File: Mathlib/Algebra/Order/Group/MinMax.lean

full_name: max_one_div_max_inv_one_eq_self
code: @[to_additive (attr := simp)]
theorem max_one_div_max_inv_one_eq_self (a : α) : max a 1 / max a⁻¹ 1 = a 
goal: max a 1 / max a⁻¹ 1 = a

full_name: max_zero_sub_max_neg_zero_eq_self
code: @[to_additive (attr := simp)]
theorem max_one_div_max_inv_one_eq_self (a : α) : max a 1 / max a⁻¹ 1 = a 
goal: max a 0 - max (-a) 0 = a

full_name: max_neg_zero
code: @[to_additive]
lemma max_inv_one (a : α) : max a⁻¹ 1 = a⁻¹ * max a 1 
goal: max (-a) 0 = -a + max a 0

full_name: max_inv_one
code: @[to_additive]
lemma max_inv_one (a : α) : max a⁻¹ 1 = a⁻¹ * max a 1 
goal: max a⁻¹ 1 = a⁻¹ * max a 1

full_name: min_inv_inv'
code: @[to_additive min_neg_neg]
theorem min_inv_inv' (a b : α) : min a⁻¹ b⁻¹ = (max a b)⁻¹ 
goal: min a⁻¹ b⁻¹ = (max a b)⁻¹

full_name: min_neg_neg
code: @[to_additive min_neg_neg]
theorem min_inv_inv' (a b : α) : min a⁻¹ b⁻¹ = (max a b)⁻¹ 
goal: min (-a) (-b) = -max a b

full_name: max_inv_inv'
code: @[to_additive max_neg_neg]
theorem max_inv_inv' (a b : α) : max a⁻¹ b⁻¹ = (min a b)⁻¹ 
goal: max a⁻¹ b⁻¹ = (min a b)⁻¹

full_name: max_neg_neg
code: @[to_additive max_neg_neg]
theorem max_inv_inv' (a b : α) : max a⁻¹ b⁻¹ = (min a b)⁻¹ 
goal: max (-a) (-b) = -min a b

full_name: min_sub_sub_right
code: @[to_additive min_sub_sub_right]
theorem min_div_div_right' (a b c : α) : min (a / c) (b / c) = min a b / c 
goal: min (a - c) (b - c) = min a b - c

full_name: min_div_div_right'
code: @[to_additive min_sub_sub_right]
theorem min_div_div_right' (a b c : α) : min (a / c) (b / c) = min a b / c 
goal: min (a / c) (b / c) = min a b / c

full_name: max_div_div_right'
code: @[to_additive max_sub_sub_right]
theorem max_div_div_right' (a b c : α) : max (a / c) (b / c) = max a b / c 
goal: max (a / c) (b / c) = max a b / c

full_name: max_sub_sub_right
code: @[to_additive max_sub_sub_right]
theorem max_div_div_right' (a b c : α) : max (a / c) (b / c) = max a b / c 
goal: max (a - c) (b - c) = max a b - c

full_name: min_sub_sub_left
code: @[to_additive min_sub_sub_left]
theorem min_div_div_left' (a b c : α) : min (a / b) (a / c) = a / max b c 
goal: min (a - b) (a - c) = a - max b c

full_name: min_div_div_left'
code: @[to_additive min_sub_sub_left]
theorem min_div_div_left' (a b c : α) : min (a / b) (a / c) = a / max b c 
goal: min (a / b) (a / c) = a / max b c

full_name: max_sub_sub_left
code: @[to_additive max_sub_sub_left]
theorem max_div_div_left' (a b c : α) : max (a / b) (a / c) = a / min b c 
goal: max (a - b) (a - c) = a - min b c

full_name: max_div_div_left'
code: @[to_additive max_sub_sub_left]
theorem max_div_div_left' (a b c : α) : max (a / b) (a / c) = a / min b c 
goal: max (a / b) (a / c) = a / min b c

full_name: max_sub_max_le_max
code: theorem max_sub_max_le_max (a b c d : α) : max a b - max c d ≤ max (a - c) (b - d) 
goal: max a b - max c d ≤ max (a - c) (b - d)

full_name: abs_max_sub_max_le_max
code: theorem abs_max_sub_max_le_max (a b c d : α) : |max a b - max c d| ≤ max |a - c| |b - d| 
goal: |max a b - max c d| ≤ max |a - c| |b - d|

full_name: abs_min_sub_min_le_max
code: theorem abs_min_sub_min_le_max (a b c d : α) : |min a b - min c d| ≤ max |a - c| |b - d| 
goal: |min a b - min c d| ≤ max |a - c| |b - d|

full_name: abs_max_sub_max_le_abs
code: theorem abs_max_sub_max_le_abs (a b c : α) : |max a c - max b c| ≤ |a - b| 
goal: |max a c - max b c| ≤ |a - b|