Proof of `Coproduct and shuffle identities` (6th statement)
groundedproofs/Lax825748Proofs/TriangularPairing.lean · lax-825748
What this proof establishes
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
Expand each multi-index into its list of repeated labels. Below the diagonal use vanishing; on the diagonal the surviving permutations preserve labels, so their number is the product of the factorials of the multiplicities.