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Proof step 45 from proof dls-split (previous step)

# x1 = # rx1, # x0 = # rx0 ⊦ x0 = [], x1 = [], dls(head, prev, x0 + a ' + x1, rx0 + r ' + rx1, next, tail) = _∃(λ r0, r1. dls(head, prev, x0, rx0, r, r0) * r => mkcell(r0, r1, a) * dls(r1, r, x1, rx1, next, tail))

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 r0, r1. dls(head, prev, x0, rx0, r, r0) * r => mkcell(r0, r1, a) * dls(r1, r, x1, rx1, next, tail)), dls(head, prev, x0 + a ' + x1, rx0 + r ' + rx1, next, tail)] flags: rewrite

Additional information

[Concretesimprules(()), Extraterms((_∃ (λ r0, r1. dls(head, prev, x0, rx0, r, r0) * r => mkcell(r0, r1, a) * dls(r1, r, x1, rx1, next, tail)) dls (head, prev, x0 + a ' + x1, rx0 + r ' + rx1, next, tail)))]