Teorema di Bertamini

Last year as a birthday present I had a theorem named after me. I came across it again now so I am going to copy it here below for everybody to enjoy:

Teorema di Bertamini


Let

T1 = Ca(T1, ℕ) | Cb(ℕ, ℕ)fη: T1 × T1 → T1
fη(Ca(x, y), z) = Cb(Cb(Ca(x, x), x), y)
fη(Cb(x, y), z) = fη(x, fη(x, fη(x, z)))

then

fη(fη(x, y), z) = fη(fη(x, y), x)
Proof outline: induction on x

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