Prove Equivalence of Two Functions - Convolution Identity

[muzialis]

Hi there,
working on a physical problem I found two functions that should be equivalent, and indeed they seem to be after a numerical check.

The functions are shown in the attached PDF. I can not figure a way to prove their equivalence analytically (the double integral especially gives me grief when trying to "unravel" it, to get to a single integral expression)
Any help would be so appreciated, thank you very much

 

[haruspex]

G(2t-τ₁-τ₂) = G(t-τ₁) G(t-τ₂)/c
The double integral then factors into two separate integrals which are identical in effect.