Module: Mathlib.Order.BooleanAlgebra.Basic

Goal state before:
pp: case le
α : Type u
β : Type u_1
x y z : α
e : α ≃ β
inst✝ : BooleanAlgebra β
top : Top α := ⋯
compl : Compl α := ⋯
himp : HImp α := ⋯
generalizedBooleanAlgebra : GeneralizedBooleanAlgebra α := ⋯
⊢ ∀ {x y : α}, e x ≤ e y ↔ x ≤ y

pp: case lt
α : Type u
β : Type u_1
x y z : α
e : α ≃ β
inst✝ : BooleanAlgebra β
top : Top α := ⋯
compl : Compl α := ⋯
himp : HImp α := ⋯
generalizedBooleanAlgebra : GeneralizedBooleanAlgebra α := ⋯
⊢ ∀ {x y : α}, e x < e y ↔ x < y

pp: case map_sup
α : Type u
β : Type u_1
x y z : α
e : α ≃ β
inst✝ : BooleanAlgebra β
top : Top α := ⋯
compl : Compl α := ⋯
himp : HImp α := ⋯
generalizedBooleanAlgebra : GeneralizedBooleanAlgebra α := ⋯
⊢ ∀ (a b : α), e (a ⊔ b) = e a ⊔ e b

pp: case map_inf
α : Type u
β : Type u_1
x y z : α
e : α ≃ β
inst✝ : BooleanAlgebra β
top : Top α := ⋯
compl : Compl α := ⋯
himp : HImp α := ⋯
generalizedBooleanAlgebra : GeneralizedBooleanAlgebra α := ⋯
⊢ ∀ (a b : α), e (a ⊓ b) = e a ⊓ e b

pp: case map_top
α : Type u
β : Type u_1
x y z : α
e : α ≃ β
inst✝ : BooleanAlgebra β
top : Top α := ⋯
compl : Compl α := ⋯
himp : HImp α := ⋯
generalizedBooleanAlgebra : GeneralizedBooleanAlgebra α := ⋯
⊢ e ⊤ = ⊤

pp: case map_bot
α : Type u
β : Type u_1
x y z : α
e : α ≃ β
inst✝ : BooleanAlgebra β
top : Top α := ⋯
compl : Compl α := ⋯
himp : HImp α := ⋯
generalizedBooleanAlgebra : GeneralizedBooleanAlgebra α := ⋯
⊢ e ⊥ = ⊥

pp: case map_compl
α : Type u
β : Type u_1
x y z : α
e : α ≃ β
inst✝ : BooleanAlgebra β
top : Top α := ⋯
compl : Compl α := ⋯
himp : HImp α := ⋯
generalizedBooleanAlgebra : GeneralizedBooleanAlgebra α := ⋯
⊢ ∀ (a : α), e aᶜ = (e a)ᶜ

pp: case map_sdiff
α : Type u
β : Type u_1
x y z : α
e : α ≃ β
inst✝ : BooleanAlgebra β
top : Top α := ⋯
compl : Compl α := ⋯
himp : HImp α := ⋯
generalizedBooleanAlgebra : GeneralizedBooleanAlgebra α := ⋯
⊢ ∀ (a b : α), e (a \ b) = e a \ e b

pp: case map_himp
α : Type u
β : Type u_1
x y z : α
e : α ≃ β
inst✝ : BooleanAlgebra β
top : Top α := ⋯
compl : Compl α := ⋯
himp : HImp α := ⋯
generalizedBooleanAlgebra : GeneralizedBooleanAlgebra α := ⋯
⊢ ∀ (a b : α), e (a ⇨ b) = e a ⇨ e b

Tactic:
<;>

Goal state after:
case le
α : Type u
β : Type u_1
x y z : α
e : α ≃ β
inst✝ : BooleanAlgebra β
top : Top α := ⋯
compl : Compl α := ⋯
himp : HImp α := ⋯
generalizedBooleanAlgebra : GeneralizedBooleanAlgebra α := ⋯
⊢ ∀ {x y : α}, e x ≤ e y ↔ x ≤ y

case lt
α : Type u
β : Type u_1
x y z : α
e : α ≃ β
inst✝ : BooleanAlgebra β
top : Top α := ⋯
compl : Compl α := ⋯
himp : HImp α := ⋯
generalizedBooleanAlgebra : GeneralizedBooleanAlgebra α := ⋯
⊢ ∀ {x y : α}, e x < e y ↔ x < y

case map_sup
α : Type u
β : Type u_1
x y z : α
e : α ≃ β
inst✝ : BooleanAlgebra β
top : Top α := ⋯
compl : Compl α := ⋯
himp : HImp α := ⋯
generalizedBooleanAlgebra : GeneralizedBooleanAlgebra α := ⋯
⊢ ∀ (a b : α), e (a ⊔ b) = e a ⊔ e b

case map_inf
α : Type u
β : Type u_1
x y z : α
e : α ≃ β
inst✝ : BooleanAlgebra β
top : Top α := ⋯
compl : Compl α := ⋯
himp : HImp α := ⋯
generalizedBooleanAlgebra : GeneralizedBooleanAlgebra α := ⋯
⊢ ∀ (a b : α), e (a ⊓ b) = e a ⊓ e b

case map_top
α : Type u
β : Type u_1
x y z : α
e : α ≃ β
inst✝ : BooleanAlgebra β
top : Top α := ⋯
compl : Compl α := ⋯
himp : HImp α := ⋯
generalizedBooleanAlgebra : GeneralizedBooleanAlgebra α := ⋯
⊢ e ⊤ = ⊤

case map_bot
α : Type u
β : Type u_1
x y z : α
e : α ≃ β
inst✝ : BooleanAlgebra β
top : Top α := ⋯
compl : Compl α := ⋯
himp : HImp α := ⋯
generalizedBooleanAlgebra : GeneralizedBooleanAlgebra α := ⋯
⊢ e ⊥ = ⊥

case map_compl
α : Type u
β : Type u_1
x y z : α
e : α ≃ β
inst✝ : BooleanAlgebra β
top : Top α := ⋯
compl : Compl α := ⋯
himp : HImp α := ⋯
generalizedBooleanAlgebra : GeneralizedBooleanAlgebra α := ⋯
⊢ ∀ (a : α), e aᶜ = (e a)ᶜ

case map_sdiff
α : Type u
β : Type u_1
x y z : α
e : α ≃ β
inst✝ : BooleanAlgebra β
top : Top α := ⋯
compl : Compl α := ⋯
himp : HImp α := ⋯
generalizedBooleanAlgebra : GeneralizedBooleanAlgebra α := ⋯
⊢ ∀ (a b : α), e (a \ b) = e a \ e b

case map_himp
α : Type u
β : Type u_1
x y z : α
e : α ≃ β
inst✝ : BooleanAlgebra β
top : Top α := ⋯
compl : Compl α := ⋯
himp : HImp α := ⋯
generalizedBooleanAlgebra : GeneralizedBooleanAlgebra α := ⋯
⊢ ∀ (a b : α), e (a ⇨ b) = e a ⇨ e b