File: Mathlib/Data/PSigma/Order.lean

full_name: PSigma.«_aux_Mathlib_Data_PSigma_Order___macroRules_PSigma_termΣₗ'_,__1»
code: /-- The notation `Σₗ' i, α i` refers to a sigma type which is locally equipped with the
lexicographic order. -/
-- TODO: make `Lex` be `Sort u -> Sort u` so we can remove `.{_+1, _+1}`
notation3 "Σₗ' "(...)", "r:(scoped p => _root_.Lex (PSigma.{_+1, _+1} p)) => r
goal: Lean.Macro

full_name: PSigma.Lex.le
code: /-- The lexicographical `≤` on a sigma type. -/
instance le [LT ι] [∀ i, LE (α i)] : LE (Σₗ' i, α i) 
goal: LE (Σₗ' (i : ι), α i)

full_name: PSigma.Lex.lt
code: /-- The lexicographical `<` on a sigma type. -/
instance lt [LT ι] [∀ i, LT (α i)] : LT (Σₗ' i, α i) 
goal: LT (Σₗ' (i : ι), α i)

full_name: PSigma.Lex.preorder
code: instance preorder [Preorder ι] [∀ i, Preorder (α i)] : Preorder (Σₗ' i, α i) 
goal: Preorder (Σₗ' (i : ι), α i)

full_name: PSigma.Lex.partialOrder
code: /-- Dictionary / lexicographic partial_order for dependent pairs. -/
instance partialOrder [PartialOrder ι] [∀ i, PartialOrder (α i)] : PartialOrder (Σₗ' i, α i) 
goal: PartialOrder (Σₗ' (i : ι), α i)

full_name: PSigma.Lex.linearOrder
code: /-- Dictionary / lexicographic linear_order for pairs. -/
instance linearOrder [LinearOrder ι] [∀ i, LinearOrder (α i)] : LinearOrder (Σₗ' i, α i) 
goal: LinearOrder (Σₗ' (i : ι), α i)

full_name: PSigma.Lex.orderBot
code: /-- The lexicographical linear order on a sigma type. -/
instance orderBot [PartialOrder ι] [OrderBot ι] [∀ i, Preorder (α i)] [OrderBot (α ⊥)] :
    OrderBot (Σₗ' i, α i) 
goal: OrderBot (Σₗ' (i : ι), α i)

full_name: PSigma.Lex.orderTop
code: /-- The lexicographical linear order on a sigma type. -/
instance orderTop [PartialOrder ι] [OrderTop ι] [∀ i, Preorder (α i)] [OrderTop (α ⊤)] :
    OrderTop (Σₗ' i, α i) 
goal: OrderTop (Σₗ' (i : ι), α i)

full_name: PSigma.Lex.boundedOrder
code: /-- The lexicographical linear order on a sigma type. -/
instance boundedOrder [PartialOrder ι] [BoundedOrder ι] [∀ i, Preorder (α i)] [OrderBot (α ⊥)]
    [OrderTop (α ⊤)] : BoundedOrder (Σₗ' i, α i) 
goal: BoundedOrder (Σₗ' (i : ι), α i)

full_name: PSigma.Lex.denselyOrdered
code: instance denselyOrdered [Preorder ι] [DenselyOrdered ι] [∀ i, Nonempty (α i)] [∀ i, Preorder (α i)]
    [∀ i, DenselyOrdered (α i)] : DenselyOrdered (Σₗ' i, α i) 
goal: DenselyOrdered (Σₗ' (i : ι), α i)

full_name: PSigma.Lex.denselyOrdered_of_noMaxOrder
code: instance denselyOrdered_of_noMaxOrder [Preorder ι] [∀ i, Preorder (α i)]
    [∀ i, DenselyOrdered (α i)] [∀ i, NoMaxOrder (α i)] : DenselyOrdered (Σₗ' i, α i) 
goal: DenselyOrdered (Σₗ' (i : ι), α i)

full_name: PSigma.Lex.denselyOrdered_of_noMinOrder
code: instance denselyOrdered_of_noMinOrder [Preorder ι] [∀ i, Preorder (α i)]
    [∀ i, DenselyOrdered (α i)] [∀ i, NoMinOrder (α i)] : DenselyOrdered (Σₗ' i, α i) 
goal: DenselyOrdered (Σₗ' (i : ι), α i)

full_name: PSigma.Lex.noMaxOrder_of_nonempty
code: instance noMaxOrder_of_nonempty [Preorder ι] [∀ i, Preorder (α i)] [NoMaxOrder ι]
    [∀ i, Nonempty (α i)] : NoMaxOrder (Σₗ' i, α i) 
goal: NoMaxOrder (Σₗ' (i : ι), α i)

full_name: PSigma.Lex.noMinOrder_of_nonempty
code: instance noMinOrder_of_nonempty [Preorder ι] [∀ i, Preorder (α i)] [NoMinOrder ι]
    [∀ i, Nonempty (α i)] : NoMinOrder (Σₗ' i, α i) 
goal: NoMinOrder (Σₗ' (i : ι), α i)

full_name: PSigma.Lex.noMaxOrder
code: instance noMaxOrder [Preorder ι] [∀ i, Preorder (α i)] [∀ i, NoMaxOrder (α i)] :
    NoMaxOrder (Σₗ' i, α i) 
goal: NoMaxOrder (Σₗ' (i : ι), α i)

full_name: PSigma.Lex.noMinOrder
code: instance noMinOrder [Preorder ι] [∀ i, Preorder (α i)] [∀ i, NoMinOrder (α i)] :
    NoMinOrder (Σₗ' i, α i) 
goal: NoMinOrder (Σₗ' (i : ι), α i)