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Proof step 39 from proof dls-last (previous step)

# x = # rx ⊦ dls(head, prev, x + a ', rx + tail0 ', next, tail) = _∃(λ r. ⌜tail0 = tail⌝ ∧ tail => mkcell(r, next, a) * dls(head, prev, x, rx, tail, r))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ P0 = P1 ↔ (∀ P, H. ((P0 * P))(H) ↔ ((P1 * P))(H))

Rule argument

spec: heap-sep inst: cell-heap name: Eq-P seq: ⊦ P0 = P1 ↔ (∀ P, H. ((P0 * P))(H) ↔ ((P1 * P))(H)) subst: [P1, P0] → [_∃ (λ r. ⌜tail0 = tail⌝ ∧ tail => mkcell(r, next, a) * dls(head, prev, x, rx, tail, r)), dls(head, prev, x + a ', rx + tail0 ', next, tail)] flags: rewrite

Additional information

[Concretesimprules(()), Extraterms((_∃ (λ r. ⌜tail0 = tail⌝ ∧ tail => mkcell(r, next, a) * dls(head, prev, x, rx, tail, r)) dls(head, prev, x + a ', rx + tail0 ', next, tail)))]