Plain-language statement
Bob makes few queries, regardless of Alice and Vera
Exact Lean statement
theorem bob_debate_cost (o : Oracle) (alice : Alice) (vera : Vera) (t : ℕ):
(debate alice (bob s b q) vera t).cost' o BobId ≤ (t+1) * samples ((b-s)/2) qFormal artifact
Lean source
theorem bob_debate_cost (o : Oracle) (alice : Alice) (vera : Vera) (t : ℕ): (debate alice (bob s b q) vera t).cost' o BobId ≤ (t+1) * samples ((b-s)/2) q := by simp only [debate, Comp.cost', Comp.cost_bind] have e : ∀ x, ((t:ℝ) + 1) * samples x q = (t + 1) * samples x q + 0 := by simp only [add_zero, forall_const] rw [e] apply add_le_add · rw [←Nat.cast_add_one]; apply bob_steps_cost · refine exp_le_of_forall_le (fun y m ↦ ?_) induction y; repeat simp only [Comp.cost_pure, le_refl]- Project
- debate
- License
- Apache-2.0
- Commit
- de3a6e500ae1
- Source
- Debate/Cost.lean:103-112
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Related declarations
Alice pr le
alice_pr_le
Plain-language statement
Honest Alice has error ≥ e with probability ≤ q
Source project: debate
Person-level attribution pending.
Alice steps cost
alice_steps_cost
Plain-language statement
Alice makes few queries, regardless of Bob and Vera
Source project: debate
Person-level attribution pending.
Alices close
alices_close
Plain-language statement
Alice produces (p,y) with p close to o.probs y with good probability
Source project: debate
Person-level attribution pending.