Subtracting two simple, seemingly compatible functions (f - g) results in wrong answer upon evaluation (typeof(f) = Chebyshev ⨁ CosSpace ⨁ SinSpace and typeof(g) = Chebyshev)

using ApproxFun
Dc = Chebyshev(Interval(0,1.))
Df = Fourier(Interval(0,1.))
rx = Fun(t -> cospi(2*t), Df)
ry = Fun(t -> sinpi(2*t), Df)
twoπx = Fun(x -> 2π*x, Dc)
ell = sqrt(differentiate(rx)^2 + differentiate(ry)^2)
L = cumsum(ell)
println(L(1) == twoπx(1)) # expected value: true
println((L - twoπx)(1) ≈ 0) # therefore, expected value: true
println((L - twoπx)(1) == L(1)) # expected value: false

Doing this on a chalkboard we would find L := 2πx and so (L - twoπx) ≡ 0. However, the actual results from this example are: true, false, true.

Start by running the Julia reproduction in the issue and verify the three printed results. Trace subtraction and evaluation for L, twoπx, and the Chebyshev ⨁ CosSpace ⨁ SinSpace representation. Done means evaluating (L - twoπx)(1) agrees with the expected zero result without breaking the shown equality checks.