic.NormNum
+import Tactic.RingExp
 
 #align_import imo.imo2021_q1 from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
 
@@ -134,7 +134,7 @@ theorem exists_triplet_summing_to_squares (n : ℕ) (hn : 100 ≤ n) :
     all_goals norm_num
 #align imo2021_q1.exists_triplet_summing_to_squares Imo2021Q1.exists_triplet_summing_to_squares
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b «expr ∈ » B) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (a b «expr ∈ » B) -/
 -- Since it will be more convenient to work with sets later on, we will translate the above claim
 -- to state that there always exists a set B ⊆ [n, 2n] of cardinality at least 3, such that each
 -- pair of pairwise unequal elements of B sums to a perfect square.
@@ -169,9 +169,9 @@ end imo2021_q1
 
 open imo2021_q1
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (A «expr ⊆ » finset.Icc[finset.Icc] n «expr * »(2, n)) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b «expr ∈ » A) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b «expr ∈ » «expr \ »(finset.Icc[finset.Icc] n «expr * »(2, n), A)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (A «expr ⊆ » finset.Icc[finset.Icc] n «expr * »(2, n)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (a b «expr ∈ » A) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (a b «expr ∈ » «expr \ »(finset.Icc[finset.Icc] n «expr * »(2, n), A)) -/
 theorem imo2021_q1 :
     ∀ n : ℕ,
       100 ≤ n →

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

@@ -2,11 +2,6 @@
 Copyright (c) 2021 Mantas Bakšys. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mantas Bakšys
-
-! This file was ported from Lean 3 source module imo.imo2021_q1
-! leanprover-community/mathlib commit 08b081ea92d80e3a41f899eea36ef6d56e0f1db0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Real.Sqrt
 import Mathbin.Tactic.IntervalCases
@@ -15,6 +10,8 @@ import Mathbin.Tactic.NormCast
 import Mathbin.Tactic.NormNum
 import Mathbin.Tactic.RingExp
 
+#align_import imo.imo2021_q1 from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
+
 /-!
 # IMO 2021 Q1
 
@@ -137,7 +134,7 @@ theorem exists_triplet_summing_to_squares (n : ℕ) (hn : 100 ≤ n) :
     all_goals norm_num
 #align imo2021_q1.exists_triplet_summing_to_squares Imo2021Q1.exists_triplet_summing_to_squares
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (a b «expr ∈ » B) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b «expr ∈ » B) -/
 -- Since it will be more convenient to work with sets later on, we will translate the above claim
 -- to state that there always exists a set B ⊆ [n, 2n] of cardinality at least 3, such that each
 -- pair of pairwise unequal elements of B sums to a perfect square.
@@ -172,9 +169,9 @@ end imo2021_q1
 
 open imo2021_q1
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (A «expr ⊆ » finset.Icc[finset.Icc] n «expr * »(2, n)) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (a b «expr ∈ » A) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (a b «expr ∈ » «expr \ »(finset.Icc[finset.Icc] n «expr * »(2, n), A)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (A «expr ⊆ » finset.Icc[finset.Icc] n «expr * »(2, n)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b «expr ∈ » A) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b «expr ∈ » «expr \ »(finset.Icc[finset.Icc] n «expr * »(2, n), A)) -/
 theorem imo2021_q1 :
     ∀ n : ℕ,
       100 ≤ n →

mathlib commit https://github.com/leanprover-community/mathlib/commit/bf2428c9486c407ca38b5b3fb10b87dad0bc99fa

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mantas Bakšys
 
 ! This file was ported from Lean 3 source module imo.imo2021_q1
-! leanprover-community/mathlib commit 308826471968962c6b59c7ff82a22757386603e3
+! leanprover-community/mathlib commit 08b081ea92d80e3a41f899eea36ef6d56e0f1db0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -18,6 +18,9 @@ import Mathbin.Tactic.RingExp
 /-!
 # IMO 2021 Q1
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Let `n≥100` be an integer. Ivan writes the numbers `n, n+1,..., 2n` each on different cards.
 He then shuffles these `n+1` cards, and divides them into two piles. Prove that at least one
 of the piles contains two cards such that the sum of their numbers is a perfect square.

