Question regarding to Government Debt in Williamson Textbook
Given the clarification from the OP in the comments, there appears to be a mix-up here.

We learn that the author explains as follows: 


  This is an open market operation wherein the fiscal authority
  issues debt, and the monetary authority purchases some of this debt by
  issuing new money.


This sentence describes a situation where the monetary authority is separate from government. But if this were so, we could not have in the same budget constraint both inflows from bond issue and from increase of the money supply.

Namely, the budget constraint describes a different situation, one where the government is a single entity that has three options to finance itself:
1) Collect Taxes from the private sector
2) Issue bonds that are purchased by the private sector
3) Issue new money by fiat

In such a case, with fixed outlays in the left-hand side, more money issuance allows indeed for less debt.

I note the the author writes "the monetary authority purchases some of this debt". This complicates things a bit, it means that part of the debt is bought by the private sector, and then we could have a partial substitution effect, but then we would have to distinguish between "debt held by the monetary authority" and "debt held by the private sector", etc.