import type { HilbertAxiomPayload, HilbertDerivedPayload, PropAtom, PropFormula, PropProofStep } from "../../../models";
/**
 * Represents a complete proof in Hilbert-style calculus.
 * Manages a sequence of proof steps where the final step is the goal formula.
 * Each step can be an axiom, premise, or derived from previous steps.
 *
 * @category Hilbert Calculus
 */
export declare class HilbertProof {
    private steps;
    private readonly goal;
    /**
     * Creates a new Hilbert 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;
    /**
     * Adds a premise (given assumption) to the proof.
     * @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 axiom step to the proof.
     * @param payload - The axiom payload containing formulas and schema
     * @param comment - Optional explanation for the axiom
     * @returns The added proof step
     */
    addAxiom(payload: HilbertAxiomPayload, comment?: string): PropProofStep;
    /**
     * Adds a derived step to the proof using a Hilbert calculus rule.
     * @param payload - The derived step payload containing formulas, schema, and step references
     * @param comment - Optional explanation for the derivation
     * @returns The added proof step
     */
    addDerivedStep(payload: HilbertDerivedPayload, comment?: string): PropProofStep[];
    /**
     * Checks if the proof is complete (last step matches the goal).
     * @returns True if the last step's formula matches the goal
     */
    isComplete(): boolean;
    /**
     * Gets the last step in the proof (which should be the goal).
     * @returns The final proof step, or undefined if no steps exist
     */
    getLastStep(): PropProofStep | undefined;
    /**
     * Reiterates (repeats) a previously proved step.
     * Allows referring to a formula from an earlier step in the 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;
    /**
     * Clears all steps from the proof.
     */
    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;
}