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Proof step 73 from proof refine-add (previous step)

((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, 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 ⊦ # xs + 1 = h0, r = null, r ∈ H1, 2 ≤ n, ∃ n0. ((ls(r, a ' + xs) * ls(rys, ys) * del-list(to_delete0, n0)))((H1 ++ r)[r, a × rxs]) ∧ n0 ≤ (# xs + 1) + # ys ∧ n0 + # xs < h0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 74:
((ls(rys, ys) * ls(rxs, xs)))(H1), ((del-list(to_delete, n) * ls(rys, ys) * ls(rxs, xs)))(H), ((ls(rxs, xs) * ls(rys, ys) * del-list(to_delete, n)))(H), n < 2, # xs + 1 < h0, # xs < h0, n + # xs ≤ h0, n ≤ # xs + # ys, ys = [] ∨ # ys = h0 ⊦ # xs + 1 = h0, r = null, ((ls(rys, ys) * ls(r, a ' + xs)))((H1 ++ r)[r, a × rxs]), r ∈ H1

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ 0 ≤ m; (s)% ⊦ ⌜bv⌝ (H) ↔ bv; (s)% ⊦ ((P0 ∧ P1))(H) ↔ P0(H) ∧ P1(H); (s)%and-com: ⊦ (P0 ∧ P1) = (P1 ∧ P0); from specification heap-sep%and-ass: ⊦ ((P0 ∧ P1) ∧ P2) = (P0 ∧ P1 ∧ P2); from specification heap-sep%sep-com: ⊦ P0 * P1 = P1 * P0; from specification heap-sep%sep-ass: ⊦ (P0 * P1) * P2 = P0 * P1 * P2; from specification heap-sep% ⊦ emp * P = P; (s)% ⊦ (⌜bv⌝ ∧ P0) * P1 = (⌜bv⌝ ∧ P0 * P1); (s)% ⊦ del-list([], n) = (emp ∧ ⌜n = 0⌝ ); (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)