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Proof step 49 from proof rem-stays-reachable-aux2 (previous step)

H[x0.last].nxt = H[H[x0.last].nxt].nxt, path(H[x0.last].nxt ' + x0, H), H[x0.last].nxt ∈ H, x0.last ∈ H ⊦ x0.last = null, H[x0.last].nxt = x0.last, H[x0.last].nxt = null, x0 = [], dups(x0), H[x0.last].nxt ∈ x0

User applied rule insert elim lemma

And obtained the following new goals

Proof step 50:
H[r].nxt = H[H[r].nxt].nxt, x0 = x + r ', path(H[r].nxt ' + x0, H), r ∈ H, H[r].nxt ∈ H ⊦ H[r].nxt = null, H[r].nxt = r, r = null, x0 = [], dups(x0), H[r].nxt ∈ x0

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] → [x0, r, x]

Additional information

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