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- h, k, l ∈ K 1 . h ⊃ k : ⊃ hl ⊃ kl . h′l ⊃ k′l . hl′ ⊃ kl′.
- h, k, l ∈ K 1 : ⊃ : (h ∪ k)l = hl ∪ kl . (h ∪ k)′l = h′l ∪ k′l . (h ∪ k)l′ = hl′ ∪ kl′.
- h, k ∈ K 1 . h = ∧ : ⊃ . hk = h′k = hk′ = ∧.
Sulla definizione 9.
- k ∈ K 1 . ⊃ ∷ x ∈ k″ . = ∴ y, z ∈ k . x ∈ y′z : − =y, z ∧.
- h, k ∈ K 1 . h ⊃ k : ⊃ . h″ ⊃ k″.
- a ∈ 1 . k ∈ K 1 . b ∈ k : ⊃ . (ab)″ ⊃ (ak)″.
Sulle definizioni 10 e 12.
- x ∈ 2 . = ∴ a, b ∈ 1. a − = b . x ∈ (ab)″ : − =a, b ∧.
- a, b ∈ 1 . a − = b : ⊃ . (ab)″ ∈ 2.
- x ∈ 3 . = ∴ a, b, c ∈ 1 − Cl. x ∈ (abc)″ : − =a, b, c ∧.
- a, b, c ∈ 1 − Cl. ⊃ . (abc)″ ∈ 3.
Sulla definizione 14.
- h ∈ Cnv. = ∴ h K 1 : a, b ∈ h . ⊃a, b . ab ⊃ h.
- h, k ∈ Cnv. ⊃ . h ∩ k ∈ Cnv.
{Hp. ⊃ ∴ h, k ∈ K 1 : a, b ∈ h . ⊃a, b . ab ⊃ h : a, b ∈ k . ⊃a, b . ab ⊃ k ∴ ⊃ ∴ h ∩ k ∈ K 1 : a, b ∈ h ∩ k . ⊃a, b . ab ⊃ hk ∴ ⊃ . Ts}.
- k ∈ Cnv. l ∈ K 1 . l ⊃ k . a ∈ k : ⊃ . al ⊃ k.
- k ∈ Cnv. a, b, c ∈ k : ⊃ . abc ⊃ k.
- k ∈ Cnv. a, b, c, d ∈ k : ⊃ . abcd ⊃ k.
- k ∈ Cnv. a, b ∈ k : ⊃ . (ab)″ ⊃ k″.
§ 4. Assiomi I, II, III, IV.
Assioma I.
- 1 − = ∧.
Assioma II.
- a ∈ 1 . ⊃ ∴ x ∈ 1 . x − = a : − =x ∧.
Assioma III.
- a ∈ 1 . ⊃ . aa = ∧.
