Convenience constructor that finds appropriate formula occurrences on its own.
Constructs a proof ending with an induction rule.
Constructs a proof ending with an induction rule.
The left subproof. The succedent of its end sequent has to contain A[0].
The right subproof. Its end sequent must contain A[x] in the antecedent and A[S(x)] in the succedent.
The occurrence of A[0] in the succedent of s1.
The occurrence of A[x] in the antecedent of s2.
The occurrence of A[s(x)] in the succedent of s2.
TODO: Find a good description for this
A proof ending with an induction rule. Its main formula will be A[term].
Binary induction rule:
Γ |- Δ, A[0] A[x], Π |- Λ, A[s(x)] -----------------------------------------(ind) Γ, Π |- Δ, Λ, A[t]