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Proof step 14 from proof refine-get (previous step)

H[r] = a × r1, ((lls(rxs, r, x) * ls(r, x1) * ls(rys, ys) * del-list(to_delete, n0)))(H), ((ls(rxs, x + x1) * ls(rys, ys) * del-list(to_delete, n0)))(H), # x + # x1 < h0, # x < h0, n0 ≤ (# x + # x1) + # ys, n0 + # x + # x1 ≤ h0, ys = [] ∨ # ys = h0 ⊦ r = null, ∃ x0. x1 = a ' + x0 ∧ (∃ r0. (((lls(rxs, r0, x) * r0 => a × r1) * ls(r1, x0) * ls(rys, ys) * del-list(to_delete, n0)))(H)) ∧ n0 ≤ (# x + # x0 + 1) + # ys ∧ n0 + # x + # x0 < h0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
((r => a × r1 * ls(r1, y) * lls(rxs, r, x) * ls(rys, ys) * del-list(to_delete, n0)))(H), ((ls(rxs, x + a ' + y) * ls(rys, ys) * del-list(to_delete, n0)))(H), # x + # y + 1 < h0, # x < h0, n0 + # x + # y < h0, n0 ≤ # x + (# y + 1) + # ys, ys = [] ∨ # ys = h0 ⊦ r = null, ∃ r0. (((lls(rxs, r0, x) * r0 => a × r1) * ls(r1, y) * ls(rys, ys) * del-list(to_delete, n0)))(H)

Rule argument

Additional information

Used simplifier rules: ⊦ a ' + x = a ' + y ↔ x = y; (s)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + 1 ≤ n ↔ m < n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m +1 = m + 1; (s)% ⊦ #(a ' + x) = (# x)+1; (s)% ⊦ a ∈ b ' + x ↔ a = b ∨ a ∈ x; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list%in-14: ⊦ a ' + x = y → a ∈ y; (forward) from specification list% ⊦ a × r = a0 × r0 ↔ a = a0 ∧ r = r0; (ws)% ⊦ ((r => ce * P))(H) → (H[r] = ce0 ↔ ce = ce0); (s)%sep-com: ⊦ P0 * P1 = P1 * P0; from specification heap-sep%sep-ass: ⊦ (P0 * P1) * P2 = P0 * P1 * P2; from specification heap-sep%r ≠ null ⊦ H[r] = ce → ( ((ls(r, x) * P))(H) ↔ (∃ a, y, r0. ((r => a × r0 * ls(r0, y) * P))(H) ∧ x = a ' + y)); (as)