6 | fifteen = 15 | step s1 s2 = toNat s1 + toNat s2def Threeven (i : Nat) := ∃ k, i = 3 * ktheorem three_divides_six : Threeven 6 := by exists 2theorem three_divides_fifteen : Threeven 15 := by exists 5theorem three_divides_threeven_plus_threeven (a : Nat) (b : Nat) (ha : Threeven a) (hb : Threeven b) : Threeven (a + b) := by obtain ⟨a', ha⟩ := ha obtain ⟨b', hb⟩ := hb exists a' + b' rw [ha, hb, Nat.mul_add]theorem S.is_threeven (s : S) : Threeven s.toNat := by induction s with | six = apply three_divides_six | fifteen = apply three_divides_fifteen | step a b ha hb = rw [S.toNat] apply three_divides_threeven_plus_threeven · exact ha · exact hb"
cond, Int, Int,
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