import { FpC, FrC } from '../towers/index.js';
import { Field } from 'o1js';
declare const Sp1PlonkProof_base: (new (value: {
    l_com_x: import("o1js").CanonicalForeignField;
    l_com_y: import("o1js").CanonicalForeignField;
    r_com_x: import("o1js").CanonicalForeignField;
    r_com_y: import("o1js").CanonicalForeignField;
    o_com_x: import("o1js").CanonicalForeignField;
    o_com_y: import("o1js").CanonicalForeignField;
    h0_x: import("o1js").CanonicalForeignField;
    h0_y: import("o1js").CanonicalForeignField;
    h1_x: import("o1js").CanonicalForeignField;
    h1_y: import("o1js").CanonicalForeignField;
    h2_x: import("o1js").CanonicalForeignField;
    h2_y: import("o1js").CanonicalForeignField;
    l_at_zeta: import("o1js").CanonicalForeignField;
    r_at_zeta: import("o1js").CanonicalForeignField;
    o_at_zeta: import("o1js").CanonicalForeignField;
    s1_at_zeta: import("o1js").CanonicalForeignField;
    s2_at_zeta: import("o1js").CanonicalForeignField;
    grand_product_x: import("o1js").CanonicalForeignField;
    grand_product_y: import("o1js").CanonicalForeignField;
    grand_product_at_omega_zeta: import("o1js").CanonicalForeignField;
    batch_opening_at_zeta_x: import("o1js").CanonicalForeignField;
    batch_opening_at_zeta_y: import("o1js").CanonicalForeignField;
    batch_opening_at_zeta_omega_x: import("o1js").CanonicalForeignField;
    batch_opening_at_zeta_omega_y: import("o1js").CanonicalForeignField;
    qcp_0_at_zeta: import("o1js").CanonicalForeignField;
    qcp_0_wire_x: import("o1js").CanonicalForeignField;
    qcp_0_wire_y: import("o1js").CanonicalForeignField;
}) => {
    l_com_x: import("o1js").CanonicalForeignField;
    l_com_y: import("o1js").CanonicalForeignField;
    r_com_x: import("o1js").CanonicalForeignField;
    r_com_y: import("o1js").CanonicalForeignField;
    o_com_x: import("o1js").CanonicalForeignField;
    o_com_y: import("o1js").CanonicalForeignField;
    h0_x: import("o1js").CanonicalForeignField;
    h0_y: import("o1js").CanonicalForeignField;
    h1_x: import("o1js").CanonicalForeignField;
    h1_y: import("o1js").CanonicalForeignField;
    h2_x: import("o1js").CanonicalForeignField;
    h2_y: import("o1js").CanonicalForeignField;
    l_at_zeta: import("o1js").CanonicalForeignField;
    r_at_zeta: import("o1js").CanonicalForeignField;
    o_at_zeta: import("o1js").CanonicalForeignField;
    s1_at_zeta: import("o1js").CanonicalForeignField;
    s2_at_zeta: import("o1js").CanonicalForeignField;
    grand_product_x: import("o1js").CanonicalForeignField;
    grand_product_y: import("o1js").CanonicalForeignField;
    grand_product_at_omega_zeta: import("o1js").CanonicalForeignField;
    batch_opening_at_zeta_x: import("o1js").CanonicalForeignField;
    batch_opening_at_zeta_y: import("o1js").CanonicalForeignField;
    batch_opening_at_zeta_omega_x: import("o1js").CanonicalForeignField;
    batch_opening_at_zeta_omega_y: import("o1js").CanonicalForeignField;
    qcp_0_at_zeta: import("o1js").CanonicalForeignField;
    qcp_0_wire_x: import("o1js").CanonicalForeignField;
    qcp_0_wire_y: import("o1js").CanonicalForeignField;
}) & {
    _isStruct: true;
} & Omit<import("node_modules/o1js/dist/node/lib/provable/types/provable-intf.js").Provable<{
    l_com_x: import("o1js").CanonicalForeignField;
    l_com_y: import("o1js").CanonicalForeignField;
    r_com_x: import("o1js").CanonicalForeignField;
    r_com_y: import("o1js").CanonicalForeignField;
    o_com_x: import("o1js").CanonicalForeignField;
    o_com_y: import("o1js").CanonicalForeignField;
    h0_x: import("o1js").CanonicalForeignField;
    h0_y: import("o1js").CanonicalForeignField;
    h1_x: import("o1js").CanonicalForeignField;
    h1_y: import("o1js").CanonicalForeignField;
    h2_x: import("o1js").CanonicalForeignField;
    h2_y: import("o1js").CanonicalForeignField;
    l_at_zeta: import("o1js").CanonicalForeignField;
    r_at_zeta: import("o1js").CanonicalForeignField;
