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Proof step 58 from proof refine-add (previous step)

xs_len = # xs, xs_len0 = # xs, # xs + 1 ≠ h0, r ≠ null, ((del-list(to_delete, n) * ls(rys, ys) * ls(rxs, xs)))(H), ((ls(rxs, xs) * ls(rys, ys) * del-list(to_delete, n)))(H), # xs + 1 < h0, # xs < h0, n + # xs ≤ h0, n ≤ # xs + # ys, ¬ r ∈ H1, 2 ≤ n → ((del-list(to_delete0, n - 2) * ls(rys, ys) * ls(rxs, xs)))(H1), n < 2 → to_delete0 = [] ∧ ((ls(rys, ys) * ls(rxs, xs)))(H1), ys = [] ∨ # ys = h0 ⊦ ⟨caterpillar_add#(a, h0; xs, xs_len0, ys)⟩ ∃ n. ((ls(r, xs) * ls(rys, ys) * del-list(to_delete0, n)))((H1 ++ r)[r, a × rxs]) ∧ n ≤ # xs + # ys ∧ n + # xs ≤ h0 ∧ 1 + xs_len = xs_len0

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 59:
h = h0, xs_len = xs_len0, xs_len0 = # xs, xs_len1 = # xs, ((ls(rxs, xs) * ls(rys, ys) * del-list(to_delete, n)))(H), ((del-list(to_delete, n) * ls(rys, ys) * ls(rxs, xs)))(H), # xs < h0, # xs + 1 < h0, n ≤ # xs + # ys, n + # xs ≤ h0, n < 2 → to_delete0 = [] ∧ ((ls(rys, ys) * ls(rxs, xs)))(H1), 2 ≤ n → ((del-list(to_delete0, n - 2) * ls(rys, ys) * ls(rxs, xs)))(H1), ys = [] ∨ # ys = h0 ⊦ ⟨if xs_len + 1 = h then {ys := a + xs; xs_len := 0; xs := []} else {xs := a + xs; xs_len := 1 + xs_len}⟩ ∃ n. ((ls(r, xs) * ls(rys, ys) * del-list(to_delete0, n)))((H1 ++ r)[r, a × rxs]) ∧ n ≤ # xs + # ys ∧ n + # xs ≤ h0 ∧ 1 + xs_len1 = xs_len, # xs + 1 = h0, r = null, r ∈ H1

Rule argument

pos: right 1

Additional information

Used simplifier rules: caterpillar_add#(a, h; xs, xs_len, ys) {if xs_len + 1 = h then {ys := a + xs; xs_len := 0; xs := []} else {xs := a + xs; xs_len := 1 + xs_len} };