User blog:Alemagno12/Middle Term Theta

This is an OCF I made that has four entries. It has the property Θ(ωx,0,0,0) = ψ(ΩΩ x ).

Define:
 * cof(0) = 0
 * cof(ω) = ω
 * cof(Ω) = Ω
 * cof(S(x)) = 0
 * cof(x+y) = cof(y)
 * maxcof(S) = max{x|x=cof(y)∧y∈S}
 * maxcof({a,b,c,d}) = 0: cof(Θ(a,b,c,d)) = ω
 * maxcof({a,b,c,d}) > 0, maxcof({c,d}) < Ω: cof(Θ(a,b,c,d)) = ω
 * maxcof({a,b,c,d}) > 0, maxcof({c,d}) = Ω: cof(Θ(a,b,c,d)) = Ω
 * ω[n] = n
 * Ω[n] = n
 * x+0 = x
 * x+S(y) = S(x+y)
 * cof(y) > 0: (x+y)[n] = x+(y[n])
 * Θ(0,0,0,0) = ω
 * Θ(0,0,0,x+1)[0] = 0
 * Θ(0,0,0,x+1)[n+1] = Θ(0,0,0,x+1)[n]+Θ(0,0,0,x)
 * [WIP]