Oracle fold succ prob
Oracle.fold_succ_prob
Plain-language statement
(o.fold (n+1)).prob y decomposes as a product
Exact Lean statement
lemma Oracle.fold_succ_prob (o : Oracle) {n : ℕ} (y : Vector Bool (n+1)) :
(o.fold (n+1)).prob y = (o.fold n).prob y.tail * (o _ y.tail).prob y.headFormal artifact
Lean source
lemma Oracle.fold_succ_prob (o : Oracle) {n : ℕ} (y : Vector Bool (n+1)) : (o.fold (n+1)).prob y = (o.fold n).prob y.tail * (o _ y.tail).prob y.head := by simp only [Oracle.fold, prob_bind, prob_pure, Vector.eq_cons_iff, ite_and_one_zero, exp_mul_const, @eq_comm _ y.head] rw [←exp_eq_prob, ←exp_mul_const]; apply exp_congr' · intro x; by_cases yx : y.tail = x · simp only [yx, if_true, mul_one, one_mul]; apply congr_arg₂ _ rfl; apply exp_eq_prob · simp only [yx, if_false, mul_zero]; split_ifs with h; simp [h] at yx; simp [h] · intro _; exact Classical.dec _- Project
- debate
- License
- Apache-2.0
- Commit
- de3a6e500ae1
- Source
- Debate/Details.lean:198-206
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.