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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.


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


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


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.