User blog comment:B1mb0w/Recursion and Summation Functions/@comment-35470197-20190405011534

In Rule r5, the short-hand \(C\) in the second explanation looks ambiguous. First, \(C\) is defined as the short-hand of the \(M^c(\ldots)\) when you are referring to\(M^{c+1}(\ldots)\). Onthe other hand, if you are referring to expressions in which \(c\) appears in another form than \(c+1\), e.g. the first occurrence of \(c\) in \(t_0(c,s)(t_0(c+1,0))\) in Rule r5, how do you intend to solve the short-handing? If you ignore such appearence of \(c\), then \(C\) in the equality \(t_0(c,s)(t_0(c+1,0)) = C\) in Rule r5 should be the short-hand of \(t_0(c,s)(t_0(c,0))\). It does not coincides with \(t_0(c,0)\).