Module: Mathlib.Geometry.Euclidean.Incenter

Goal state before:
pp: case pos
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
n : ℕ
inst✝ : NeZero n
s : Simplex ℝ P n
signs₁ signs₂ : Finset (Fin (n + 1))
h₁ : s.ExcenterExists signs₁
h₂ : s.ExcenterExists signs₂
h : s.excenterWeights signs₁ = s.excenterWeights signs₂
hn₁ : ∑ i, s.excenterWeightsUnnorm signs₁ i ≠ 0
hn₂ : ∑ i, s.excenterWeightsUnnorm signs₂ i ≠ 0
hs : SignType.sign (∑ i, s.excenterWeightsUnnorm signs₁ i)⁻¹ = -SignType.sign (∑ i, s.excenterWeightsUnnorm signs₂ i)⁻¹
i : Fin (n + 1)
h✝¹ : i ∈ signs₁
h✝ : i ∈ signs₂
hi : -SignType.sign (-1) = SignType.sign (-1)
⊢ i ∈ signs₁ ↔ i ∈ signs₂ᶜ

pp: case neg
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
n : ℕ
inst✝ : NeZero n
s : Simplex ℝ P n
signs₁ signs₂ : Finset (Fin (n + 1))
h₁ : s.ExcenterExists signs₁
h₂ : s.ExcenterExists signs₂
h : s.excenterWeights signs₁ = s.excenterWeights signs₂
hn₁ : ∑ i, s.excenterWeightsUnnorm signs₁ i ≠ 0
hn₂ : ∑ i, s.excenterWeightsUnnorm signs₂ i ≠ 0
hs : SignType.sign (∑ i, s.excenterWeightsUnnorm signs₁ i)⁻¹ = -SignType.sign (∑ i, s.excenterWeightsUnnorm signs₂ i)⁻¹
i : Fin (n + 1)
h✝¹ : i ∈ signs₁
h✝ : i ∉ signs₂
hi : -SignType.sign (-1) = SignType.sign 1
⊢ i ∈ signs₁ ↔ i ∈ signs₂ᶜ

pp: case pos
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
n : ℕ
inst✝ : NeZero n
s : Simplex ℝ P n
signs₁ signs₂ : Finset (Fin (n + 1))
h₁ : s.ExcenterExists signs₁
h₂ : s.ExcenterExists signs₂
h : s.excenterWeights signs₁ = s.excenterWeights signs₂
hn₁ : ∑ i, s.excenterWeightsUnnorm signs₁ i ≠ 0
hn₂ : ∑ i, s.excenterWeightsUnnorm signs₂ i ≠ 0
hs : SignType.sign (∑ i, s.excenterWeightsUnnorm signs₁ i)⁻¹ = -SignType.sign (∑ i, s.excenterWeightsUnnorm signs₂ i)⁻¹
i : Fin (n + 1)
h✝¹ : i ∉ signs₁
h✝ : i ∈ signs₂
hi : -SignType.sign 1 = SignType.sign (-1)
⊢ i ∈ signs₁ ↔ i ∈ signs₂ᶜ

pp: case neg
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
n : ℕ
inst✝ : NeZero n
s : Simplex ℝ P n
signs₁ signs₂ : Finset (Fin (n + 1))
h₁ : s.ExcenterExists signs₁
h₂ : s.ExcenterExists signs₂
h : s.excenterWeights signs₁ = s.excenterWeights signs₂
hn₁ : ∑ i, s.excenterWeightsUnnorm signs₁ i ≠ 0
hn₂ : ∑ i, s.excenterWeightsUnnorm signs₂ i ≠ 0
hs : SignType.sign (∑ i, s.excenterWeightsUnnorm signs₁ i)⁻¹ = -SignType.sign (∑ i, s.excenterWeightsUnnorm signs₂ i)⁻¹
i : Fin (n + 1)
h✝¹ : i ∉ signs₁
h✝ : i ∉ signs₂
hi : -SignType.sign 1 = SignType.sign 1
⊢ i ∈ signs₁ ↔ i ∈ signs₂ᶜ