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

@@ -134,7 +134,7 @@ theorem exists_triplet_summing_to_squares (n : ℕ) (hn : 100 ≤ n) :
     all_goals norm_num
 #align imo2021_q1.exists_triplet_summing_to_squares Imo2021Q1.exists_triplet_summing_to_squares
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b «expr ∈ » B) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (a b «expr ∈ » B) -/
 -- Since it will be more convenient to work with sets later on, we will translate the above claim
 -- to state that there always exists a set B ⊆ [n, 2n] of cardinality at least 3, such that each
 -- pair of pairwise unequal elements of B sums to a perfect square.
@@ -169,9 +169,9 @@ end imo2021_q1
 
 open imo2021_q1
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (A «expr ⊆ » finset.Icc[finset.Icc] n «expr * »(2, n)) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b «expr ∈ » A) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a b «expr ∈ » «expr \ »(finset.Icc[finset.Icc] n «expr * »(2, n), A)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (A «expr ⊆ » finset.Icc[finset.Icc] n «expr * »(2, n)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (a b «expr ∈ » A) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (a b «expr ∈ » «expr \ »(finset.Icc[finset.Icc] n «expr * »(2, n), A)) -/
 theorem imo2021_q1 :
     ∀ n : ℕ,
       100 ≤ n →

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3209ddf94136d36e5e5c624b10b2a347cc9d090

Move the content of Data.Nat.ForSqrt and Data.Nat.Sqrt to Data.Nat.Defs by using Nat-specific Std lemmas rather than the mathlib general ones. This makes it ready to move to Std if wanted.

@@ -4,7 +4,6 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mantas Bakšys
 -/
 import Mathlib.Data.Nat.Interval
-import Mathlib.Data.Nat.Sqrt
 import Mathlib.Tactic.IntervalCases
 import Mathlib.Tactic.Linarith
 

Standardizes the following names for distributivity laws across Finset and Set:

• inter_union_distrib_left
• inter_union_distrib_right
• union_inter_distrib_left
• union_inter_distrib_right

Makes arguments explicit in:

• Set.union_inter_distrib_right
• Set.union_inter_distrib_left
• Set.inter_union_distrib_right

Deprecates these theorem names:

• Finset.inter_distrib_left
• Finset.inter_distrib_right
• Finset.union_distrib_right
• Finset.union_distrib_left
• Set.inter_distrib_left
• Set.inter_distrib_right
• Set.union_distrib_right
• Set.union_distrib_left

Fixes use of deprecated names and implicit arguments in these files:

• Topology/Basic
• Topology/Connected/Basic
• MeasureTheory/MeasurableSpace/Basic
• MeasureTheory/Covering/Differentiation
• MeasureTheory/Constructions/BorelSpace/Basic
• Data/Set/Image
• Data/Set/Basic
• Data/PFun
• Data/Matroid/Dual
• Data/Finset/Sups
• Data/Finset/Basic
• Combinatorics/SetFamily/FourFunctions
• Combinatorics/Additive/SalemSpencer
• Counterexamples/Phillips.lean
• Archive/Imo/Imo2021Q1.lean

@@ -124,7 +124,7 @@ theorem imo2021_q1 :
   have hBsub : B ⊆ Finset.Icc n (2 * n) := by
     intro c hcB; simpa only [Finset.mem_Icc] using h₂ c hcB
   have hB' : 2 * 1 < (B ∩ (Finset.Icc n (2 * n) \ A) ∪ B ∩ A).card := by
-    rw [← inter_distrib_left, sdiff_union_self_eq_union, union_eq_left.2 hA,
+    rw [← inter_union_distrib_left, sdiff_union_self_eq_union, union_eq_left.2 hA,
       inter_eq_left.2 hBsub]
     exact Nat.succ_le_iff.mp hB
   -- Since B has cardinality greater or equal to 3, there must exist a subset C ⊆ B such that

