α : Type u_1
inst✝² : GeneralizedBooleanAlgebra α
inst✝¹ : DecidableRel Disjoint
inst✝ : DecidableRel fun x x_1 => x ≤ x_1
s : Finset α
u✝ v a✝ b u a : α
⊢ (if Disjoint u a ∧ u ≤ a then (a ⊔ u) \ u else a) = a
α : Type u_1
inst✝² : GeneralizedBooleanAlgebra α
inst✝¹ : DecidableRel Disjoint
inst✝ : DecidableRel fun x x_1 => x ≤ x_1
s : Finset α
u✝ v a✝ b u a : α
⊢ compress u u a = a
unfold compress
case inl
α : Type u_1
inst✝² : GeneralizedBooleanAlgebra α
inst✝¹ : DecidableRel Disjoint
inst✝ : DecidableRel fun x x_1 => x ≤ x_1
s : Finset α
u✝ v a✝ b u a : α
h✝ : Disjoint u a ∧ u ≤ a
⊢ (a ⊔ u) \ u = a

case inr
α : Type u_1
inst✝² : GeneralizedBooleanAlgebra α
inst✝¹ : DecidableRel Disjoint
inst✝ : DecidableRel fun x x_1 => x ≤ x_1
s : Finset α
u✝ v a✝ b u a : α
h✝ : ¬(Disjoint u a ∧ u ≤ a)
⊢ a = a
α : Type u_1
inst✝² : GeneralizedBooleanAlgebra α
inst✝¹ : DecidableRel Disjoint
inst✝ : DecidableRel fun x x_1 => x ≤ x_1
s : Finset α
u✝ v a✝ b u a : α
⊢ (if Disjoint u a ∧ u ≤ a then (a ⊔ u) \ u else a) = a
split_ifs
no goals
case inl
α : Type u_1
inst✝² : GeneralizedBooleanAlgebra α
inst✝¹ : DecidableRel Disjoint
inst✝ : DecidableRel fun x x_1 => x ≤ x_1
s : Finset α
u✝ v a✝ b u a : α
h✝ : Disjoint u a ∧ u ≤ a
⊢ (a ⊔ u) \ u = a
exact ‹Disjoint u a ∧ u ≤ a›.1.symm.sup_sdiff_cancel_right
no goals
case inr
α : Type u_1
inst✝² : GeneralizedBooleanAlgebra α
inst✝¹ : DecidableRel Disjoint
inst✝ : DecidableRel fun x x_1 => x ≤ x_1
s : Finset α
u✝ v a✝ b u a : α
h✝ : ¬(Disjoint u a ∧ u ≤ a)
⊢ a = a
rfl