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Proof step 3 from proof refine-add (previous step)

prefixn(h, xs + ys) = prefixn(h, xs0), # xs < h, # xs + # ys ≤ # xs0, ys = [] ∨ # ys = h ⊦ ⟪tree_buffer_add#(a; xs0)⟫ ⟨xs_len := # xs; caterpillar_add#(a, h; xs, xs_len, ys)⟩ (prefixn(h, xs + ys) = prefixn(h, xs0) ∧ # xs + # ys ≤ # xs0)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 4:
prefixn(h, xs1 + ys) = prefixn(h, xs0), xs = xs0, # xs1 < h, # xs1 + # ys ≤ # xs0, ys = [] ∨ # ys = h ⊦ ⟪xs := a + xs⟫ ⟨xs_len := # xs1; caterpillar_add#(a, h; xs1, xs_len, ys)⟩ (prefixn(h, xs1 + ys) = prefixn(h, xs) ∧ # xs1 + # ys ≤ # xs)

Rule argument

pos: right 1

Additional information

Used simplifier rules: tree_buffer_add#(a; xs){xs := a + xs};