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Proof step 68 from proof refine-add (previous step)

((ls(rxs, xs) * ls(rys, ys) * del-list(to_delete, n1 + 2)))(H), ((del-list(to_delete, n1 + 2) * ls(rys, ys) * ls(rxs, xs)))(H), ((del-list(to_delete0, n1) * ls(rys, ys) * ls(rxs, xs)))(H1), # xs < h0, # xs + 1 < h0, n1 + 2 ≤ # xs + # ys, (n1 + 2) + # xs ≤ h0, 2 ≤ # xs + # ys, ys = [] ∨ # ys = h0 ⊦ # xs + # ys = 0, # xs + 1 = h0, r = null, r ∈ H1, ((ls(r, a ' + xs) * ls(rys, ys) * del-list(to_delete0, n1)))((H1 ++ r)[r, a × rxs]) ∧ n1 ≤ (# xs + 1) + # ys ∧ n1 + # xs < h0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 69:
((ls(rxs, xs) * ls(rys, ys) * del-list(to_delete, n1 + 2)))(H), ((del-list(to_delete, n1 + 2) * ls(rys, ys) * ls(rxs, xs)))(H), ((del-list(to_delete0, n1) * ls(rys, ys) * ls(rxs, xs)))(H1), # xs < h0, # xs + 1 < h0, n1 + # xs < h0, n1 + 2 ≤ # xs + # ys, (n1 + 2) + # xs ≤ h0, 2 ≤ # xs + # ys, n1 ≤ (# xs + 1) + # ys, ys = [] ∨ # ys = h0 ⊦ # xs + # ys = 0, # xs + 1 = h0, r = null, ((ls(r, a ' + xs) * ls(rys, ys) * del-list(to_delete0, n1)))((H1 ++ r)[r, a × rxs]), r ∈ H1

Rule argument

Additional information

Used simplifier rules: ⊦ m + m0 ≤ m ↔ m0 = 0; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m < m + n ↔ n ≠ 0; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ n + m ≤ m0 → ¬ n0 + m0 < m; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)