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -48,13 +48,13 @@ namespace Imo2021Q1
 -- n ≤ 2 * l ^ 2 - 4 * l and 2 * l ^ 2 + 4 * l ≤ 2 * n for n ≥ 100.
 theorem exists_numbers_in_interval (n : ℕ) (hn : 100 ≤ n) :
     ∃ l : ℕ, n + 4 * l ≤ 2 * l ^ 2 ∧ 2 * l ^ 2 + 4 * l ≤ 2 * n := by
-  have hn' : 1 ≤ Nat.sqrt (n + 1)
-  · rw [Nat.le_sqrt]
+  have hn' : 1 ≤ Nat.sqrt (n + 1) := by
+    rw [Nat.le_sqrt]
     linarith
   have h₁ := Nat.sqrt_le' (n + 1)
   have h₂ := Nat.succ_le_succ_sqrt' (n + 1)
-  have h₃ : 10 ≤ (n + 1).sqrt
-  · rw [Nat.le_sqrt]
+  have h₃ : 10 ≤ (n + 1).sqrt := by
+    rw [Nat.le_sqrt]
     linarith only [hn]
   rw [← Nat.sub_add_cancel hn'] at h₁ h₂ h₃
   set l := (n + 1).sqrt - 1

Changes in this PR shouldn't change the public API. The only changes about ∃ x ∈ s, _ is inside a proof.

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>

@@ -110,7 +110,7 @@ end Imo2021Q1
 open Imo2021Q1
 
 theorem imo2021_q1 :
-    ∀ n : ℕ, 100 ≤ n → ∀ (A) (_ : A ⊆ Finset.Icc n (2 * n)),
+    ∀ n : ℕ, 100 ≤ n → ∀ A ⊆ Finset.Icc n (2 * n),
     (∃ a ∈ A, ∃ b ∈ A, a ≠ b ∧ ∃ k : ℕ, a + b = k ^ 2) ∨
     ∃ a ∈ Finset.Icc n (2 * n) \ A, ∃ b ∈ Finset.Icc n (2 * n) \ A,
       a ≠ b ∧ ∃ k : ℕ, a + b = k ^ 2 := by

Follow-up #9184

@@ -82,7 +82,7 @@ theorem exists_triplet_summing_to_squares (n : ℕ) (hn : 100 ≤ n) :
 theorem exists_finset_3_le_card_with_pairs_summing_to_squares (n : ℕ) (hn : 100 ≤ n) :
     ∃ B : Finset ℕ,
       2 * 1 + 1 ≤ B.card ∧
-      (∀ (a) (_ : a ∈ B) (b) (_ : b ∈ B), a ≠ b → ∃ k, a + b = k ^ 2) ∧
+      (∀ a ∈ B, ∀ b ∈ B, a ≠ b → ∃ k, a + b = k ^ 2) ∧
       ∀ c ∈ B, n ≤ c ∧ c ≤ 2 * n := by
   obtain ⟨a, b, c, hna, hab, hbc, hcn, h₁, h₂, h₃⟩ := exists_triplet_summing_to_squares n hn
   refine' ⟨{a, b, c}, _, _, _⟩
@@ -111,8 +111,8 @@ open Imo2021Q1
 
 theorem imo2021_q1 :
     ∀ n : ℕ, 100 ≤ n → ∀ (A) (_ : A ⊆ Finset.Icc n (2 * n)),
-    (∃ (a : _) (_ : a ∈ A) (b : _) (_ : b ∈ A), a ≠ b ∧ ∃ k : ℕ, a + b = k ^ 2) ∨
-    ∃ (a : _) (_ : a ∈ Finset.Icc n (2 * n) \ A) (b : _) (_ : b ∈ Finset.Icc n (2 * n) \ A),
+    (∃ a ∈ A, ∃ b ∈ A, a ≠ b ∧ ∃ k : ℕ, a + b = k ^ 2) ∨
+    ∃ a ∈ Finset.Icc n (2 * n) \ A, ∃ b ∈ Finset.Icc n (2 * n) \ A,
       a ≠ b ∧ ∃ k : ℕ, a + b = k ^ 2 := by
   intro n hn A hA
   -- For each n ∈ ℕ such that 100 ≤ n, there exists a pairwise unequal triplet {a, b, c} ⊆ [n, 2n]

