Interface talk:Basic arithmetic

Todos
Variants of LessEqualMultiplicationRR
 * LessEqualMultiplicationLL: a ≤ b → c · a ≤ c · b (lemul2 in peano_thms)
 * LessEqualMultiplication: a0 ≤ a1 ∧ b0 ≤ b1 → a0 · b0 ≤ a1 · b1 (listed in Hirst &amp; Hirst as "Inequalities can be multiplied")
 * Strict inequality versions, for example b ≠ 0 → (a0 < a1 → a0 · b < a1 · b) ("Strict inequality is preserved by nonzero multiplication" in Hirst &amp; Hirst)

No zero divisors: a · b = 0 → (a = 0 ∨ b = 0)

More generic total order properties:
 * ¬ (a < b) ↔ a ≥ b
 * ¬ (a ≤ b) ↔ a > b

Maybes:


 * a ≠ 0 ↔ a > 0 (easy consequence of ZeroSmallest and LessThanLessEqual)

Kingdon 14:13, 8 September 2010 (UTC)