Given an LKsk proof proof, compute the set of projections for it.
Given an LKsk proof proof, compute the set of projections for it.
The original proof.
A characteristic function indicating which formula occurrences in the conclusion are cut ancestors
A predicate deciding if a cut-formula should be included in the projection
A set of pairs (projection, cut_ancs) where cut_ancs indicates the cut ancestors of the projection's conclusion
finds the successor cut-ancestor sequent from two parents
finds the successor cut-ancestor sequent from two parents
must be the same as the contents of the conclusion of pm1._1 and pm2._1
child proof of binary inference with left parent pm1._1 and right parent pm2._1
connector from pm1._1 to child
connector from pm2._1 to child
a pair proof + cut_ancestor sequent
a pair proof + cut_ancestor sequent
the default to take if a formula has no parent
the cut ancestorship sequent for the parent of pm._1
given an inference from pm._1 to child, infer the child_s cut_anc sequent from pm._2
given an inference from pm._1 to child, infer the child_s cut_anc sequent from pm._2
must be the same as the contents of the conclusion of pm._1
a child proof of pm._1
connector from parent child to pm._1
a pair proof + cut_ancestor sequent
the default to take if a formula has no parent
the cut ancestorship sequent for the parent of pm._1
finds the cut ancestor sequent in the parent connected with the occurrence connector