    o_at_zeta: import("o1js").CanonicalForeignField;
    s1_at_zeta: import("o1js").CanonicalForeignField;
    s2_at_zeta: import("o1js").CanonicalForeignField;
    grand_product_x: import("o1js").CanonicalForeignField;
    grand_product_y: import("o1js").CanonicalForeignField;
    grand_product_at_omega_zeta: import("o1js").CanonicalForeignField;
    batch_opening_at_zeta_x: import("o1js").CanonicalForeignField;
    batch_opening_at_zeta_y: import("o1js").CanonicalForeignField;
    batch_opening_at_zeta_omega_x: import("o1js").CanonicalForeignField;
    batch_opening_at_zeta_omega_y: import("o1js").CanonicalForeignField;
    qcp_0_at_zeta: import("o1js").CanonicalForeignField;
    qcp_0_wire_x: import("o1js").CanonicalForeignField;
    qcp_0_wire_y: import("o1js").CanonicalForeignField;
}, {
    l_com_x: bigint;
    l_com_y: bigint;
    r_com_x: bigint;
    r_com_y: bigint;
    o_com_x: bigint;
    o_com_y: bigint;
    h0_x: bigint;
    h0_y: bigint;
    h1_x: bigint;
    h1_y: bigint;
    h2_x: bigint;
    h2_y: bigint;
    l_at_zeta: bigint;
    r_at_zeta: bigint;
    o_at_zeta: bigint;
    s1_at_zeta: bigint;
    s2_at_zeta: bigint;
    grand_product_x: bigint;
    grand_product_y: bigint;
    grand_product_at_omega_zeta: bigint;
    batch_opening_at_zeta_x: bigint;
    batch_opening_at_zeta_y: bigint;
    batch_opening_at_zeta_omega_x: bigint;
    batch_opening_at_zeta_omega_y: bigint;
    qcp_0_at_zeta: bigint;
    qcp_0_wire_x: bigint;
    qcp_0_wire_y: bigint;
}>, "fromFields"> & {
    fromFields: (fields: import("node_modules/o1js/dist/node/lib/provable/field.js").Field[]) => {
        l_com_x: import("o1js").CanonicalForeignField;
        l_com_y: import("o1js").CanonicalForeignField;
        r_com_x: import("o1js").CanonicalForeignField;
        r_com_y: import("o1js").CanonicalForeignField;
        o_com_x: import("o1js").CanonicalForeignField;
        o_com_y: import("o1js").CanonicalForeignField;
        h0_x: import("o1js").CanonicalForeignField;
        h0_y: import("o1js").CanonicalForeignField;
        h1_x: import("o1js").CanonicalForeignField;
        h1_y: import("o1js").CanonicalForeignField;
        h2_x: import("o1js").CanonicalForeignField;
        h2_y: import("o1js").CanonicalForeignField;
        l_at_zeta: import("o1js").CanonicalForeignField;
        r_at_zeta: import("o1js").CanonicalForeignField;
        o_at_zeta: import("o1js").CanonicalForeignField;
        s1_at_zeta: import("o1js").CanonicalForeignField;
        s2_at_zeta: import("o1js").CanonicalForeignField;
        grand_product_x: import("o1js").CanonicalForeignField;
        grand_product_y: import("o1js").CanonicalForeignField;
        grand_product_at_omega_zeta: import("o1js").CanonicalForeignField;
        batch_opening_at_zeta_x: import("o1js").CanonicalForeignField;
        batch_opening_at_zeta_y: import("o1js").CanonicalForeignField;
        batch_opening_at_zeta_omega_x: import("o1js").CanonicalForeignField;
        batch_opening_at_zeta_omega_y: import("o1js").CanonicalForeignField;
        qcp_0_at_zeta: import("o1js").CanonicalForeignField;
        qcp_0_wire_x: import("o1js").CanonicalForeignField;
        qcp_0_wire_y: import("o1js").CanonicalForeignField;
    };
} & {
    fromValue: (value: {
        l_com_x: bigint | import("o1js").CanonicalForeignField;
        l_com_y: bigint | import("o1js").CanonicalForeignField;
        r_com_x: bigint | import("o1js").CanonicalForeignField;
        r_com_y: bigint | import("o1js").CanonicalForeignField;
        o_com_x: bigint | import("o1js").CanonicalForeignField;
        o_com_y: bigint | import("o1js").CanonicalForeignField;
        h0_x: bigint | import("o1js").CanonicalForeignField;
        h0_y: bigint | import("o1js").CanonicalForeignField;
        h1_x: bigint | import("o1js").CanonicalForeignField;
        h1_y: bigint | import("o1js").CanonicalForeignField;
        h2_x: bigint | import("o1js").CanonicalForeignField;
