\\Q(n) ≡ ∀k,m∈ℕ ( k+m = n ⇒ ( m > 1 ∧ ¬∃d∈ℕ ( d > 1 ∧ d | k ∧ d | m ) ⇒ ∃x,y∈ℕ ( k·x = m·y+1 ) ) ) Given a ∈ ℕ If ∀i∈ℕ ( i<a ⇒ P(i) ) Given b ∈ ℕ Given c ∈ ℕ If b + c = a If c > 1 ∧ ¬∃d∈ℕ ( d > 1 ∧ d | b ∧ d | c ) If b = c c > 1 ∧ c | c ∧ c | c c > 1 ∧ c | b ∧ c | c ∃d∈ℕ ( d > 1 ∧ d | b ∧ d | c ) ¬∃d∈ℕ ( d > 1 ∧ d | b ∧ d | c ) ⊥ ∃x,y∈ℕ (b·x = c·y+1 ) ) ) If b < c If b = 0 c > 1 ∧ c | 0 ∧ c | c [c|o lemma] c > 1 ∧ c | b ∧ c | c