Theorems · Theorem · combinatorics

Finset.piAntidiag_insert

∀ {ι : Type u_1} {μ : Type u_2} [inst : DecidableEq ι] [inst_1 : AddCancelCommMonoid μ]
  [inst_2 : Finset.HasAntidiagonal μ] [inst_3 : DecidableEq μ] {i : ι} {s : Finset ι} [inst_4 : DecidableEq (ι → μ)],
  i ∉ s →
    ∀ (n : μ),
      (insert i s).piAntidiag n =
        (Finset.HasAntidiagonal.antidiagonal n).biUnion fun p =>
          Finset.image (fun f j => f j + if j = i then p.1 else 0) (s.piAntidiag p.2)

Defined in

Mathlib.Algebra.Order.Antidiag.Pi

Cited by

0 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqAddCancelCommMonoidFinset.HasAntidiagonalDecidableEqDecidableEq