Create an LKRuleCreationException with a message starting with "Cannot create $longName: ..."
Create an LKRuleCreationException with a message starting with "Cannot create $longName: ..."
The rest of the message.
An LKProof ending with an induction over the natural numbers:
An LKProof ending with an induction over the natural numbers:
(π1) (π2) Γ :- Δ, A[0] A[y], Π :- Λ, A[y] ------------------------------------ind Γ, Π :- Δ, Λ, ∀x. A[x]Note that there is an eigenvariable condition on x, i.e. x must not occur freely in Π :- Λ.
Each of the aux formulas can be given as an index or a formula. If it is given as a formula, the constructor will attempt to find an appropriate index on its own.
The subproof π1
The index of A[0] or the formula itself.
The subproof π2
The index of A[y] or the formula itself.
The index of A[sy] or the formula itself.
The formula ∀x. A[x].
An LKProof ending with an induction over the natural numbers:
An LKProof ending with an induction over the natural numbers:
(π1) (π2) Γ :- Δ, A[0] A[y], Π :- Λ, A[y] ------------------------------------ind Γ, Π :- Δ, Λ, ∀x. A[x]Note that there is an eigenvariable condition on x, i.e. x must not occur freely in Π :- Λ.
The subproof π1
The index of A[0].
The subproof π2
The index of A[y].
The index of A[sy].
The formula ∀x. A[x].
Combines findIndicesOrFormulasInPremise and validateIndices.
Combines findIndicesOrFormulasInPremise and validateIndices. That is, it will return a pair of lists of indices and throw an exception if either list contains a -1.
The sequent in question.
The list of indices or formulas in the antecedent.
The list of indices or formulas in the succedent.
The long name of the rule.
The long name of the rule.
Throws an exception if the output of findFormulasInPremise contains any -1 entries.
Throws an exception if the output of findFormulasInPremise contains any -1 entries.
The sequent in question.
The list of formulas in the antecedent.
The list of indices corresponding to antFormulas.
The list of formulas in the succedent.
The list indices corresponding to sucFormulas.