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Archive/Imo/Imo1994Q1.lean

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@@ -3,6 +3,7 @@ Copyright (c) 2021 Antoine Labelle. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Antoine Labelle
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-/
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import Mathlib.Algebra.Group.Fin.Basic
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import Mathlib.Algebra.Order.BigOperators.Group.Finset
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import Mathlib.Data.Finset.Sort
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import Mathlib.Data.Fin.Interval

Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean

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@@ -219,7 +219,7 @@ theorem oangle_ne_zero_and_ne_pi_iff_affineIndependent {p₁ p₂ p₃ : P} :
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∡ p₁ p₂ p₃ ≠ 0 ∧ ∡ p₁ p₂ p₃ ≠ π ↔ AffineIndependent ℝ ![p₁, p₂, p₃] := by
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rw [oangle, o.oangle_ne_zero_and_ne_pi_iff_linearIndependent,
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affineIndependent_iff_linearIndependent_vsub ℝ _ (1 : Fin 3), ←
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linearIndependent_equiv (finSuccAboveEquiv (1 : Fin 3)).toEquiv]
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linearIndependent_equiv (finSuccAboveEquiv (1 : Fin 3))]
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convert Iff.rfl
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ext i
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fin_cases i <;> rfl

Mathlib/Order/Fin/Basic.lean

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@@ -336,6 +336,14 @@ def OrderIso.finTwoArrowIso (α : Type*) [Preorder α] : (Fin 2 → α) ≃o α
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{ OrderIso.piFinTwoIso fun _ => α with toEquiv := finTwoArrowEquiv α }
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#align order_iso.fin_two_arrow_iso OrderIso.finTwoArrowIso
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/-- Order isomorphism between `Π j : Fin (n + 1), α j` and
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`α i × Π j : Fin n, α (Fin.succAbove i j)`. -/
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def OrderIso.piFinSuccAboveIso (α : Fin (n + 1) → Type*) [∀ i, LE (α i)]
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(i : Fin (n + 1)) : (∀ j, α j) ≃o α i × ∀ j, α (i.succAbove j) where
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toEquiv := Equiv.piFinSuccAbove α i
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map_rel_iff' := Iff.symm i.forall_iff_succAbove
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#align order_iso.pi_fin_succ_above_iso OrderIso.piFinSuccAboveIso
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/-- `Fin.succAbove` as an order isomorphism between `Fin n` and `{x : Fin (n + 1) // x ≠ p}`. -/
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def finSuccAboveOrderIso (p : Fin (n + 1)) : Fin n ≃o { x : Fin (n + 1) // x ≠ p } where
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__ := finSuccAboveEquiv p

Mathlib/SetTheory/Game/PGame.lean

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@@ -3,7 +3,6 @@ Copyright (c) 2019 Mario Carneiro. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Reid Barton, Mario Carneiro, Isabel Longbottom, Scott Morrison
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-/
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import Mathlib.Algebra.Group.Fin.Basic
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import Mathlib.Data.List.InsertNth
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import Mathlib.Logic.Relation
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import Mathlib.Logic.Small.Defs

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