import { type Expr } from "../expr.js";
import { type Rule } from "../rule.js";
export interface MultiplyBothSidesParams {
    /** Cloned before inserting, so callers may pass subtrees of the equation. */
    readonly factor: Expr;
}
/**
 * Multiplies both sides by a user-chosen expression — a solution-GAINING
 * move: wherever the factor is 0 the new equation is trivially true, so it
 * may admit solutions the original does not. The rule therefore emits an
 * Extension carrying the pre-move equation; the derivation is not settled
 * until candidate solutions are checked against it (checkSolution).
 */
export declare const multiplyBothSides: Rule<MultiplyBothSidesParams>;
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