A sequence of proofs showing that each type constructor preserves the validity of the main formula.
The formula we want to prove via induction.
A list of lists containing the auxiliary formulas of the rule.
A list of lists containing the auxiliary formulas of the rule. The first list constains the auxiliary formulas in the first premise and so on.
A list of lists of SequentIndices denoting the auxiliary formula(s) of the rule.
A list of lists of SequentIndices denoting the auxiliary formula(s) of the rule. The first list contains the auxiliary formulas in the first premise and so on.
A sequence of proofs showing that each type constructor preserves the validity of the main formula.
The conclusion of the rule.
The conclusion of the rule.
Operations that view the sub-proofs as a DAG, which ignore duplicate sub-proofs, see DagProof.DagLikeOps for a list.
Operations that view the sub-proofs as a DAG, which ignore duplicate sub-proofs, see DagProof.DagLikeOps for a list.
Depth of the proof, which is the maximum length of a path you can take via immediateSubProofs.
Depth of the proof, which is the maximum length of a path you can take via immediateSubProofs.
The end-sequent of the rule.
The end-sequent of the rule.
The immediate subproofs of this rule.
The immediate subproofs of this rule.
The name of this rule (in words).
The name of this rule (in words).
The formula we want to prove via induction.
The list of main formulas of the rule.
The list of main formulas of the rule.
A list of SequentIndices denoting the main formula(s) of the rule.
A list of SequentIndices denoting the main formula(s) of the rule.
The name of this rule (in symbols).
The name of this rule (in symbols).
A list of occurrence connectors, one for each immediate subproof.
A list of occurrence connectors, one for each immediate subproof.
The upper sequents of the rule.
The upper sequents of the rule.
Set of all (transitive) sub-proofs including this.
Set of all (transitive) sub-proofs including this.
Operations that view the sub-proofs as a tree, see DagProof.TreeLikeOps for a list.
Operations that view the sub-proofs as a tree, see DagProof.TreeLikeOps for a list.
Checks whether indices are in the right place and premise is defined at all of them.
Checks whether indices are in the right place and premise is defined at all of them.
The sequent to be checked.
Indices that should be in the antecedent.
Indices that should be in the succedent.
An LKProof ending with an induction rule:
This induction rule can handle inductive data types. The cases are proofs that the various type constructors preserve the formula we want to prove. They are provided via the InductionCase class.
A sequence of proofs showing that each type constructor preserves the validity of the main formula.
The formula we want to prove via induction.