Proof of `Tree decompositions from recursive balanced separators` (1st statement)
groundedproofs/Lax263307Proofs/SeparatorDecompositions.lean · lax-263307
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
Join the child trees at a new separator root. Vertices of the separator occur throughout the tree; each other vertex has exactly its original connected set of child bags. Closure of the partition covers every edge.