File: Mathlib/Algebra/Order/Monoid/Units.lean

full_name: Units.instPreorder
code: @[to_additive]
instance [Monoid α] [Preorder α] : Preorder αˣ 
goal: Preorder αˣ

full_name: AddUnits.instPreorder
code: @[to_additive]
instance [Monoid α] [Preorder α] : Preorder αˣ 
goal: Preorder (AddUnits α)

full_name: AddUnits.val_le_val
code: @[to_additive (attr := simp, norm_cast)]
theorem val_le_val [Monoid α] [Preorder α] {a b : αˣ} : (a : α) ≤ b ↔ a ≤ b 
goal: ↑a ≤ ↑b ↔ a ≤ b

full_name: Units.val_le_val
code: @[to_additive (attr := simp, norm_cast)]
theorem val_le_val [Monoid α] [Preorder α] {a b : αˣ} : (a : α) ≤ b ↔ a ≤ b 
goal: ↑a ≤ ↑b ↔ a ≤ b

full_name: AddUnits.val_lt_val
code: @[to_additive (attr := simp, norm_cast)]
theorem val_lt_val [Monoid α] [Preorder α] {a b : αˣ} : (a : α) < b ↔ a < b 
goal: ↑a < ↑b ↔ a < b

full_name: Units.val_lt_val
code: @[to_additive (attr := simp, norm_cast)]
theorem val_lt_val [Monoid α] [Preorder α] {a b : αˣ} : (a : α) < b ↔ a < b 
goal: ↑a < ↑b ↔ a < b

full_name: Units.instPartialOrderUnits
code: @[to_additive]
instance instPartialOrderUnits [Monoid α] [PartialOrder α] : PartialOrder αˣ 
goal: PartialOrder αˣ

full_name: AddUnits.instPartialOrderAddUnits
code: @[to_additive]
instance instPartialOrderUnits [Monoid α] [PartialOrder α] : PartialOrder αˣ 
goal: PartialOrder (AddUnits α)

full_name: AddUnits.instLinearOrder
code: @[to_additive]
instance [Monoid α] [LinearOrder α] : LinearOrder αˣ 
goal: LinearOrder (AddUnits α)

full_name: Units.instLinearOrder
code: @[to_additive]
instance [Monoid α] [LinearOrder α] : LinearOrder αˣ 
goal: LinearOrder αˣ

full_name: Units.orderEmbeddingVal
code: /-- `val : αˣ → α` as an order embedding. -/
@[to_additive (attr := simps (config := .asFn))
  "`val : add_units α → α` as an order embedding."]
def orderEmbeddingVal [Monoid α] [LinearOrder α] : αˣ ↪o α 
goal: αˣ ↪o α

full_name: AddUnits.orderEmbeddingVal
code: /-- `val : αˣ → α` as an order embedding. -/
@[to_additive (attr := simps (config := .asFn))
  "`val : add_units α → α` as an order embedding."]
def orderEmbeddingVal [Monoid α] [LinearOrder α] : αˣ ↪o α 
goal: AddUnits α ↪o α

full_name: AddUnits.orderEmbeddingVal_apply
code: /-- `val : αˣ → α` as an order embedding. -/
@[to_additive (attr := simps (config := .asFn))
  "`val : add_units α → α` as an order embedding."]
def orderEmbeddingVal [Monoid α] [LinearOrder α] : αˣ ↪o α 
goal: ⇑AddUnits.orderEmbeddingVal = AddUnits.val

full_name: Units.orderEmbeddingVal_apply
code: /-- `val : αˣ → α` as an order embedding. -/
@[to_additive (attr := simps (config := .asFn))
  "`val : add_units α → α` as an order embedding."]
def orderEmbeddingVal [Monoid α] [LinearOrder α] : αˣ ↪o α 
goal: ⇑Units.orderEmbeddingVal = Units.val

full_name: Units.max_val
code: @[to_additive (attr := simp, norm_cast)]
theorem max_val [Monoid α] [LinearOrder α] {a b : αˣ} : (max a b).val = max a.val b.val 
goal: ↑(max a b) = max ↑a ↑b

full_name: AddUnits.max_val
code: @[to_additive (attr := simp, norm_cast)]
theorem max_val [Monoid α] [LinearOrder α] {a b : αˣ} : (max a b).val = max a.val b.val 
goal: ↑(max a b) = max ↑a ↑b

full_name: Units.min_val
code: @[to_additive (attr := simp, norm_cast)]
theorem min_val [Monoid α] [LinearOrder α] {a b : αˣ} : (min a b).val = min a.val b.val 
goal: ↑(min a b) = min ↑a ↑b

full_name: AddUnits.min_val
code: @[to_additive (attr := simp, norm_cast)]
theorem min_val [Monoid α] [LinearOrder α] {a b : αˣ} : (min a b).val = min a.val b.val 
goal: ↑(min a b) = min ↑a ↑b