        h2_y: bigint | import("o1js").CanonicalForeignField;
        l_at_zeta: bigint | import("o1js").CanonicalForeignField;
        r_at_zeta: bigint | import("o1js").CanonicalForeignField;
        o_at_zeta: bigint | import("o1js").CanonicalForeignField;
        s1_at_zeta: bigint | import("o1js").CanonicalForeignField;
        s2_at_zeta: bigint | import("o1js").CanonicalForeignField;
        grand_product_x: bigint | import("o1js").CanonicalForeignField;
        grand_product_y: bigint | import("o1js").CanonicalForeignField;
        grand_product_at_omega_zeta: bigint | import("o1js").CanonicalForeignField;
        batch_opening_at_zeta_x: bigint | import("o1js").CanonicalForeignField;
        batch_opening_at_zeta_y: bigint | import("o1js").CanonicalForeignField;
        batch_opening_at_zeta_omega_x: bigint | import("o1js").CanonicalForeignField;
        batch_opening_at_zeta_omega_y: bigint | import("o1js").CanonicalForeignField;
        qcp_0_at_zeta: bigint | import("o1js").CanonicalForeignField;
        qcp_0_wire_x: bigint | import("o1js").CanonicalForeignField;
        qcp_0_wire_y: bigint | import("o1js").CanonicalForeignField;
    }) => {
        l_com_x: import("o1js").CanonicalForeignField;
        l_com_y: import("o1js").CanonicalForeignField;
        r_com_x: import("o1js").CanonicalForeignField;
        r_com_y: import("o1js").CanonicalForeignField;
        o_com_x: import("o1js").CanonicalForeignField;
        o_com_y: import("o1js").CanonicalForeignField;
        h0_x: import("o1js").CanonicalForeignField;
        h0_y: import("o1js").CanonicalForeignField;
        h1_x: import("o1js").CanonicalForeignField;
        h1_y: import("o1js").CanonicalForeignField;
        h2_x: import("o1js").CanonicalForeignField;
        h2_y: import("o1js").CanonicalForeignField;
        l_at_zeta: import("o1js").CanonicalForeignField;
        r_at_zeta: import("o1js").CanonicalForeignField;
        o_at_zeta: import("o1js").CanonicalForeignField;
        s1_at_zeta: import("o1js").CanonicalForeignField;
        s2_at_zeta: import("o1js").CanonicalForeignField;
        grand_product_x: import("o1js").CanonicalForeignField;
        grand_product_y: import("o1js").CanonicalForeignField;
        grand_product_at_omega_zeta: import("o1js").CanonicalForeignField;
        batch_opening_at_zeta_x: import("o1js").CanonicalForeignField;
        batch_opening_at_zeta_y: import("o1js").CanonicalForeignField;
        batch_opening_at_zeta_omega_x: import("o1js").CanonicalForeignField;
        batch_opening_at_zeta_omega_y: import("o1js").CanonicalForeignField;
        qcp_0_at_zeta: import("o1js").CanonicalForeignField;
        qcp_0_wire_x: import("o1js").CanonicalForeignField;
        qcp_0_wire_y: import("o1js").CanonicalForeignField;
    };
    toInput: (x: {
        l_com_x: import("o1js").CanonicalForeignField;
        l_com_y: import("o1js").CanonicalForeignField;
        r_com_x: import("o1js").CanonicalForeignField;
        r_com_y: import("o1js").CanonicalForeignField;
        o_com_x: import("o1js").CanonicalForeignField;
        o_com_y: import("o1js").CanonicalForeignField;
        h0_x: import("o1js").CanonicalForeignField;
        h0_y: import("o1js").CanonicalForeignField;
        h1_x: import("o1js").CanonicalForeignField;
        h1_y: import("o1js").CanonicalForeignField;
        h2_x: import("o1js").CanonicalForeignField;
        h2_y: import("o1js").CanonicalForeignField;
        l_at_zeta: import("o1js").CanonicalForeignField;
        r_at_zeta: import("o1js").CanonicalForeignField;
        o_at_zeta: import("o1js").CanonicalForeignField;
        s1_at_zeta: import("o1js").CanonicalForeignField;
        s2_at_zeta: import("o1js").CanonicalForeignField;
        grand_product_x: import("o1js").CanonicalForeignField;
        grand_product_y: import("o1js").CanonicalForeignField;
        grand_product_at_omega_zeta: import("o1js").CanonicalForeignField;
