English
For propositions a, b, c, the conjunction is associative: (a ∧ b) ∧ c = a ∧ (b ∧ c).
Русский
Утверждение логической связки: (a ∧ b) ∧ c = a ∧ (b ∧ c).
LaTeX
$$$(a \\land b) \\land c = a \\land (b \\land c).$$$
Lean4
theorem sbtw_cons [IsOrderedRing R] {p : P} {l : List P} :
(p :: l).Sbtw R ↔ l.Pairwise (Sbtw R p) ∧ l.Sbtw R ∧ l ≠ [p] :=
by
rw [sbtw_iff_triplewise_and_ne_pair, ← not_exists, triplewise_cons]
simp only [cons.injEq, exists_eq_left', and_assoc, and_congr_right_iff, ne_eq, and_congr_left_iff]
intro hp hne
rw [sbtw_iff_triplewise_and_ne_pair, iff_self_and, ← not_exists]
rintro hl ⟨a, rfl⟩
simp at hp