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Proof step 6 from proof dls-one (previous step)

⊦ dls(head, prev, a ', r ', next, tail) = (⌜head = r ∧ tail = r⌝ ∧ head => mkcell(prev, next, a))

User applied rule insert lemma

And obtained the following new goals

Proof step 1:
⊦ dls(head, prev, a ' + x, rx, next, tail) = _∃(λ r. ⌜rx ≠ [] ∧ head = rx.first⌝ ∧ head => mkcell(prev, r, a) * dls(r, head, x, rx.rest, next, tail))

Rule argument

spec: inst: name: dls-rec seq: ⊦ dls(head, prev, a ' + x, rx, next, tail) = _∃ (λ r. ⌜rx ≠ [] ∧ head = rx.first⌝ ∧ head => mkcell(prev, r, a) * dls(r, head, x, rx.rest, next, tail)) subst: [head, prev, a, x, rx, next, tail] → [head, prev, a, [], r ', next, tail] flags: current, []

Additional information

[Concretesimprules(()), Extraterms((headpreva[]r 'nexttail))]