        batch_opening_at_zeta_x: import("o1js").CanonicalForeignField;
        batch_opening_at_zeta_y: import("o1js").CanonicalForeignField;
        batch_opening_at_zeta_omega_x: import("o1js").CanonicalForeignField;
        batch_opening_at_zeta_omega_y: import("o1js").CanonicalForeignField;
        qcp_0_at_zeta: import("o1js").CanonicalForeignField;
        qcp_0_wire_x: import("o1js").CanonicalForeignField;
        qcp_0_wire_y: import("o1js").CanonicalForeignField;
    }) => {
        fields?: Field[] | undefined;
        packed?: [Field, number][] | undefined;
    };
    toJSON: (x: {
        l_com_x: import("o1js").CanonicalForeignField;
        l_com_y: import("o1js").CanonicalForeignField;
        r_com_x: import("o1js").CanonicalForeignField;
        r_com_y: import("o1js").CanonicalForeignField;
        o_com_x: import("o1js").CanonicalForeignField;
        o_com_y: import("o1js").CanonicalForeignField;
        h0_x: import("o1js").CanonicalForeignField;
        h0_y: import("o1js").CanonicalForeignField;
        h1_x: import("o1js").CanonicalForeignField;
        h1_y: import("o1js").CanonicalForeignField;
        h2_x: import("o1js").CanonicalForeignField;
        h2_y: import("o1js").CanonicalForeignField;
        l_at_zeta: import("o1js").CanonicalForeignField;
        r_at_zeta: import("o1js").CanonicalForeignField;
        o_at_zeta: import("o1js").CanonicalForeignField;
        s1_at_zeta: import("o1js").CanonicalForeignField;
        s2_at_zeta: import("o1js").CanonicalForeignField;
        grand_product_x: import("o1js").CanonicalForeignField;
        grand_product_y: import("o1js").CanonicalForeignField;
        grand_product_at_omega_zeta: import("o1js").CanonicalForeignField;
        batch_opening_at_zeta_x: import("o1js").CanonicalForeignField;
        batch_opening_at_zeta_y: import("o1js").CanonicalForeignField;
        batch_opening_at_zeta_omega_x: import("o1js").CanonicalForeignField;
        batch_opening_at_zeta_omega_y: import("o1js").CanonicalForeignField;
        qcp_0_at_zeta: import("o1js").CanonicalForeignField;
        qcp_0_wire_x: import("o1js").CanonicalForeignField;
        qcp_0_wire_y: import("o1js").CanonicalForeignField;
    }) => {
        l_com_x: string;
        l_com_y: string;
        r_com_x: string;
        r_com_y: string;
        o_com_x: string;
        o_com_y: string;
        h0_x: string;
        h0_y: string;
        h1_x: string;
        h1_y: string;
        h2_x: string;
        h2_y: string;
        l_at_zeta: string;
        r_at_zeta: string;
        o_at_zeta: string;
        s1_at_zeta: string;
        s2_at_zeta: string;
        grand_product_x: string;
        grand_product_y: string;
        grand_product_at_omega_zeta: string;
        batch_opening_at_zeta_x: string;
        batch_opening_at_zeta_y: string;
        batch_opening_at_zeta_omega_x: string;
        batch_opening_at_zeta_omega_y: string;
        qcp_0_at_zeta: string;
        qcp_0_wire_x: string;
        qcp_0_wire_y: string;
    };
    fromJSON: (x: {
        l_com_x: string;
        l_com_y: string;
        r_com_x: string;
        r_com_y: string;
        o_com_x: string;
        o_com_y: string;
        h0_x: string;
        h0_y: string;
        h1_x: string;
        h1_y: string;
        h2_x: string;
        h2_y: string;
        l_at_zeta: string;
        r_at_zeta: string;
        o_at_zeta: string;
        s1_at_zeta: string;
        s2_at_zeta: string;
        grand_product_x: string;
        grand_product_y: string;
        grand_product_at_omega_zeta: string;
        batch_opening_at_zeta_x: string;
        batch_opening_at_zeta_y: string;
        batch_opening_at_zeta_omega_x: string;
        batch_opening_at_zeta_omega_y: string;
        qcp_0_at_zeta: string;
        qcp_0_wire_x: string;
        qcp_0_wire_y: string;
    }) => {
        l_com_x: import("o1js").CanonicalForeignField;
        l_com_y: import("o1js").CanonicalForeignField;
        r_com_x: import("o1js").CanonicalForeignField;
