import type { NaturalDerivedPayload, PropAtom, PropFormula, PropProofStep } from "../../../models";
/**
 * Represents a complete proof in Natural Deduction style calculus.
 * Manages a sequence of proof steps where the final step is the goal formula.
 * Supports premises, assumptions (sub-proofs), and derived steps using natural deduction rules.
 * Tracks nesting levels to manage sub-proofs and ensures proofs are properly closed at level 0.
 *
 * @category Natural Calculus
 */
export declare class NaturalProof {
    private steps;
    private readonly goal;
    private currentLevel;
    /**
     * Creates a new Natural Deduction proof with a goal formula.
     * @param goal - The target formula to prove
     */
    constructor(goal: PropFormula);
    /**
     * Gets all proof steps in order.
     * @returns Array of proof steps
     */
    getSteps(): readonly PropProofStep[];
    /**
     * Gets the goal formula of this proof.
     * @returns The target formula
     */
    getGoal(): PropFormula;
    /**
     * Gets the number of steps in the proof.
     * @returns The current step count
     */
    getStepCount(): number;
    /**
     * Gets a specific step by index (1-based).
     * @param index - The step number (1-based)
     * @returns The proof step, or undefined if not found
     */
    getStep(index: number): PropProofStep | undefined;
    /**
     * Gets the current nesting level for sub-proofs.
     * @returns The current level (0 = main proof, > 0 = inside assumption)
     */
    getCurrentLevel(): number;
    /**
     * Adds a premise (given assumption) to the proof at the current level.
     * @param formula - The premise formula
     * @param comment - Optional explanation for the premise
     * @returns The added proof step
     */
    addPremise(formula: PropFormula, comment?: string): PropProofStep;
    /**
     * Adds an assumption (opens a sub-proof) at the next level.
     * Creates a new assumption that increases the nesting level.
     * @param formula - The assumption formula
     * @param comment - Optional explanation for the assumption
     * @returns The added proof step
     */
    addAssumption(formula: PropFormula, comment?: string): PropProofStep;
    /**
     * Adds a derived step using a Natural Deduction rule.
     * Can be used to apply rules within the current level (including sub-proofs).
     * @param payload - The derived step payload containing formulas, rule, and step references
     * @param comment - Optional explanation for the derivation
     * @returns The array of added proof steps
     */
    addDerivedStep(payload: NaturalDerivedPayload, comment?: string): PropProofStep[];
    /**
     * Reiterates (repeats) a previously proved step at the current level (inside a sub-proof).
     * Allows referring to a formula from an outer level within an inner sub-proof.
     * @param fromIndex - The index of the step to reiterate (1-based)
     * @param comment - Optional explanation for the reiteration
     * @returns The added reiteration step
     * @throws {Error} if the step index is invalid
     */
    reiterateStep(fromIndex: number, comment?: string): PropProofStep;
    /**
     * Finds the most recent assumption at the current level.
     * Used to identify the premise F when closing a sub-proof.
     * @returns The latest assumption step at the current level, or undefined if not found
     */
    private findCurrentAssumption;
    /**
     * Closes a sub-proof by applying Implication Introduction.
     * Automatically takes the assumption (most recent step at current level) and the
     * derived conclusion (last step at current level) to create an implication F=>G,
     * then adds this implication at level-1.
     * @param comment - Optional explanation for the implication closure
     * @returns The added proof step
     */
    closeSubProof(comment?: string): PropProofStep;
    /**
     * Gets the last step in the proof.
     * @returns The final proof step, or undefined if no steps exist
     */
    getLastStep(): PropProofStep | undefined;
    /**
     * Checks if the proof is complete.
     * A proof is complete when:
     * 1. The last step's formula structurally equals the goal formula
     * 2. All sub-proofs are closed (current level is 0)
     * @returns True if the proof is complete
     */
    isComplete(): boolean;
    /**
     * Clears all steps from the proof and resets the level to 0.
     */
    clear(): void;
    /**
     * Replaces all occurrences of an atom with a formula or atom in all proof steps.
     * The goal formula is not modified.
     *
     * @param atom - The atomic proposition to replace
     * @param substitute - The formula or atom to substitute
     */
    replace(atom: PropAtom, substitute: PropFormula | PropAtom): void;
}