Generates a sequent containing, in addition to the formulas in the bottommost sequent of s1, the chain of equations f(n) = s(f(n-1)),...,f(1)=s(f(0)), f(0) = 0.s The generates proof employs only the axiom of transitivity and (x=y -> s(x) = s(y)))
Generates a sequent containing, in addition to the formulas in the bottommost sequent of s1, the chain of equations f(n) = s(f(n-1)),...,f(1)=s(f(0)), f(0) = 0.s The generates proof employs only the axiom of transitivity and (x=y -> s(x) = s(y)))
TODO should be private - but scala shell does not allow access modifiers when :loading a file
Given a proof s1, produced by EqChainProof, generates a proof that eliminates the chains of equasions and proves the final sequent FZero, FSucc, TR, Plus |- f(n) = n.
Given a proof s1, produced by EqChainProof, generates a proof that eliminates the chains of equasions and proves the final sequent FZero, FSucc, TR, Plus |- f(n) = n.
TODO should be private - but scala shell does not allow access modifiers when :loading a file
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)}