        r_com_y: import("o1js").CanonicalForeignField;
        o_com_x: import("o1js").CanonicalForeignField;
        o_com_y: import("o1js").CanonicalForeignField;
        h0_x: import("o1js").CanonicalForeignField;
        h0_y: import("o1js").CanonicalForeignField;
        h1_x: import("o1js").CanonicalForeignField;
        h1_y: import("o1js").CanonicalForeignField;
        h2_x: import("o1js").CanonicalForeignField;
        h2_y: import("o1js").CanonicalForeignField;
        l_at_zeta: import("o1js").CanonicalForeignField;
        r_at_zeta: import("o1js").CanonicalForeignField;
        o_at_zeta: import("o1js").CanonicalForeignField;
        s1_at_zeta: import("o1js").CanonicalForeignField;
        s2_at_zeta: import("o1js").CanonicalForeignField;
        grand_product_x: import("o1js").CanonicalForeignField;
        grand_product_y: import("o1js").CanonicalForeignField;
        grand_product_at_omega_zeta: import("o1js").CanonicalForeignField;
        batch_opening_at_zeta_x: import("o1js").CanonicalForeignField;
        batch_opening_at_zeta_y: import("o1js").CanonicalForeignField;
        batch_opening_at_zeta_omega_x: import("o1js").CanonicalForeignField;
        batch_opening_at_zeta_omega_y: import("o1js").CanonicalForeignField;
        qcp_0_at_zeta: import("o1js").CanonicalForeignField;
        qcp_0_wire_x: import("o1js").CanonicalForeignField;
        qcp_0_wire_y: import("o1js").CanonicalForeignField;
    };
    empty: () => {
        l_com_x: import("o1js").CanonicalForeignField;
        l_com_y: import("o1js").CanonicalForeignField;
        r_com_x: import("o1js").CanonicalForeignField;
        r_com_y: import("o1js").CanonicalForeignField;
        o_com_x: import("o1js").CanonicalForeignField;
        o_com_y: import("o1js").CanonicalForeignField;
        h0_x: import("o1js").CanonicalForeignField;
        h0_y: import("o1js").CanonicalForeignField;
        h1_x: import("o1js").CanonicalForeignField;
        h1_y: import("o1js").CanonicalForeignField;
        h2_x: import("o1js").CanonicalForeignField;
        h2_y: import("o1js").CanonicalForeignField;
        l_at_zeta: import("o1js").CanonicalForeignField;
        r_at_zeta: import("o1js").CanonicalForeignField;
        o_at_zeta: import("o1js").CanonicalForeignField;
        s1_at_zeta: import("o1js").CanonicalForeignField;
        s2_at_zeta: import("o1js").CanonicalForeignField;
        grand_product_x: import("o1js").CanonicalForeignField;
        grand_product_y: import("o1js").CanonicalForeignField;
        grand_product_at_omega_zeta: import("o1js").CanonicalForeignField;
        batch_opening_at_zeta_x: import("o1js").CanonicalForeignField;
        batch_opening_at_zeta_y: import("o1js").CanonicalForeignField;
        batch_opening_at_zeta_omega_x: import("o1js").CanonicalForeignField;
        batch_opening_at_zeta_omega_y: import("o1js").CanonicalForeignField;
        qcp_0_at_zeta: import("o1js").CanonicalForeignField;
        qcp_0_wire_x: import("o1js").CanonicalForeignField;
        qcp_0_wire_y: import("o1js").CanonicalForeignField;
    };
};
declare class Sp1PlonkProof extends Sp1PlonkProof_base {
    deserialize(hexProof: string): Sp1PlonkProof;
}
type ProofType = {
    l_com_x: FpC;
    l_com_y: FpC;
    r_com_x: FpC;
    r_com_y: FpC;
    o_com_x: FpC;
    o_com_y: FpC;
    h0_x: FpC;
    h0_y: FpC;
    h1_x: FpC;
    h1_y: FpC;
    h2_x: FpC;
    h2_y: FpC;
    l_at_zeta: FrC;
    r_at_zeta: FrC;
    o_at_zeta: FrC;
    s1_at_zeta: FrC;
    s2_at_zeta: FrC;
    grand_product_x: FpC;
    grand_product_y: FpC;
    grand_product_at_omega_zeta: FrC;
    batch_opening_at_zeta_x: FpC;
    batch_opening_at_zeta_y: FpC;
    batch_opening_at_zeta_omega_x: FpC;
    batch_opening_at_zeta_omega_y: FpC;
    qcp_0_at_zeta: FrC;
    qcp_0_wire_x: FpC;
    qcp_0_wire_y: FpC;
};
declare const deserializeProof: (hexProof: string) => ProofType;
export { Sp1PlonkProof, deserializeProof };