∆L is basically compression.
L = Original length
When compression increases, original length decreases - fact - hence, inverse proportionality.
You can also prove it like this:
Strain = extension/original length => e / L
Compression = 1/e
Therefore, strain = 1/eL
When you look at this equation, you'll see that 1/e (compression ∆L) and L are inversely proportional.