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Proof step 31 from proof refine-get (previous step)

(((lls(rxs, null, x0) * ls(rys, x1 + y)) * del-list(to_delete, n0)))(H), ((ls(rxs, x0) * ls(rys, x1 + y) * del-list(to_delete, n0)))(H), ((ls(rxs, x0) * lls(rys, r, x1) * ls(r, y) * del-list(to_delete, n0)))(H), # x0 < h0, n0 + # x0 ≤ h0, # x0 + # x1 ≤ h0, n0 ≤ # x0 + # x1 + # y, x1 + y = [] ∨ # x1 + # y = h0 ⊦ ∃ n. ((ls(rxs, x0) * ls(rys, x1 + y) * del-list(to_delete, n)))(H) ∧ n ≤ # x0 + # x1 + # y ∧ n + # x0 ≤ h0, # x0 + # x1 < h0 ∧ r ≠ null

Heuristic quantifier closing applied rule exists right

And closed the goal!

Rule argument

pos: right 1 terms: n0

Additional information

Used simplifier rules: sep-ass: ⊦ (P0 * P1) * P2 = P0 * P1 * P2; from specification heap-sep%sep-com: ⊦ P0 * P1 = P1 * P0; from specification heap-sep%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: n0