// hevm: flattened sources of /nix/store/8xb41r4qd0cjb63wcrxf1qmfg88p0961-dss-6fd7de0/src/join.sol
pragma solidity =0.5.12;

////// /nix/store/8xb41r4qd0cjb63wcrxf1qmfg88p0961-dss-6fd7de0/src/lib.sol
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

/* pragma solidity 0.5.12; */

contract LibNote {
    event LogNote(
        bytes4   indexed  sig,
        address  indexed  usr,
        bytes32  indexed  arg1,
        bytes32  indexed  arg2,
        bytes             data
    ) anonymous;

    modifier note {
        _;
        assembly {
            // log an 'anonymous' event with a constant 6 words of calldata
            // and four indexed topics: selector, caller, arg1 and arg2
            let mark := msize                         // end of memory ensures zero
            mstore(0x40, add(mark, 288))              // update free memory pointer
            mstore(mark, 0x20)                        // bytes type data offset
            mstore(add(mark, 0x20), 224)              // bytes size (padded)
            calldatacopy(add(mark, 0x40), 0, 224)     // bytes payload
            log4(mark, 288,                           // calldata
                 shl(224, shr(224, calldataload(0))), // msg.sig
                 caller,                              // msg.sender
                 calldataload(4),                     // arg1
                 calldataload(36)                     // arg2
                )
        }
    }
}

////// /nix/store/8xb41r4qd0cjb63wcrxf1qmfg88p0961-dss-6fd7de0/src/join.sol
/// join.sol -- Basic token adapters

// Copyright (C) 2018 Rain <[email protected]>
//
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU Affero General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU Affero General Public License for more details.
//
// You should have received a copy of the GNU Affero General Public License
// along with this program.  If not, see <https://www.gnu.org/licenses/>.

/* pragma solidity 0.5.12; */

/* import "./lib.sol"; */

contract GemLike {
    function decimals() public view returns (uint);
    function transfer(address,uint) external returns (bool);
    function transferFrom(address,address,uint) external returns (bool);
}

contract DSTokenLike {
    function mint(address,uint) external;
    function burn(address,uint) external;
}

contract VatLike {
    function slip(bytes32,address,int) external;
    function move(address,address,uint) external;
}

/*
    Here we provide *adapters* to connect the Vat to arbitrary external
    token implementations, creating a bounded context for the Vat. The
    adapters here are provided as working examples:

      - `GemJoin`: For well behaved ERC20 tokens, with simple transfer
                   semantics.

      - `ETHJoin`: For native Ether.

      - `DaiJoin`: For connecting internal Dai balances to an external
                   `DSToken` implementation.

    In practice, adapter implementations will be varied and specific to
    individual collateral types, accounting for different transfer
    semantics and token standards.

    Adapters need to implement two basic methods:

      - `join`: enter collateral into the system
      - `exit`: remove collateral from the system

*/

contract GemJoin is LibNote {
    // --- Auth ---
    mapping (address => uint) public wards;
    function rely(address usr) external note auth { wards[usr] = 1; }
    function deny(address usr) external note auth { wards[usr] = 0; }
    modifier auth {
        require(wards[msg.sender] == 1, "GemJoin/not-authorized");
        _;
    }

    VatLike public vat;
    bytes32 public ilk;
    GemLike public gem;
    uint    public dec;
    uint    public live;  // Access Flag

    constructor(address vat_, bytes32 ilk_, address gem_) public {
        wards[msg.sender] = 1;
        live = 1;
        vat = VatLike(vat_);
        ilk = ilk_;
        gem = GemLike(gem_);
        dec = gem.decimals();
    }
    function cage() external note auth {
        live = 0;
    }
    function join(address usr, uint wad) external note {
        require(live == 1, "GemJoin/not-live");
        require(int(wad) >= 0, "GemJoin/overflow");
        vat.slip(ilk, usr, int(wad));
        require(gem.transferFrom(msg.sender, address(this), wad), "GemJoin/failed-transfer");
    }
    function exit(address usr, uint wad) external note {
        require(wad <= 2 ** 255, "GemJoin/overflow");
        vat.slip(ilk, msg.sender, -int(wad));
        require(gem.transfer(usr, wad), "GemJoin/failed-transfer");
    }
}

