Plain-language statement
Completeness for any valid parameters
Exact Lean statement
theorem completeness_p (o : Oracle) (L : o.lipschitz t k) (eve : Bob)
{w d : ℝ} (p : Params w d k t) (m : w ≤ (o.final t).prob true) :
d ≤ ((debate (alice p.c p.q) eve (vera p.c p.s p.v) t).prob' o).prob trueFormal artifact
Lean source
theorem completeness_p (o : Oracle) (L : o.lipschitz t k) (eve : Bob) {w d : ℝ} (p : Params w d k t) (m : w ≤ (o.final t).prob true) : d ≤ ((debate (alice p.c p.q) eve (vera p.c p.s p.v) t).prob' o).prob true := by refine le_trans (le_trans p.complete ?_) (completeness' o L eve p.c0 p.cs p.q0 p.q1 p.v0 p.v1) refine mul_le_mul_of_nonneg_left (add_le_add (add_le_add_right m _) ?_) (by linarith [p.v1]) rw [neg_le_neg_iff, sub_le_iff_le_add, add_comm, ←sub_le_iff_le_add, mul_comm, sub_eq_add_neg, ←mul_neg, ←Nat.cast_add_one] apply one_add_mul_le_pow; linarith [p.q1]- Project
- debate
- License
- Apache-2.0
- Commit
- de3a6e500ae1
- Source
- Debate/Details.lean:634-641
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Person-level attribution pending.
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alices_close
Plain-language statement
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Source project: debate
Person-level attribution pending.