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -124,7 +124,7 @@ theorem imo2021_q1 :
   have hBsub : B ⊆ Finset.Icc n (2 * n) := by
     intro c hcB; simpa only [Finset.mem_Icc] using h₂ c hcB
   have hB' : 2 * 1 < (B ∩ (Finset.Icc n (2 * n) \ A) ∪ B ∩ A).card := by
-    rw [←inter_distrib_left, sdiff_union_self_eq_union, union_eq_left.2 hA,
+    rw [← inter_distrib_left, sdiff_union_self_eq_union, union_eq_left.2 hA,
       inter_eq_left.2 hBsub]
     exact Nat.succ_le_iff.mp hB
   -- Since B has cardinality greater or equal to 3, there must exist a subset C ⊆ B such that

Rename union_eq_left_iff_subset to union_eq_left to match sup_eq_left. Similarly for the right and inter versions.

@@ -40,6 +40,7 @@ Then, by the Pigeonhole principle, at least two numbers in the triplet must lie
 which finishes the proof.
 -/
 
+open Finset
 
 namespace Imo2021Q1
 
@@ -123,8 +124,8 @@ theorem imo2021_q1 :
   have hBsub : B ⊆ Finset.Icc n (2 * n) := by
     intro c hcB; simpa only [Finset.mem_Icc] using h₂ c hcB
   have hB' : 2 * 1 < (B ∩ (Finset.Icc n (2 * n) \ A) ∪ B ∩ A).card := by
-    rw [← Finset.inter_distrib_left, Finset.sdiff_union_self_eq_union,
-      Finset.union_eq_left_iff_subset.mpr hA, (Finset.inter_eq_left_iff_subset _ _).mpr hBsub]
+    rw [←inter_distrib_left, sdiff_union_self_eq_union, union_eq_left.2 hA,
+      inter_eq_left.2 hBsub]
     exact Nat.succ_le_iff.mp hB
   -- Since B has cardinality greater or equal to 3, there must exist a subset C ⊆ B such that
   -- for any A ⊆ [n, 2n], either C ⊆ A or C ⊆ [n, 2n] \ A and C has cardinality greater

• depends on: #5966

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

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Mantas Bakšys. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mantas Bakšys
-
-! This file was ported from Lean 3 source module imo.imo2021_q1
-! leanprover-community/mathlib commit 308826471968962c6b59c7ff82a22757386603e3
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Nat.Interval
 import Mathlib.Data.Nat.Sqrt
 import Mathlib.Tactic.IntervalCases
 import Mathlib.Tactic.Linarith
 
+#align_import imo.imo2021_q1 from "leanprover-community/mathlib"@"308826471968962c6b59c7ff82a22757386603e3"
+
 /-!
 # IMO 2021 Q1
 

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

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

@@ -60,7 +60,7 @@ theorem exists_numbers_in_interval (n : ℕ) (hn : 100 ≤ n) :
     linarith only [hn]
   rw [← Nat.sub_add_cancel hn'] at h₁ h₂ h₃
   set l := (n + 1).sqrt - 1
-  refine ⟨l, ?_,  ?_⟩
+  refine ⟨l, ?_, ?_⟩
   · calc n + 4 * l ≤ (l ^ 2 + 4 * l + 2) + 4 * l := by linarith only [h₂]
       _ ≤ 2 * l ^ 2 := by nlinarith only [h₃]
   · linarith only [h₁]

This PR completes the port of the entire Probability folder to mathlib4.

