How can i make sure liquidity is not changed after the swap using the next price.

[vishwa7dcap786]

i understand the logic in this page about this formula Δ P= Δy/L

https://uniswapv3book.com/milestone_1/first-swap.html

But how can i verify that liquidity is not changed after the swap by substituting values of Δ P and Δy and get L = 1517.8825 while the new price is 5,003