Well in Bitcoin investment no money is made permanent for a particular usage, the usage of this funds are not rigid but flexible and adjustable base on situation and or circumstances. There could be times when emergency fund can be used in the place of discretion fund when there is no discretion but that doesn't mean that it will remain permanent but these only happens when there is a financial difficulty or mismanagement of fund or when our source of income are whimpy. But However I don't mean to say yhat it is advisable to misplace the usage of each of this funds but we just need to know that sometimea we just need to be flexible in our investment approach in other not to follow a wrong investment approach expecialy anything that will leed to selling of Bitcoin when our target has not been met.
On no account are you expected to use your emergency fund as discretionary income because their usage are different. Discretionary income are funds remaining after taking out your expenses and from that discretionary income you buy Bitcoin and build out your emergency fund as well as reserve funds and floating cash. It is a very bad cashflow management practice tho turn your emergency fund in when there is no real emergency thereby defeating it's purpose.
When you run into a financial difficulty or there is a decrease in your income supply which makes you not tho have discretionary income for buying Bitcoin, you can pause your buying Bitcoin until you've sorted yourself out and not converting your emergency fund into discretionary income in order to buy Bitcoin. Peradventure there comes a real emergency when you've used up your emergency fund inappropriately, you'll have to tamper with your Bitcoin portfolio to solve it which you would've been able to avoid if you have not mishandled your emergency fund in the first place.