simp only [ge_iff_le, not_le, gt_iff_lt, Set.Icc_prod_Icc, Prod.mk_le_mk, not_and, Prod.mk_lt_mk, Set.mem_iInter, Set.mem_Icc, and_imp]
x : ℝ × ℝ
⊢ x ∈ ⋂ α, ⋂ (_ : 0 ≤ α ∧ α ≤ 1), Set.Icc α 1 ×ˢ Set.Icc 0 α ↔ x ∈ Set.singleton (1, 0)
x : ℝ × ℝ
⊢ (∀ (i : ℝ), 0 ≤ i → i ≤ 1 → (i, 0) ≤ x ∧ x ≤ (1, i)) ↔ x ∈ Set.singleton (1, 0)