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Quote: Originally Posted by Sneaky Can I write it like this: Claim: ∀n∈ℕ>0, ∀t∈ℕ, 0≤t<2^n → ∃ subset A s.t. A⊆B_n ˄ ∑[x∈A]x = t. Let P(n) be the predicate that ∀t, 0≤t<2^n → ∃ subset A s.t. A⊆B_n ˄ ∑[x∈A]x = t. Excellent.