Theorem: Finset.mul_subset_right (LeanCamCombi/Kneser/MulStab.lean)

State before:
ι : Type u_1
α : Type u_2
inst✝¹ : Group α
inst✝ : DecidableEq α
s t : Finset α
a : α
⊢ s ⊆ t.mulStab → s * t ⊆ t
Tactic:
obtain rfl | ht := t.eq_empty_or_nonempty
State after:
case inl
ι : Type u_1
α : Type u_2
inst✝¹ : Group α
inst✝ : DecidableEq α
s : Finset α
a : α
⊢ s ⊆ ∅.mulStab → s * ∅ ⊆ ∅

case inr
ι : Type u_1
α : Type u_2
inst✝¹ : Group α
inst✝ : DecidableEq α
s t : Finset α
a : α
ht : t.Nonempty
⊢ s ⊆ t.mulStab → s * t ⊆ t

State before:
case inl
ι : Type u_1
α : Type u_2
inst✝¹ : Group α
inst✝ : DecidableEq α
s : Finset α
a : α
⊢ s ⊆ ∅.mulStab → s * ∅ ⊆ ∅
Tactic:
simp
State after:
no goals

State before:
case inr
ι : Type u_1
α : Type u_2
inst✝¹ : Group α
inst✝ : DecidableEq α
s t : Finset α
a : α
ht : t.Nonempty
⊢ s ⊆ t.mulStab → s * t ⊆ t
Tactic:
exact (mul_subset_right_iff ht).2
State after:
no goals