mathlib documentation

data.finset.nat_antidiagonal

The "antidiagonal" {(0,n), (1,n-1), ..., (n,0)} as a finset. #

The antidiagonal of a natural number n is the finset of pairs (i,j) such that i+j = n.

Equations
@[simp]

A pair (i,j) is contained in the antidiagonal of n if and only if i+j=n.

@[simp]

The cardinality of the antidiagonal of n is n+1.

@[simp]

The antidiagonal of 0 is the list [(0,0)]

theorem finset.nat.antidiagonal_congr {n : } {p q : × } (hp : p finset.nat.antidiagonal n) (hq : q finset.nat.antidiagonal n) :
p = q p.fst = q.fst

A point in the antidiagonal is determined by its first co-ordinate.