@@ -8,11 +8,10 @@ Authors: Mantas Bakšys
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathlib.Data.Real.Sqrt
+import Mathlib.Data.Nat.Interval
+import Mathlib.Data.Nat.Sqrt
 import Mathlib.Tactic.IntervalCases
 import Mathlib.Tactic.Linarith
-import Mathlib.Tactic.NormCast
-import Mathlib.Tactic.NormNum
 
 /-!
 # IMO 2021 Q1
@@ -33,96 +32,50 @@ equations
 
 which can be solved to give
 
-    a = 2 * l * l - 4 * l
-    b = 2 * l * l + 1
-    c = 2 * l * l + 4 * l
+    a = 2 * l ^ 2 - 4 * l
+    b = 2 * l ^ 2 + 1
+    c = 2 * l ^ 2 + 4 * l
 
 Therefore, it is enough to show that there exists a natural number l such that
-`n ≤ 2 * l * l - 4 * l` and `2 * l * l + 4 * l ≤ 2 * n` for `n ≥ 100`.
+`n ≤ 2 * l ^ 2 - 4 * l` and `2 * l ^ 2 + 4 * l ≤ 2 * n` for `n ≥ 100`.
 
 Then, by the Pigeonhole principle, at least two numbers in the triplet must lie in the same pile,
 which finishes the proof.
 -/
 
