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Formal Proof Search & Tactic Space Explorer

MCTS & Lean 4 Tactic Expansion Visualizer

Theorem Presets

Search Algorithm

MCTS Hyperparameters

Exploration Constant (C_puct) 1.41

Rollout Depth 4

Interactive Tactics

Custom Goal Builder

Goal State Inspector

n : ℕ

∀ n : ℕ, 2 * (∑ i in range n, i) = n * (n - 1)

Kernel Telemetry

Kernel Check VALID

Node Visits 1

Tree Depth 0

Value Q(s) 0.50

Reasoning Mode Comparison

Formal Tactic Search 0% Hallucination

Each tactic is checked by the Lean formal kernel. Invalid steps produce 0 value, completely pruning bad branches.

Probabilistic Text Step Fuzzy / Plausible

Informal text generation may output syntactically clean lines with subtle logical leaps or unverified algebraic slips.

Proof Output Terminal

-- Lean 4 Proof Script theorem nat_sum_formula : ∀ n : ℕ, 2 * (∑ i in range n, i) = n * (n - 1) := by sorry