α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
f g : Perm α
h : Disjoint f g
⊢ card (support (f * g)) = card (support f ∪ support g)

α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
f g : Perm α
h : Disjoint f g
⊢ _root_.Disjoint (support f) (support g)
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
f g : Perm α
h : Disjoint f g
⊢ card (support (f * g)) = card (support f) + card (support g)
rw [← Finset.card_disjoint_union]
case e_s
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
f g : Perm α
h : Disjoint f g
⊢ support (f * g) = support f ∪ support g
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
f g : Perm α
h : Disjoint f g
⊢ card (support (f * g)) = card (support f ∪ support g)
congr
case e_s.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
f g : Perm α
h : Disjoint f g
a✝ : α
⊢ a✝ ∈ support (f * g) ↔ a✝ ∈ support f ∪ support g
case e_s
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
f g : Perm α
h : Disjoint f g
⊢ support (f * g) = support f ∪ support g
ext
no goals
case e_s.a
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
f g : Perm α
h : Disjoint f g
a✝ : α
⊢ a✝ ∈ support (f * g) ↔ a✝ ∈ support f ∪ support g
simp [h.support_mul]
no goals
α : Type u_1
inst✝¹ : DecidableEq α
inst✝ : Fintype α
f g : Perm α
h : Disjoint f g
⊢ _root_.Disjoint (support f) (support g)
simpa using h.disjoint_support