sbtw_cons — Mathlib

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

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