Proof of `Saturating and Perfect Matchings, Decided in the Same Time` (4th statement)
groundedproofs/Lax117284Proofs/Bipartite/MachineTotal.lean · lax-117284
What this proof establishes
no assumptions
Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.
Description
The total program reads the word into an array, validates the syntactic conditions of in linear time, checks that every listed edge crosses the split while counting the degrees of the symmetrized word, builds that word by a counting sort (each left row the union of its own row and the transposed right rows), runs Kuhn's algorithm on it and compares the size of the matching with the number of left vertices; on any failed check it answers . The program is compiled for the length-prefixed word, runs at every word length from on, and within instructions.