bb9e3ddae2
@Armael: this change may affect your project. The file `doc/changes.md` explains the motivation for the change.
25 lines
976 B
Text
25 lines
976 B
Text
def pairs_with_sum' : Π (m n) {d}, m + n = d → list {p : ℕ × ℕ // p.1 + p.2 = d}
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| 0 n d h := [⟨(0, n), h⟩]
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| (m+1) n d h := ⟨(m+1, n), h⟩ :: pairs_with_sum' m (n+1) (by simp at h; simp [h])
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def pairs_with_sum (n) : list {p : ℕ × ℕ // p.1 + p.2 = n} :=
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pairs_with_sum' n 0 rfl
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inductive bin_tree
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| leaf : bin_tree
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| branch : bin_tree → bin_tree → bin_tree
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open bin_tree
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def size : bin_tree → ℕ
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| leaf := 0
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| (branch l r) := size l + size r + 1
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def trees_of_size : Π s, list {bt : bin_tree // size bt = s}
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| 0 := [⟨leaf, rfl⟩]
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| (n+1) :=
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do ⟨(s1, s2), (h : s1 + s2 = n)⟩ ← pairs_with_sum n,
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⟨t1, sz1⟩ ← have s1 < n+1, by apply nat.lt_succ_of_le; rw ←h; apply nat.le_add_right,
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trees_of_size s1,
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⟨t2, sz2⟩ ← have s2 < n+1, by apply nat.lt_succ_of_le; rw ←h; apply nat.le_add_left,
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trees_of_size s2,
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return ⟨branch t1 t2, by rw [←h, ←sz1, ←sz2]; refl⟩
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