The LKProof ending in the sequent of this case.
The constructor c of the inductive data type that we're considering.
Indices of F(x1), ..., F(xn)
The eigenvariables of this case: x1, ..., xn, y1, ..., yn (these need to correspond to the order in c)
Index of F(c(x1,...,xn,y1,...,yn))
Index of F(c(x1,...,xn,y1,...,yn))
The constructor c of the inductive data type that we're considering.
The eigenvariables of this case: x1, ..., xn, y1, ..., yn (these need to correspond to the order in c)
Indices of F(x1), ..., F(xn)
The LKProof ending in the sequent of this case.
Proof that a given data type constructor c preserves a formula F:
The variables xi and yi are eigenvariables; xi are the eigenvariables of the same type as the inductive data type, yi are the other arguments of the constructor c. They can come in any order in the constructor.
The LKProof ending in the sequent of this case.
The constructor c of the inductive data type that we're considering.
Indices of F(x1), ..., F(xn)
The eigenvariables of this case: x1, ..., xn, y1, ..., yn (these need to correspond to the order in c)
Index of F(c(x1,...,xn,y1,...,yn))