Diagonal suprema #
A supremum over two indices of a family monotone in both is the supremum along the diagonal.
[UPSTREAM] candidate for Mathlib/Order/CompleteLattice/Basic.lean, beside
iSup_iSup_eq_left.
theorem
iSup_iSup_eq_iSup_diag
{L : Type u_1}
[CompleteLattice L]
{g : ℕ → ℕ → L}
(hg : ∀ (m n m' n' : ℕ), m ≤ m' → n ≤ n' → g m n ≤ g m' n')
:
⨆ (m : ℕ), ⨆ (n : ℕ), g m n = ⨆ (n : ℕ), g n n
For a family monotone in both indices, the double supremum is the diagonal supremum.