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Proof step 2 from proof initialization (previous step)

n0 = n, n > 0 ⊦ ⟪tree_buffer_heap_init#(n0; ; H, rxs, rys, h, xs_len, to_delete)⟫ ⟨caterpillar_init#(n; ; h0, xs, xs_len0, ys)⟩ ∃ n. ((ls(rxs, xs) * ls(rys, ys) * del-list(to_delete, n)))(H) ∧ n ≤ # xs + # ys ∧ n + # xs ≤ h ∧ h = h0 ∧ xs_len = xs_len0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
n ≠ 0 ⊦ ⟪tree_buffer_heap_init#(n; ; H, rxs, rys, h, xs_len, to_delete)⟫ ⟨caterpillar_init#(n; ; h0, xs, xs_len0, ys)⟩ ∃ n0. ((ls(rxs, xs) * ls(rys, ys) * del-list(to_delete, n0)))(H) ∧ n0 ≤ # xs + # ys ∧ n0 + # xs ≤ h0 ∧ h = h0 ∧ xs_len = xs_len0

Rule argument

Additional information

Used simplifier rules: ⊦ 0 < m ↔ m ≠ 0; (s)% ⊦ m > n ↔ n < m; (s)