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Proof step 22 from proof process-one (previous step)

((r => a0 × r0 * ls(r0, y) * del-list(rx0, n0) * P))(H) ⊦ r = null, r0 = null, ((_∃(λ x. ls(r0, x) * del-list(rx0, n0 + # y - # x) ∧ ⌜r0 ≠ null ∧ n0 + # y ≥ # x⌝ ) * P))(H -- r)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
((r => a0 × r0 * ls(r0, y) * del-list(rx0, n0) * P))(H) ⊦ r = null, r0 = null, ∃ x. # x ≤ n0 + # y ∧ (((ls(r0, x) * del-list(rx0, n0 + # y - # x)) * P))(H -- r)

Rule argument

Additional information

Used simplifier rules: ⊦ ⌜bv⌝ (H) ↔ bv; (s)% ⊦ ((P0 ∧ P1))(H) ↔ P0(H) ∧ P1(H); (s)%sep-com: ⊦ P0 * P1 = P1 * P0; from specification heap-sep%sep-ass: ⊦ (P0 * P1) * P2 = P0 * P1 * P2; from specification heap-sep%and-com: ⊦ (P0 ∧ P1) = (P1 ∧ P0); from specification heap-sep%and-ass: ⊦ ((P0 ∧ P1) ∧ P2) = (P0 ∧ P1 ∧ P2); from specification heap-sep% ⊦ (⌜bv⌝ ∧ P0) * P1 = (⌜bv⌝ ∧ P0 * P1); (s)% ⊦ ((_∃ xP * P))(H) ↔ (∃ x. ((xP(x) * P))(H)); (s)% ⊦ n ≥ m ↔ m ≤ n; (s)