Tactic:
<;>

Goal state after:
case pos
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
n : ℕ
inst✝ : NeZero n
s : Simplex ℝ P n
signs₁ signs₂ : Finset (Fin (n + 1))
h₁ : s.ExcenterExists signs₁
h₂ : s.ExcenterExists signs₂
h : s.excenterWeights signs₁ = s.excenterWeights signs₂
hn₁ : ∑ i, s.excenterWeightsUnnorm signs₁ i ≠ 0
hn₂ : ∑ i, s.excenterWeightsUnnorm signs₂ i ≠ 0
hs : SignType.sign (∑ i, s.excenterWeightsUnnorm signs₁ i)⁻¹ = -SignType.sign (∑ i, s.excenterWeightsUnnorm signs₂ i)⁻¹
i : Fin (n + 1)
h✝¹ : i ∈ signs₁
h✝ : i ∈ signs₂
hi : -SignType.sign (-1) = SignType.sign (-1)
⊢ i ∈ signs₁ ↔ i ∈ signs₂ᶜ

case neg
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
n : ℕ
inst✝ : NeZero n
s : Simplex ℝ P n
signs₁ signs₂ : Finset (Fin (n + 1))
h₁ : s.ExcenterExists signs₁
h₂ : s.ExcenterExists signs₂
h : s.excenterWeights signs₁ = s.excenterWeights signs₂
hn₁ : ∑ i, s.excenterWeightsUnnorm signs₁ i ≠ 0
hn₂ : ∑ i, s.excenterWeightsUnnorm signs₂ i ≠ 0
hs : SignType.sign (∑ i, s.excenterWeightsUnnorm signs₁ i)⁻¹ = -SignType.sign (∑ i, s.excenterWeightsUnnorm signs₂ i)⁻¹
i : Fin (n + 1)
h✝¹ : i ∈ signs₁
h✝ : i ∉ signs₂
hi : -SignType.sign (-1) = SignType.sign 1
⊢ i ∈ signs₁ ↔ i ∈ signs₂ᶜ

case pos
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
n : ℕ
inst✝ : NeZero n
s : Simplex ℝ P n
signs₁ signs₂ : Finset (Fin (n + 1))
h₁ : s.ExcenterExists signs₁
h₂ : s.ExcenterExists signs₂
h : s.excenterWeights signs₁ = s.excenterWeights signs₂
hn₁ : ∑ i, s.excenterWeightsUnnorm signs₁ i ≠ 0
hn₂ : ∑ i, s.excenterWeightsUnnorm signs₂ i ≠ 0
hs : SignType.sign (∑ i, s.excenterWeightsUnnorm signs₁ i)⁻¹ = -SignType.sign (∑ i, s.excenterWeightsUnnorm signs₂ i)⁻¹
i : Fin (n + 1)
h✝¹ : i ∉ signs₁
h✝ : i ∈ signs₂
hi : -SignType.sign 1 = SignType.sign (-1)
⊢ i ∈ signs₁ ↔ i ∈ signs₂ᶜ

case neg
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
n : ℕ
inst✝ : NeZero n
s : Simplex ℝ P n
signs₁ signs₂ : Finset (Fin (n + 1))
h₁ : s.ExcenterExists signs₁
h₂ : s.ExcenterExists signs₂
h : s.excenterWeights signs₁ = s.excenterWeights signs₂
hn₁ : ∑ i, s.excenterWeightsUnnorm signs₁ i ≠ 0
hn₂ : ∑ i, s.excenterWeightsUnnorm signs₂ i ≠ 0
hs : SignType.sign (∑ i, s.excenterWeightsUnnorm signs₁ i)⁻¹ = -SignType.sign (∑ i, s.excenterWeightsUnnorm signs₂ i)⁻¹
i : Fin (n + 1)
h✝¹ : i ∉ signs₁
h✝ : i ∉ signs₂
hi : -SignType.sign 1 = SignType.sign 1
⊢ i ∈ signs₁ ↔ i ∈ signs₂ᶜ