Your claim is that "no possibility exists to construct or to distinguish by one or many or infinitely many nodes of the tree another path."
A: actually infinite paths exist, B: the infinite tree contains a path p that can be distinguished from every path of P.
You agree
A ==> B
So if A is true your claim is false.
You want to show
~A [Follows from ( A ==> B, ~B) ==> ~A ]
by proving ~B
(Note that assuming ~A is circular)
WH: When you add subsets of nodes to the tree you create WH: other subsets nodes in the tree that you did not add.
WM: That is a bare lie.
WH: please answer yes or no. WH: When you add subsets of nodes to the tree you create WH: other subsets nodes in the tree that you did not add.
WM: Yes
WM: What unadded subset, than can be WM: (a part of) a path, is created when WM: what path is added?
As we have seen we can create a finite subset by adding a single path. However, as previously noted, to create a path requires creating an infinite subset. To do this we need to add a subset of paths.
E.g. The subset of paths added is
1000... 11000... 111000... ...
The subset of nodes that is now in the tree is
t={1,11,111, ...}
Note that t is not an element of P, so the subset t is never added to the tree.
