import type { PropFormula } from "../../../models";
/**
 * Applies the rule of Implication Introduction.
 *
 * Given a proven formula F and an arbitrary formula G,
 * it derives the implication G => F.
 *
 * This rule allows the introduction of implications in Hilbert-style calculus,
 * enabling the creation of conditional statements from established facts.
 *
 * @param formulas - An array containing [provenFormula, newFormula].
 *                   - provenFormula: The formula that has been proven
 *                   - newFormula: The arbitrary formula to be the antecedent
 * @returns The implication (newFormula => provenFormula)
 * @throws {Error} if implication creation is not applicable.
 */
export declare function implicationIntroductionRule(formulas: PropFormula[]): PropFormula[];