 
-open Real
-
 namespace Imo2021Q1
 
-theorem lower_bound (n l : ℕ) (hl : 2 + sqrt (4 + 2 * n) ≤ 2 * l) : n + 4 * l ≤ 2 * l * l := by
-  suffices 2 * ((n : ℝ) + 4 * l) - 8 * l + 4 ≤ 2 * (2 * l * l) - 8 * l + 4 by
-    simp only [mul_le_mul_left, sub_le_sub_iff_right, add_le_add_iff_right, zero_lt_two] at this
-    exact_mod_cast this
-  rw [← le_sub_iff_add_le', sqrt_le_iff, pow_two] at hl
-  convert hl.2 using 1 <;> ring
-#align imo2021_q1.lower_bound Imo2021Q1.lower_bound
-
-theorem upper_bound (n l : ℕ) (hl : (l : ℝ) ≤ sqrt (1 + n) - 1) : 2 * l * l + 4 * l ≤ 2 * n := by
-  have h1 : ∀ n : ℕ, 0 ≤ 1 + (n : ℝ) := by intro n; exact_mod_cast Nat.zero_le (1 + n)
-  rw [le_sub_iff_add_le', le_sqrt (h1 l) (h1 n), pow_two] at hl
-  rw [← add_le_add_iff_right 2, ← @Nat.cast_le ℝ]
-  simp only [Nat.cast_add, Nat.cast_mul]
-  -- Porting note: Expanded `zero_lt_two` to `zero_lt_two' ℝ`
-  convert (mul_le_mul_left (zero_lt_two' ℝ)).mpr hl using 1 <;> ring
-#align imo2021_q1.upper_bound Imo2021Q1.upper_bound
-
-theorem radical_inequality {n : ℕ} (h : 107 ≤ n) : sqrt (4 + 2 * n) ≤ 2 * (sqrt (1 + n) - 3) := by
-  have h1n : 0 ≤ 1 + (n : ℝ) := by norm_cast; exact Nat.zero_le _
-  rw [sqrt_le_iff]
-  constructor
-  · -- Porting note: Expanded `zero_lt_three` to `zero_lt_three' ℝ`
-    simp only [sub_nonneg, zero_le_mul_left, zero_lt_two, le_sqrt (zero_lt_three' ℝ).le h1n]
-    norm_cast; linarith only [h]
-  ring_nf
-  rw [pow_two, ← sqrt_mul h1n, sqrt_mul_self h1n]
-  suffices 24 * sqrt (1 + n) ≤ 2 * n + 36 by linarith
-  rw [mul_self_le_mul_self_iff]
-  swap
-  · norm_num; apply sqrt_nonneg
-  swap
-  · norm_cast; linarith
-  ring_nf
-  rw [pow_two, ← sqrt_mul h1n, sqrt_mul_self h1n]
-  -- Not splitting into cases lead to a deterministic timeout on my machine
-  obtain ⟨rfl, h'⟩ : 107 = n ∨ 107 < n := eq_or_lt_of_le h
-  · norm_num
-  · norm_cast
-    nlinarith
-#align imo2021_q1.radical_inequality Imo2021Q1.radical_inequality
-
 -- We will later make use of the fact that there exists (l : ℕ) such that
--- n ≤ 2 * l * l - 4 * l and 2 * l * l + 4 * l ≤ 2 * n for n ≥ 107.
-theorem exists_numbers_in_interval (n : ℕ) (hn : 107 ≤ n) :
-    ∃ l : ℕ, n + 4 * l ≤ 2 * l * l ∧ 2 * l * l + 4 * l ≤ 2 * n := by
-  rsuffices ⟨l, t⟩ : ∃ l : ℕ, 2 + sqrt (4 + 2 * n) ≤ 2 * (l : ℝ) ∧ (l : ℝ) ≤ sqrt (1 + n) - 1
-  · exact ⟨l, lower_bound n l t.1, upper_bound n l t.2⟩
-  let x := sqrt (1 + n) - 1
-  refine' ⟨⌊x⌋₊, _, _⟩
-  · trans 2 * (x - 1)
-    · dsimp only; linarith only [radical_inequality hn]
-    · rw [mul_le_mul_left (zero_lt_two' ℝ)]; linarith only [(Nat.lt_floor_add_one x).le]
-  · apply Nat.floor_le; rw [sub_nonneg, le_sqrt]
-    all_goals norm_cast; try simp only [one_pow, le_add_iff_nonneg_right, zero_le']
+-- n ≤ 2 * l ^ 2 - 4 * l and 2 * l ^ 2 + 4 * l ≤ 2 * n for n ≥ 100.
+theorem exists_numbers_in_interval (n : ℕ) (hn : 100 ≤ n) :
+    ∃ l : ℕ, n + 4 * l ≤ 2 * l ^ 2 ∧ 2 * l ^ 2 + 4 * l ≤ 2 * n := by
+  have hn' : 1 ≤ Nat.sqrt (n + 1)
+  · rw [Nat.le_sqrt]
+    linarith
+  have h₁ := Nat.sqrt_le' (n + 1)
+  have h₂ := Nat.succ_le_succ_sqrt' (n + 1)
+  have h₃ : 10 ≤ (n + 1).sqrt
+  · rw [Nat.le_sqrt]
+    linarith only [hn]
+  rw [← Nat.sub_add_cancel hn'] at h₁ h₂ h₃
+  set l := (n + 1).sqrt - 1
+  refine ⟨l, ?_,  ?_⟩
+  · calc n + 4 * l ≤ (l ^ 2 + 4 * l + 2) + 4 * l := by linarith only [h₂]
+      _ ≤ 2 * l ^ 2 := by nlinarith only [h₃]
+  · linarith only [h₁]
 #align imo2021_q1.exists_numbers_in_interval Imo2021Q1.exists_numbers_in_interval
 