contract ETHJoin is LibNote {
    // --- Auth ---
    mapping (address => uint) public wards;
    function rely(address usr) external note auth { wards[usr] = 1; }
    function deny(address usr) external note auth { wards[usr] = 0; }
    modifier auth {
        require(wards[msg.sender] == 1, "ETHJoin/not-authorized");
        _;
    }

    VatLike public vat;
    bytes32 public ilk;
    uint    public live;  // Access Flag

    constructor(address vat_, bytes32 ilk_) public {
        wards[msg.sender] = 1;
        live = 1;
        vat = VatLike(vat_);
        ilk = ilk_;
    }
    function cage() external note auth {
        live = 0;
    }
    function join(address usr) external payable note {
        require(live == 1, "ETHJoin/not-live");
        require(int(msg.value) >= 0, "ETHJoin/overflow");
        vat.slip(ilk, usr, int(msg.value));
    }
    function exit(address payable usr, uint wad) external note {
        require(int(wad) >= 0, "ETHJoin/overflow");
        vat.slip(ilk, msg.sender, -int(wad));
        usr.transfer(wad);
    }
}

contract DaiJoin is LibNote {
    // --- Auth ---
    mapping (address => uint) public wards;
    function rely(address usr) external note auth { wards[usr] = 1; }
    function deny(address usr) external note auth { wards[usr] = 0; }
    modifier auth {
        require(wards[msg.sender] == 1, "DaiJoin/not-authorized");
        _;
    }

    VatLike public vat;
    DSTokenLike public dai;
    uint    public live;  // Access Flag

    constructor(address vat_, address dai_) public {
        wards[msg.sender] = 1;
        live = 1;
        vat = VatLike(vat_);
        dai = DSTokenLike(dai_);
    }
    function cage() external note auth {
        live = 0;
    }
    uint constant ONE = 10 ** 27;
    function mul(uint x, uint y) internal pure returns (uint z) {
        require(y == 0 || (z = x * y) / y == x);
    }
    function join(address usr, uint wad) external note {
        vat.move(address(this), usr, mul(ONE, wad));
        dai.burn(msg.sender, wad);
    }
    function exit(address usr, uint wad) external note {
        require(live == 1, "DaiJoin/not-live");
        vat.move(msg.sender, address(this), mul(ONE, wad));
        dai.mint(usr, wad);
    }
}

// hevm: flattened sources of /nix/store/8xb41r4qd0cjb63wcrxf1qmfg88p0961-dss-6fd7de0/src/vat.sol
pragma solidity =0.5.12;

////// /nix/store/8xb41r4qd0cjb63wcrxf1qmfg88p0961-dss-6fd7de0/src/vat.sol
/// vat.sol -- Dai CDP database

// Copyright (C) 2018 Rain <[email protected]>
//
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU Affero General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU Affero General Public License for more details.
//
// You should have received a copy of the GNU Affero General Public License
// along with this program.  If not, see <https://www.gnu.org/licenses/>.

/* pragma solidity 0.5.12; */

contract Vat {
    // --- Auth ---
    mapping (address => uint) public wards;
    function rely(address usr) external note auth { require(live == 1, "Vat/not-live"); wards[usr] = 1; }
    function deny(address usr) external note auth { require(live == 1, "Vat/not-live"); wards[usr] = 0; }
    modifier auth {
        require(wards[msg.sender] == 1, "Vat/not-authorized");
        _;
    }

    mapping(address => mapping (address => uint)) public can;
    function hope(address usr) external note { can[msg.sender][usr] = 1; }
    function nope(address usr) external note { can[msg.sender][usr] = 0; }
    function wish(address bit, address usr) internal view returns (bool) {
        return either(bit == usr, can[bit][usr] == 1);
    }

