theorem extracted_formal_statement_29.{u_3, u_2} {𝓧 : Type u_2} {ι : Type u_3} [inst : DecidableEq ι] (f : (ι → 𝓧) → ℝ)
  (c : ι → ℝ) (h : ∀ (i : ι) (x : ι → 𝓧) (x' : 𝓧), f x - f (Function.update x i x') ≤ c i) (i : ι) (xi : ι → 𝓧) (x' : 𝓧)
  (this : xi = Function.update (Function.update xi i x') i (xi i)) :
  f (Function.update xi i x') - f (Function.update (Function.update xi i x') i (xi i)) ≤ c i := sorry

State before:
case mpr.right
𝓧 : Type u_2
ι : Type u_3
inst✝ : DecidableEq ι
f : (ι → 𝓧) → ℝ
c : ι → ℝ
h : ∀ (i : ι) (x : ι → 𝓧) (x' : 𝓧), f x - f (Function.update x i x') ≤ c i
i : ι
xi : ι → 𝓧
x' : 𝓧
this : xi = Function.update (Function.update xi i x') i (xi i)
⊢ f (Function.update xi i x') - f (Function.update (Function.update xi i x') i (xi i)) ≤ c i

Tactic: exact h i (Function.update xi i x') (xi i)

State after:

Relevant lemmas: