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Proof step 68 from proof reachable-addnew-rev (previous step)

path(ce.nxt ' + x1, H[H[r0].nxt, ce]), path(r ' + x + r0 ' + H[r0].nxt ' + ce.nxt ' + x1, H[H[r0].nxt, ce]), path(r ' + x + r0 ', H), r0 ∈ H, (ce.nxt ' + x1).last ∈ H, r ∈ H ⊦ H[r0].nxt = ce.nxt, H[r0].nxt = null, r = ce.nxt, r = r0, r0 = ce.nxt, r0 = null, r0 = H[r0].nxt, dups(x1), dups(x), dups(x + x1), reachable(ce.nxt, (ce.nxt ' + x1).last, H), reachable(r, (ce.nxt ' + x1).last, H), ce.nxt ∈ x1, ce.nxt ∈ x, r0 ∈ x1, r0 ∈ x, H[r0].nxt ∈ x1, H[r0].nxt ∈ x, r ∈ x1, r ∈ x, H[r0].nxt ∈ H

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: path-new-irrelevant-strong seq: ⊦ ¬ r2 ∈ H ∧ ¬ r2 ∈ x ∧ r ∈ H → (path(r ' + x, H[r2, ce]) ↔ path(r ' + x, H)) subst: [ce, r2, H, x, r] → [ce, H[r0].nxt, H, x1, ce.nxt] flags: <all paths>

Additional information

Used terms: ce, H[r0].nxt, H, x1, ce.nxt