    // --- Data ---
    struct Ilk {
        uint256 Art;   // Total Normalised Debt     [wad]
        uint256 rate;  // Accumulated Rates         [ray]
        uint256 spot;  // Price with Safety Margin  [ray]
        uint256 line;  // Debt Ceiling              [rad]
        uint256 dust;  // Urn Debt Floor            [rad]
    }
    struct Urn {
        uint256 ink;   // Locked Collateral  [wad]
        uint256 art;   // Normalised Debt    [wad]
    }

    mapping (bytes32 => Ilk)                       public ilks;
    mapping (bytes32 => mapping (address => Urn )) public urns;
    mapping (bytes32 => mapping (address => uint)) public gem;  // [wad]
    mapping (address => uint256)                   public dai;  // [rad]
    mapping (address => uint256)                   public sin;  // [rad]

    uint256 public debt;  // Total Dai Issued    [rad]
    uint256 public vice;  // Total Unbacked Dai  [rad]
    uint256 public Line;  // Total Debt Ceiling  [rad]
    uint256 public live;  // Access Flag

    // --- Logs ---
    event LogNote(
        bytes4   indexed  sig,
        bytes32  indexed  arg1,
        bytes32  indexed  arg2,
        bytes32  indexed  arg3,
        bytes             data
    ) anonymous;

    modifier note {
        _;
        assembly {
            // log an 'anonymous' event with a constant 6 words of calldata
            // and four indexed topics: the selector and the first three args
            let mark := msize                         // end of memory ensures zero
            mstore(0x40, add(mark, 288))              // update free memory pointer
            mstore(mark, 0x20)                        // bytes type data offset
            mstore(add(mark, 0x20), 224)              // bytes size (padded)
            calldatacopy(add(mark, 0x40), 0, 224)     // bytes payload
            log4(mark, 288,                           // calldata
                 shl(224, shr(224, calldataload(0))), // msg.sig
                 calldataload(4),                     // arg1
                 calldataload(36),                    // arg2
                 calldataload(68)                     // arg3
                )
        }
    }

    // --- Init ---
    constructor() public {
        wards[msg.sender] = 1;
        live = 1;
    }

    // --- Math ---
    function add(uint x, int y) internal pure returns (uint z) {
        z = x + uint(y);
        require(y >= 0 || z <= x);
        require(y <= 0 || z >= x);
    }
    function sub(uint x, int y) internal pure returns (uint z) {
        z = x - uint(y);
        require(y <= 0 || z <= x);
        require(y >= 0 || z >= x);
    }
    function mul(uint x, int y) internal pure returns (int z) {
        z = int(x) * y;
        require(int(x) >= 0);
        require(y == 0 || z / y == int(x));
    }
    function add(uint x, uint y) internal pure returns (uint z) {
        require((z = x + y) >= x);
    }
    function sub(uint x, uint y) internal pure returns (uint z) {
        require((z = x - y) <= x);
    }
    function mul(uint x, uint y) internal pure returns (uint z) {
        require(y == 0 || (z = x * y) / y == x);
    }

    // --- Administration ---
    function init(bytes32 ilk) external note auth {
        require(ilks[ilk].rate == 0, "Vat/ilk-already-init");
        ilks[ilk].rate = 10 ** 27;
    }
    function file(bytes32 what, uint data) external note auth {
        require(live == 1, "Vat/not-live");
        if (what == "Line") Line = data;
        else revert("Vat/file-unrecognized-param");
    }
    function file(bytes32 ilk, bytes32 what, uint data) external note auth {
        require(live == 1, "Vat/not-live");
        if (what == "spot") ilks[ilk].spot = data;
        else if (what == "line") ilks[ilk].line = data;
        else if (what == "dust") ilks[ilk].dust = data;
        else revert("Vat/file-unrecognized-param");
    }
    function cage() external note auth {
        live = 0;
    }

