Auxiliary structure to deal with axioms of the schema: Forall variables cond1 -> cond2 -> ...
Auxiliary structure to deal with axioms of the schema: Forall variables cond1 -> cond2 -> ... -> condn -> consequence |- ...
Proof of f(n) = g(n, 1), where f is the head recursive and g the tail recursive formulation of the factorial function
Constructs the cut-free FOL LK proof of the sequent
Constructs the cut-free FOL LK proof of the sequent
AUX, f(0) = 0, Forall x.f(s(x)) = f(x) + s(0) |- f(sn(0)) = sn(0) Where AUX is {Transitivity, Symmetry, Reflexity of =, Forall xy.x=y -> s(x) = s(y), f(0) = 0, Forall x.f(s(x)) = f(x) + s(0)}