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Proof step 72 from proof rem-stays-reachable-aux (previous step)

ce.nxt = H[H[x.last].nxt].nxt, path(H[x.last].nxt ' + x1 + H[x.last].nxt ', H), path(r ' + x, H), x.last ∈ H, H[x.last].nxt ∈ H ⊦ H[x.last].nxt = null, H[x.last].nxt = ce.nxt, x = [], dups(x), x.last ∈ x1, r ∈ x, ∃ x0. path(r ' + x0, H[x.last, ce]) ∧ (r ' + x0).last = H[x.last].nxt

User applied rule insert elim lemma

And obtained the following new goals

Proof step 73:
ce.nxt = H[H[r0].nxt].nxt, x = x2 + r0 ', path(r ' + x, H), path(H[r0].nxt ' + x1 + H[r0].nxt ', H), H[r0].nxt ∈ H, r0 ∈ H ⊦ H[r0].nxt = ce.nxt, H[r0].nxt = null, x = [], dups(x), r ∈ x, r0 ∈ x1, ∃ x0. path(r ' + x0, H[r0, ce]) ∧ (r ' + x0).last = H[r0].nxt

Rule argument

spec: list-last, inst: reflist name: last-elim seq: x0 ≠ [] ⊦ r = x0.last ∧ x1 = x0.butlast ↔ x0 = x1 + r ' subst: [x0, r, x1] → [x, r0, x2]

Additional information

Used simplifier rules: x0 ≠ [] ⊦ r = x0.last ∧ x1 = x0.butlast ↔ x0 = x1 + r '; (elim) Used terms: x, r0, x2