    // --- Fungibility ---
    function slip(bytes32 ilk, address usr, int256 wad) external note auth {
        gem[ilk][usr] = add(gem[ilk][usr], wad);
    }
    function flux(bytes32 ilk, address src, address dst, uint256 wad) external note {
        require(wish(src, msg.sender), "Vat/not-allowed");
        gem[ilk][src] = sub(gem[ilk][src], wad);
        gem[ilk][dst] = add(gem[ilk][dst], wad);
    }
    function move(address src, address dst, uint256 rad) external note {
        require(wish(src, msg.sender), "Vat/not-allowed");
        dai[src] = sub(dai[src], rad);
        dai[dst] = add(dai[dst], rad);
    }

    function either(bool x, bool y) internal pure returns (bool z) {
        assembly{ z := or(x, y)}
    }
    function both(bool x, bool y) internal pure returns (bool z) {
        assembly{ z := and(x, y)}
    }

    // --- CDP Manipulation ---
    function frob(bytes32 i, address u, address v, address w, int dink, int dart) external note {
        // system is live
        require(live == 1, "Vat/not-live");

        Urn memory urn = urns[i][u];
        Ilk memory ilk = ilks[i];
        // ilk has been initialised
        require(ilk.rate != 0, "Vat/ilk-not-init");

        urn.ink = add(urn.ink, dink);
        urn.art = add(urn.art, dart);
        ilk.Art = add(ilk.Art, dart);

        int dtab = mul(ilk.rate, dart);
        uint tab = mul(ilk.rate, urn.art);
        debt     = add(debt, dtab);

        // either debt has decreased, or debt ceilings are not exceeded
        require(either(dart <= 0, both(mul(ilk.Art, ilk.rate) <= ilk.line, debt <= Line)), "Vat/ceiling-exceeded");
        // urn is either less risky than before, or it is safe
        require(either(both(dart <= 0, dink >= 0), tab <= mul(urn.ink, ilk.spot)), "Vat/not-safe");

        // urn is either more safe, or the owner consents
        require(either(both(dart <= 0, dink >= 0), wish(u, msg.sender)), "Vat/not-allowed-u");
        // collateral src consents
        require(either(dink <= 0, wish(v, msg.sender)), "Vat/not-allowed-v");
        // debt dst consents
        require(either(dart >= 0, wish(w, msg.sender)), "Vat/not-allowed-w");

        // urn has no debt, or a non-dusty amount
        require(either(urn.art == 0, tab >= ilk.dust), "Vat/dust");

        gem[i][v] = sub(gem[i][v], dink);
        dai[w]    = add(dai[w],    dtab);

        urns[i][u] = urn;
        ilks[i]    = ilk;
    }
    // --- CDP Fungibility ---
    function fork(bytes32 ilk, address src, address dst, int dink, int dart) external note {
        Urn storage u = urns[ilk][src];
        Urn storage v = urns[ilk][dst];
        Ilk storage i = ilks[ilk];

        u.ink = sub(u.ink, dink);
        u.art = sub(u.art, dart);
        v.ink = add(v.ink, dink);
        v.art = add(v.art, dart);

        uint utab = mul(u.art, i.rate);
        uint vtab = mul(v.art, i.rate);

        // both sides consent
        require(both(wish(src, msg.sender), wish(dst, msg.sender)), "Vat/not-allowed");

        // both sides safe
        require(utab <= mul(u.ink, i.spot), "Vat/not-safe-src");
        require(vtab <= mul(v.ink, i.spot), "Vat/not-safe-dst");

        // both sides non-dusty
        require(either(utab >= i.dust, u.art == 0), "Vat/dust-src");
        require(either(vtab >= i.dust, v.art == 0), "Vat/dust-dst");
    }
    // --- CDP Confiscation ---
    function grab(bytes32 i, address u, address v, address w, int dink, int dart) external note auth {
        Urn storage urn = urns[i][u];
        Ilk storage ilk = ilks[i];

        urn.ink = add(urn.ink, dink);
        urn.art = add(urn.art, dart);
        ilk.Art = add(ilk.Art, dart);

        int dtab = mul(ilk.rate, dart);

        gem[i][v] = sub(gem[i][v], dink);
        sin[w]    = sub(sin[w],    dtab);
        vice      = sub(vice,      dtab);
    }

