Plain-language statement
Honest Bob usually rejects if Alice is off by ≥ s
Exact Lean statement
lemma bob_sound (o : Oracle) (i : OracleId) (cs : c < s) (q0 : 0 < q) {y : Vector Bool n}
(bad : |p - (o _ y).prob true| ≥ s) :
((bob' c s q i _ y p).prob' o).prob true ≤ qFormal artifact
Lean source
lemma bob_sound (o : Oracle) (i : OracleId) (cs : c < s) (q0 : 0 < q) {y : Vector Bool n} (bad : |p - (o _ y).prob true| ≥ s) : ((bob' c s q i _ y p).prob' o).prob true ≤ q := by simp only [bob', prob_bind, prob_pure, true_eq_decide_iff, not_lt, Comp.prob', Comp.prob_bind, Comp.prob_pure] rw [←pr] refine le_trans (pr_mono ?_) (alice_pr_le o i (by linarith) q0 y) intro b _ h; generalize hx : (o _ y).prob true = x; rw [hx] at bad; clear hx have e : b - x = (p - x) - (p - b) := by abel rw [e]; refine le_trans ?_ (abs_sub_abs_le_abs_sub _ _) calc (s - c) / 2 _ ≤ s - (c + s) / 2 := by linarith _ ≤ |p - x| - |p - b| := sub_le_sub bad (le_of_lt h)- Project
- debate
- License
- Apache-2.0
- Commit
- de3a6e500ae1
- Source
- Debate/Details.lean:76-88
Reuse this declaration
Bring the exact result into your workflow
The import identifies the source module. Your project still needs the pinned package dependency shown on this page.
What this badge means
This completion status comes from the project or community source. It has not yet been represented here as an independent rebuild and axiom audit.
Continue in this project
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.