Plain-language statement
Soundness for any valid parameters
Exact Lean statement
theorem soundness_p (o : Oracle) (L : o.lipschitz t k) (eve : Alice)
{w d : ℝ} (p : Params w d k t) (m : w ≤ (o.final t).prob false) :
d ≤ ((debate eve (bob p.s p.b p.q) (vera p.c p.s p.v) t).prob' o).prob falseFormal artifact
Lean source
theorem soundness_p (o : Oracle) (L : o.lipschitz t k) (eve : Alice) {w d : ℝ} (p : Params w d k t) (m : w ≤ (o.final t).prob false) : d ≤ ((debate eve (bob p.s p.b p.q) (vera p.c p.s p.v) t).prob' o).prob false := by refine le_trans (le_trans p.sound ?_) (soundness' o L eve p.c0 p.cs p.sb p.q0 p.v0 p.v1 p.qv) simp only [mul_assoc] refine mul_le_mul_of_nonneg_left (mul_le_mul ?_ ?_ ?_ ?_) (by linarith [p.v1]) · rw [mul_comm, sub_eq_add_neg, ←mul_neg, ←Nat.cast_add_one] apply one_add_mul_le_pow linarith [p.q1] · apply add_le_add_right m · linarith [p.bw] · apply pow_nonneg; linarith [p.q1]- Project
- debate
- License
- Apache-2.0
- Commit
- de3a6e500ae1
- Source
- Debate/Details.lean:644-655
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Alice pr le
alice_pr_le
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Person-level attribution pending.
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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.