case a
ι : Type u_1
α : Type u_2
inst✝¹ : CanonicallyLinearOrderedAddMonoid α
inst✝ : DecidableEq ι
f g : ι →₀ α
a✝ : ι
⊢ a✝ ∈ (f ⊓ g).support ↔ a✝ ∈ f.support ∩ g.support
ι : Type u_1
α : Type u_2
inst✝¹ : CanonicallyLinearOrderedAddMonoid α
inst✝ : DecidableEq ι
f g : ι →₀ α
⊢ (f ⊓ g).support = f.support ∩ g.support
ext
case a
ι : Type u_1
α : Type u_2
inst✝¹ : CanonicallyLinearOrderedAddMonoid α
inst✝ : DecidableEq ι
f g : ι →₀ α
a✝ : ι
⊢ ¬↑f a✝ ⊓ ↑g a✝ = 0 ↔ ¬↑f a✝ = 0 ∧ ¬↑g a✝ = 0
case a
ι : Type u_1
α : Type u_2
inst✝¹ : CanonicallyLinearOrderedAddMonoid α
inst✝ : DecidableEq ι
f g : ι →₀ α
a✝ : ι
⊢ a✝ ∈ (f ⊓ g).support ↔ a✝ ∈ f.support ∩ g.support
simp only [inf_apply, mem_support_iff, Ne.def, Finset.mem_union, Finset.mem_filter,
  Finset.mem_inter]
no goals
case a
ι : Type u_1
α : Type u_2
inst✝¹ : CanonicallyLinearOrderedAddMonoid α
inst✝ : DecidableEq ι
f g : ι →₀ α
a✝ : ι
⊢ ¬↑f a✝ ⊓ ↑g a✝ = 0 ↔ ¬↑f a✝ = 0 ∧ ¬↑g a✝ = 0
simp only [inf_eq_min, ← nonpos_iff_eq_zero, min_le_iff, not_or]