 theorem exists_triplet_summing_to_squares (n : ℕ) (hn : 100 ≤ n) :
     ∃ a b c : ℕ, n ≤ a ∧ a < b ∧ b < c ∧ c ≤ 2 * n ∧
-      (∃ k : ℕ, a + b = k * k) ∧ (∃ l : ℕ, c + a = l * l) ∧ ∃ m : ℕ, b + c = m * m := by
-  -- If n ≥ 107, we do not explicitly construct the triplet but use an existence
-  -- argument from lemma above.
-  obtain p | p : 107 ≤ n ∨ n < 107 := le_or_lt 107 n
-  · obtain ⟨l, hl1, hl2⟩ := exists_numbers_in_interval n p
-    have p : 1 < l := by contrapose! hl1; interval_cases l <;> linarith
-    have h₁ : 4 * l ≤ 2 * l * l := by linarith
-    have h₂ : 1 ≤ 2 * l := by linarith
-    refine' ⟨2 * l * l - 4 * l, 2 * l * l + 1, 2 * l * l + 4 * l, _, _, _,
-      ⟨_, ⟨2 * l - 1, _⟩, ⟨2 * l, _⟩, 2 * l + 1, _⟩⟩
-    all_goals zify [h₁, h₂]; linarith
-  -- Otherwise, if 100 ≤ n < 107, then it suffices to consider explicit
-  -- construction of a triplet {a, b, c}, which is constructed by setting l=9
-  -- in the argument at the start of the file.
-  · refine' ⟨126, 163, 198, p.le.trans _, _, _, by linarith, ⟨17, _⟩, ⟨18, _⟩, 19, _⟩
-    all_goals norm_num
+      (∃ k : ℕ, a + b = k ^ 2) ∧ (∃ l : ℕ, c + a = l ^ 2) ∧ ∃ m : ℕ, b + c = m ^ 2 := by
+  obtain ⟨l, hl1, hl2⟩ := exists_numbers_in_interval n hn
+  have p : 1 < l := by contrapose! hl1; interval_cases l <;> linarith
+  have h₁ : 4 * l ≤ 2 * l ^ 2 := by linarith
+  have h₂ : 1 ≤ 2 * l := by linarith
+  refine' ⟨2 * l ^ 2 - 4 * l, 2 * l ^ 2 + 1, 2 * l ^ 2 + 4 * l, _, _, _,
+    ⟨_, ⟨2 * l - 1, _⟩, ⟨2 * l, _⟩, 2 * l + 1, _⟩⟩
+  all_goals zify [h₁, h₂]; linarith
 #align imo2021_q1.exists_triplet_summing_to_squares Imo2021Q1.exists_triplet_summing_to_squares
 
 -- Since it will be more convenient to work with sets later on, we will translate the above claim
@@ -131,7 +84,7 @@ theorem exists_triplet_summing_to_squares (n : ℕ) (hn : 100 ≤ n) :
 theorem exists_finset_3_le_card_with_pairs_summing_to_squares (n : ℕ) (hn : 100 ≤ n) :
     ∃ B : Finset ℕ,
       2 * 1 + 1 ≤ B.card ∧
-      (∀ (a) (_ : a ∈ B) (b) (_ : b ∈ B), a ≠ b → ∃ k, a + b = k * k) ∧
+      (∀ (a) (_ : a ∈ B) (b) (_ : b ∈ B), a ≠ b → ∃ k, a + b = k ^ 2) ∧
       ∀ c ∈ B, n ≤ c ∧ c ≤ 2 * n := by
   obtain ⟨a, b, c, hna, hab, hbc, hcn, h₁, h₂, h₃⟩ := exists_triplet_summing_to_squares n hn
   refine' ⟨{a, b, c}, _, _, _⟩
@@ -160,9 +113,9 @@ open Imo2021Q1
 
 theorem imo2021_q1 :
     ∀ n : ℕ, 100 ≤ n → ∀ (A) (_ : A ⊆ Finset.Icc n (2 * n)),
-    (∃ (a : _) (_ : a ∈ A) (b : _) (_ : b ∈ A), a ≠ b ∧ ∃ k : ℕ, a + b = k * k) ∨
+    (∃ (a : _) (_ : a ∈ A) (b : _) (_ : b ∈ A), a ≠ b ∧ ∃ k : ℕ, a + b = k ^ 2) ∨
     ∃ (a : _) (_ : a ∈ Finset.Icc n (2 * n) \ A) (b : _) (_ : b ∈ Finset.Icc n (2 * n) \ A),
-      a ≠ b ∧ ∃ k : ℕ, a + b = k * k := by
+      a ≠ b ∧ ∃ k : ℕ, a + b = k ^ 2 := by
   intro n hn A hA
   -- For each n ∈ ℕ such that 100 ≤ n, there exists a pairwise unequal triplet {a, b, c} ⊆ [n, 2n]
   -- such that all pairwise sums are perfect squares. In practice, it will be easier to use

As reported on Zulip.