Lax Lean Archive

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Proof of `Exact rational search for a conditioning set` (1st statement)

groundedproofs/Lax263307Proofs/RationalConditioning.lean · lax-263307

What this proof establishes

no assumptions

thm✓Lax263307.RationalConditioning (1st statement)

Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.

Read the Lean proof on GitHub

Description

The enumeration contains at most (r+1)(n+1)r(r+1)(n+1)^r candidates.

Proof strategy

The exact count is the sum of binomial coefficients for sizes zero through rr. Bound each coefficient by a power of the order, then by (n+1)r(n+1)^r.

Attribution

The dimension and enumeration bounds in Bonnet–Chang, equations (14) and (25).