    // --- Settlement ---
    function heal(uint rad) external note {
        address u = msg.sender;
        sin[u] = sub(sin[u], rad);
        dai[u] = sub(dai[u], rad);
        vice   = sub(vice,   rad);
        debt   = sub(debt,   rad);
    }
    function suck(address u, address v, uint rad) external note auth {
        sin[u] = add(sin[u], rad);
        dai[v] = add(dai[v], rad);
        vice   = add(vice,   rad);
        debt   = add(debt,   rad);
    }

    // --- Rates ---
    function fold(bytes32 i, address u, int rate) external note auth {
        require(live == 1, "Vat/not-live");
        Ilk storage ilk = ilks[i];
        ilk.rate = add(ilk.rate, rate);
        int rad  = mul(ilk.Art, rate);
        dai[u]   = add(dai[u], rad);
        debt     = add(debt,   rad);
    }
}

// hevm: flattened sources of /nix/store/8xb41r4qd0cjb63wcrxf1qmfg88p0961-dss-6fd7de0/src/dai.sol
pragma solidity =0.5.12;

////// /nix/store/8xb41r4qd0cjb63wcrxf1qmfg88p0961-dss-6fd7de0/src/lib.sol
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

/* pragma solidity 0.5.12; */

contract LibNote {
    event LogNote(
        bytes4   indexed  sig,
        address  indexed  usr,
        bytes32  indexed  arg1,
        bytes32  indexed  arg2,
        bytes             data
    ) anonymous;

    modifier note {
        _;
        assembly {
            // log an 'anonymous' event with a constant 6 words of calldata
            // and four indexed topics: selector, caller, arg1 and arg2
            let mark := msize                         // end of memory ensures zero
            mstore(0x40, add(mark, 288))              // update free memory pointer
            mstore(mark, 0x20)                        // bytes type data offset
            mstore(add(mark, 0x20), 224)              // bytes size (padded)
            calldatacopy(add(mark, 0x40), 0, 224)     // bytes payload
            log4(mark, 288,                           // calldata
                 shl(224, shr(224, calldataload(0))), // msg.sig
                 caller,                              // msg.sender
                 calldataload(4),                     // arg1
                 calldataload(36)                     // arg2
                )
        }
    }
}

////// /nix/store/8xb41r4qd0cjb63wcrxf1qmfg88p0961-dss-6fd7de0/src/dai.sol
// Copyright (C) 2017, 2018, 2019 dbrock, rain, mrchico

// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU Affero General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU Affero General Public License for more details.
//
// You should have received a copy of the GNU Affero General Public License
// along with this program.  If not, see <https://www.gnu.org/licenses/>.

/* pragma solidity 0.5.12; */

/* import "./lib.sol"; */

contract Dai is LibNote {
    // --- Auth ---
    mapping (address => uint) public wards;
    function rely(address guy) external note auth { wards[guy] = 1; }
    function deny(address guy) external note auth { wards[guy] = 0; }
    modifier auth {
        require(wards[msg.sender] == 1, "Dai/not-authorized");
        _;
    }

    // --- ERC20 Data ---
    string  public constant name     = "Dai Stablecoin";
    string  public constant symbol   = "DAI";
    string  public constant version  = "1";
    uint8   public constant decimals = 18;
    uint256 public totalSupply;

    mapping (address => uint)                      public balanceOf;
    mapping (address => mapping (address => uint)) public allowance;
    mapping (address => uint)                      public nonces;

    event Approval(address indexed src, address indexed guy, uint wad);
    event Transfer(address indexed src, address indexed dst, uint wad);

