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Proof step 127 from proof rem-stays-reachable-aux2 (previous step)

x0.last = (r ' + x1).last, H[H[r0].nxt].nxt = r0, path(r ' + x1 + H[r0].nxt ', H), path(r0 ' + x0, H), path(r ' + x1, H), r0 ∈ H, x0.last ∈ H, H[r0].nxt ∈ H ⊦ H[r0].nxt = null, H[r0].nxt = r0, r = H[r0].nxt, r0 = null, r0 = r, x0 = [], dups(x1), dups(x0), H[r0].nxt ∈ x1, r0 ∈ x1, r ∈ x1, r0 ∈ x0

User applied rule insert elim lemma

And obtained the following new goals

Proof step 128:
H[H[r0].nxt].nxt = r0, r1 = (r ' + x1).last, x0 = x + r1 ', path(r ' + x1, H), path(r0 ' + x0, H), path(r ' + x1 + H[r0].nxt ', H), H[r0].nxt ∈ H, r1 ∈ H, r0 ∈ H ⊦ H[r0].nxt = r0, H[r0].nxt = null, r = H[r0].nxt, r0 = r, r0 = null, x0 = [], dups(x0), dups(x1), r0 ∈ x0, r ∈ x1, r0 ∈ x1, H[r0].nxt ∈ x1

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, r1, x]

Additional information

Used simplifier rules: x0 ≠ [] ⊦ r = x0.last ∧ x1 = x0.butlast ↔ x0 = x1 + r '; (elim) Used terms: x0, r1, x