Module: Mathlib.Order.Interval.Finset.Defs

Goal state before:
pp: case top.top.top
α : Type u_1
β : Type u_2
inst✝² : PartialOrder α
inst✝¹ : OrderTop α
inst✝ : LocallyFiniteOrder α
⊢ (⊤ ∈
      match ⊤, ⊤ with
      | none, x => ∅
      | Option.some a, none => Finset.map Embedding.coeWithTop (Ioi a)
      | Option.some a, Option.some b => Finset.map Embedding.coeWithTop (Ioo a b)) ↔
    ⊤ < ⊤ ∧ ⊤ < ⊤

pp: case top.top.coe
α : Type u_1
β : Type u_2
inst✝² : PartialOrder α
inst✝¹ : OrderTop α
inst✝ : LocallyFiniteOrder α
a✝ : α
⊢ (↑a✝ ∈
      match ⊤, ⊤ with
      | none, x => ∅
      | Option.some a, none => Finset.map Embedding.coeWithTop (Ioi a)
      | Option.some a, Option.some b => Finset.map Embedding.coeWithTop (Ioo a b)) ↔
    ⊤ < ↑a✝ ∧ ↑a✝ < ⊤

pp: case top.coe.top
α : Type u_1
β : Type u_2
inst✝² : PartialOrder α
inst✝¹ : OrderTop α
inst✝ : LocallyFiniteOrder α
a✝ : α
⊢ (⊤ ∈
      match ⊤, ↑a✝ with
      | none, x => ∅
      | Option.some a, none => Finset.map Embedding.coeWithTop (Ioi a)
      | Option.some a, Option.some b => Finset.map Embedding.coeWithTop (Ioo a b)) ↔
    ⊤ < ⊤ ∧ ⊤ < ↑a✝

pp: case top.coe.coe
α : Type u_1
β : Type u_2
inst✝² : PartialOrder α
inst✝¹ : OrderTop α
inst✝ : LocallyFiniteOrder α
a✝¹ a✝ : α
⊢ (↑a✝ ∈
      match ⊤, ↑a✝¹ with
      | none, x => ∅
      | Option.some a, none => Finset.map Embedding.coeWithTop (Ioi a)
      | Option.some a, Option.some b => Finset.map Embedding.coeWithTop (Ioo a b)) ↔
    ⊤ < ↑a✝ ∧ ↑a✝ < ↑a✝¹

pp: case coe.top.top
α : Type u_1
β : Type u_2
inst✝² : PartialOrder α
inst✝¹ : OrderTop α
inst✝ : LocallyFiniteOrder α
a✝ : α
⊢ (⊤ ∈
      match ↑a✝, ⊤ with
      | none, x => ∅
      | Option.some a, none => Finset.map Embedding.coeWithTop (Ioi a)
      | Option.some a, Option.some b => Finset.map Embedding.coeWithTop (Ioo a b)) ↔
    ↑a✝ < ⊤ ∧ ⊤ < ⊤

pp: case coe.top.coe
α : Type u_1
β : Type u_2
inst✝² : PartialOrder α
inst✝¹ : OrderTop α
inst✝ : LocallyFiniteOrder α
a✝¹ a✝ : α
⊢ (↑a✝ ∈
      match ↑a✝¹, ⊤ with
      | none, x => ∅
      | Option.some a, none => Finset.map Embedding.coeWithTop (Ioi a)
      | Option.some a, Option.some b => Finset.map Embedding.coeWithTop (Ioo a b)) ↔
    ↑a✝¹ < ↑a✝ ∧ ↑a✝ < ⊤

pp: case coe.coe.top
α : Type u_1
β : Type u_2
inst✝² : PartialOrder α
inst✝¹ : OrderTop α
inst✝ : LocallyFiniteOrder α
a✝¹ a✝ : α
⊢ (⊤ ∈
      match ↑a✝¹, ↑a✝ with
      | none, x => ∅
      | Option.some a, none => Finset.map Embedding.coeWithTop (Ioi a)
      | Option.some a, Option.some b => Finset.map Embedding.coeWithTop (Ioo a b)) ↔
    ↑a✝¹ < ⊤ ∧ ⊤ < ↑a✝

pp: case coe.coe.coe
α : Type u_1
β : Type u_2
inst✝² : PartialOrder α
inst✝¹ : OrderTop α
inst✝ : LocallyFiniteOrder α
a✝² a✝¹ a✝ : α
⊢ (↑a✝ ∈
      match ↑a✝², ↑a✝¹ with
      | none, x => ∅
      | Option.some a, none => Finset.map Embedding.coeWithTop (Ioi a)
      | Option.some a, Option.some b => Finset.map Embedding.coeWithTop (Ioo a b)) ↔
    ↑a✝² < ↑a✝ ∧ ↑a✝ < ↑a✝¹

