theorem extracted_formal_statement_55.{v} {ι : Type v} [inst : Nonempty ι] {f : ι → ℝ} {a : ℝ} (hf : ∀ (i : ι), |f i| ≤ a)
  ⦃x : ℝ⦄ (i : ι) (heq : f i = x) (this : |x| ≤ a) : x ≤ a := sorry

State before:
case h
ι : Type v
inst✝ : Nonempty ι
f : ι → ℝ
a : ℝ
hf : ∀ (i : ι), |f i| ≤ a
x : ℝ
i : ι
heq : f i = x
this : |x| ≤ a
⊢ x ≤ a

Tactic: exact le_of_max_le_left this

State after:

Relevant lemmas:
le_of_max_le_left : ∀ {α : Type u} [inst : LinearOrder α] {a b c : α}, a ⊔ b ≤ c → a ≤ c