Proof of `Extracting a leaf with all remaining exact-image caps`
groundedproofs/Lax342547Proofs/LeafExtraction.lean · lax-342547
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
Choose an admissible extension of maximal nominal rank, retaining the strict mass lower bound. If a positive-rank test violates the desired relative cap, its nonempty intersection supplies a consistent join. The rank and mass identities make that join a larger admissible extension.