    // --- Math ---
    function add(uint x, uint y) internal pure returns (uint z) {
        require((z = x + y) >= x);
    }
    function sub(uint x, uint y) internal pure returns (uint z) {
        require((z = x - y) <= x);
    }

    // --- EIP712 niceties ---
    bytes32 public DOMAIN_SEPARATOR;
    // bytes32 public constant PERMIT_TYPEHASH = keccak256("Permit(address holder,address spender,uint256 nonce,uint256 expiry,bool allowed)");
    bytes32 public constant PERMIT_TYPEHASH = 0xea2aa0a1be11a07ed86d755c93467f4f82362b452371d1ba94d1715123511acb;

    constructor(uint256 chainId_) public {
        wards[msg.sender] = 1;
        DOMAIN_SEPARATOR = keccak256(abi.encode(
            keccak256("EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)"),
            keccak256(bytes(name)),
            keccak256(bytes(version)),
            chainId_,
            address(this)
        ));
    }

    // --- Token ---
    function transfer(address dst, uint wad) external returns (bool) {
        return transferFrom(msg.sender, dst, wad);
    }
    function transferFrom(address src, address dst, uint wad)
        public returns (bool)
    {
        require(balanceOf[src] >= wad, "Dai/insufficient-balance");
        if (src != msg.sender && allowance[src][msg.sender] != uint(-1)) {
            require(allowance[src][msg.sender] >= wad, "Dai/insufficient-allowance");
            allowance[src][msg.sender] = sub(allowance[src][msg.sender], wad);
        }
        balanceOf[src] = sub(balanceOf[src], wad);
        balanceOf[dst] = add(balanceOf[dst], wad);
        emit Transfer(src, dst, wad);
        return true;
    }
    function mint(address usr, uint wad) external auth {
        balanceOf[usr] = add(balanceOf[usr], wad);
        totalSupply    = add(totalSupply, wad);
        emit Transfer(address(0), usr, wad);
    }
    function burn(address usr, uint wad) external {
        require(balanceOf[usr] >= wad, "Dai/insufficient-balance");
        if (usr != msg.sender && allowance[usr][msg.sender] != uint(-1)) {
            require(allowance[usr][msg.sender] >= wad, "Dai/insufficient-allowance");
            allowance[usr][msg.sender] = sub(allowance[usr][msg.sender], wad);
        }
        balanceOf[usr] = sub(balanceOf[usr], wad);
        totalSupply    = sub(totalSupply, wad);
        emit Transfer(usr, address(0), wad);
    }
    function approve(address usr, uint wad) external returns (bool) {
        allowance[msg.sender][usr] = wad;
        emit Approval(msg.sender, usr, wad);
        return true;
    }

    // --- Alias ---
    function push(address usr, uint wad) external {
        transferFrom(msg.sender, usr, wad);
    }
    function pull(address usr, uint wad) external {
        transferFrom(usr, msg.sender, wad);
    }
    function move(address src, address dst, uint wad) external {
        transferFrom(src, dst, wad);
    }

    // --- Approve by signature ---
    function permit(address holder, address spender, uint256 nonce, uint256 expiry,
                    bool allowed, uint8 v, bytes32 r, bytes32 s) external
    {
        bytes32 digest =
            keccak256(abi.encodePacked(
                "\x19\x01",
                DOMAIN_SEPARATOR,
                keccak256(abi.encode(PERMIT_TYPEHASH,
                                     holder,
                                     spender,
                                     nonce,
                                     expiry,
                                     allowed))
        ));

        require(holder != address(0), "Dai/invalid-address-0");
        require(holder == ecrecover(digest, v, r, s), "Dai/invalid-permit");
        require(expiry == 0 || now <= expiry, "Dai/permit-expired");
        require(nonce == nonces[holder]++, "Dai/invalid-nonce");
        uint wad = allowed ? uint(-1) : 0;
        allowance[holder][spender] = wad;
        emit Approval(holder, spender, wad);
    }
}