at.logic.gapt.proofs.expansion
Decodes a term into its corresponding instance.
Decodes a term into its corresponding instance.
The resulting instance can contain alpha in the inductive case.
Encodes an expansion proof (of an instance proof).
Encodes an expansion proof (of an instance proof).
The shallow formulas of the expansion sequents should be subsumed by formulas in the end-sequent.
Encodes an expansion sequent (of an instance proof).
Encodes an expansion sequent (of an instance proof).
The shallow formulas of the expansion sequents should be subsumed by formulas in the end-sequent.
Encodes a sequent consisting of instances of an instance sequent.
Maps a function symbol to its corresponding formula in the end-sequent.
Maps a function symbol to the index of its corresponding formula in the end-sequent.
The propositional matrices phi of the end-sequent.
Assigns each formula in the end-sequent a fresh function symbol name used to encode its instances.
Assigns each formula in the end-sequent a fresh function symbol name used to encode its instances.
The quantified variables of each formula in the end-sequent.
The propositional matrices of the end-sequent, where the formulas in the antecedent are negated.
The function symbols used to encode the instances of each formula in the end-sequent.
Encodes instances of an end-sequent as terms.
Only instances of weak quantifiers are recorded, instances of strong quantifiers or free variables are ignored.
The end-sequent will be internally transformed into one which is in variable normal form.
In the case of cut-introduction, the end-sequent has no free variables and no strong quantifiers and we're encoding a Herbrand sequent as a set of terms. A term r_i(t_1,...,t_n) encodes an instance of the formula "forall x_1 ... x_n, phi(x_1,...,x_n)" using the instances (t_1,...,t_n).
In the case of inductive proofs, the end-sequent contains strong quantifiers variable (alpha). Here, we consider proofs of instance sequents, which are obtained by e.g. substituting a numeral for alpha. Hence the formulas occurring in the end-sequents of instance proofs are substitution instances of endSequent; the encoded terms still only capture the instances used in the instance proofs--i.e. not alpha.