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theorem proved term proof

no_sublinear_universal_decoder

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formal statement (Lean)

 226theorem no_sublinear_universal_decoder
 227    (n : ℕ) (M : Finset (Fin n)) (hM : M.card < n)
 228    (decoder : ({i // i ∈ M} → Bool) → Bool) :
 229    ¬ ∀ (b : Bool) (R : Fin n → Bool),
 230        decoder (restrict (enc b R) M) = b :=

proof body

Term-mode proof.

 231  omega_n_queries M decoder hM
 232
 233/-! ## Part 5: The Circuit–R̂ Separation Structure -/
 234
 235/-- The **circuit separation claim**: R̂ decides SAT in O(n) recognition steps,
 236    while any circuit deciding SAT requires reading all n inputs.
 237
 238    Three proved components + one open gap. -/

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