Tactic:
<;>

Goal state after:
case top.top.top
α : Type u_1
β : Type u_2
inst✝² : PartialOrder α
inst✝¹ : OrderTop α
inst✝ : LocallyFiniteOrder α
⊢ (⊤ ∈
      match ⊤, ⊤ with
      | none, x => ∅
      | Option.some a, none => Finset.map Embedding.coeWithTop (Ioi a)
      | Option.some a, Option.some b => Finset.map Embedding.coeWithTop (Ioo a b)) ↔
    ⊤ < ⊤ ∧ ⊤ < ⊤

case top.top.coe
α : Type u_1
β : Type u_2
inst✝² : PartialOrder α
inst✝¹ : OrderTop α
inst✝ : LocallyFiniteOrder α
a✝ : α
⊢ (↑a✝ ∈
      match ⊤, ⊤ with
      | none, x => ∅
      | Option.some a, none => Finset.map Embedding.coeWithTop (Ioi a)
      | Option.some a, Option.some b => Finset.map Embedding.coeWithTop (Ioo a b)) ↔
    ⊤ < ↑a✝ ∧ ↑a✝ < ⊤

case top.coe.top
α : Type u_1
β : Type u_2
inst✝² : PartialOrder α
inst✝¹ : OrderTop α
inst✝ : LocallyFiniteOrder α
a✝ : α
⊢ (⊤ ∈
      match ⊤, ↑a✝ with
      | none, x => ∅
      | Option.some a, none => Finset.map Embedding.coeWithTop (Ioi a)
      | Option.some a, Option.some b => Finset.map Embedding.coeWithTop (Ioo a b)) ↔
    ⊤ < ⊤ ∧ ⊤ < ↑a✝

case top.coe.coe
α : Type u_1
β : Type u_2
inst✝² : PartialOrder α
inst✝¹ : OrderTop α
inst✝ : LocallyFiniteOrder α
a✝¹ a✝ : α
⊢ (↑a✝ ∈
      match ⊤, ↑a✝¹ with
      | none, x => ∅
      | Option.some a, none => Finset.map Embedding.coeWithTop (Ioi a)
      | Option.some a, Option.some b => Finset.map Embedding.coeWithTop (Ioo a b)) ↔
    ⊤ < ↑a✝ ∧ ↑a✝ < ↑a✝¹

case coe.top.top
α : Type u_1
β : Type u_2
inst✝² : PartialOrder α
inst✝¹ : OrderTop α
inst✝ : LocallyFiniteOrder α
a✝ : α
⊢ (⊤ ∈
      match ↑a✝, ⊤ with
      | none, x => ∅
      | Option.some a, none => Finset.map Embedding.coeWithTop (Ioi a)
      | Option.some a, Option.some b => Finset.map Embedding.coeWithTop (Ioo a b)) ↔
    ↑a✝ < ⊤ ∧ ⊤ < ⊤

case coe.top.coe
α : Type u_1
β : Type u_2
inst✝² : PartialOrder α
inst✝¹ : OrderTop α
inst✝ : LocallyFiniteOrder α
a✝¹ a✝ : α
⊢ (↑a✝ ∈
      match ↑a✝¹, ⊤ with
      | none, x => ∅
      | Option.some a, none => Finset.map Embedding.coeWithTop (Ioi a)
      | Option.some a, Option.some b => Finset.map Embedding.coeWithTop (Ioo a b)) ↔
    ↑a✝¹ < ↑a✝ ∧ ↑a✝ < ⊤

case coe.coe.top
α : Type u_1
β : Type u_2
inst✝² : PartialOrder α
inst✝¹ : OrderTop α
inst✝ : LocallyFiniteOrder α
a✝¹ a✝ : α
⊢ (⊤ ∈
      match ↑a✝¹, ↑a✝ with
      | none, x => ∅
      | Option.some a, none => Finset.map Embedding.coeWithTop (Ioi a)
      | Option.some a, Option.some b => Finset.map Embedding.coeWithTop (Ioo a b)) ↔
    ↑a✝¹ < ⊤ ∧ ⊤ < ↑a✝

case coe.coe.coe
α : Type u_1
β : Type u_2
inst✝² : PartialOrder α
inst✝¹ : OrderTop α
inst✝ : LocallyFiniteOrder α
a✝² a✝¹ a✝ : α
⊢ (↑a✝ ∈
      match ↑a✝², ↑a✝¹ with
      | none, x => ∅
      | Option.some a, none => Finset.map Embedding.coeWithTop (Ioi a)
      | Option.some a, Option.some b => Finset.map Embedding.coeWithTop (Ioo a b)) ↔
    ↑a✝² < ↑a✝ ∧ ↑a✝ < ↑a✝¹