Theorem: ENat.tsum_le_union (Matroid/ForMathlib/ENatTopology.lean)

State before:
α : Type u_1
β : Type u_2
ι : Type u_3
s✝ : Set α
n : ℕ∞
f g : α → ℕ∞
s t : Set α
⊢ ∑' (x : ↑(s ∪ t)), f ↑x ≤ ∑' (x : ↑s), f ↑x + ∑' (x : ↑t), f ↑x
Tactic:
rw [← diff_union_self, ENat.tsum_union_disjoint disjoint_sdiff_left]
State after:
α : Type u_1
β : Type u_2
ι : Type u_3
s✝ : Set α
n : ℕ∞
f g : α → ℕ∞
s t : Set α
⊢ ∑' (x : ↑(s \ t)), f ↑x + ∑' (x : ↑t), f ↑x ≤ ∑' (x : ↑s), f ↑x + ∑' (x : ↑t), f ↑x

State before:
α : Type u_1
β : Type u_2
ι : Type u_3
s✝ : Set α
n : ℕ∞
f g : α → ℕ∞
s t : Set α
⊢ ∑' (x : ↑(s \ t)), f ↑x + ∑' (x : ↑t), f ↑x ≤ ∑' (x : ↑s), f ↑x + ∑' (x : ↑t), f ↑x
Tactic:
exact add_le_add_right (ENat.tsum_le_of_subset diff_subset) _
State after:
no goals