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Proof step 74 from proof rem-stays-reachable-aux2 (previous step)

(x2.last ' + x0).last = x2.last, x2.last = (r ' + x).last, x2 = (x + H[x2.last].nxt ') + r0 ' + y, path(r ' + x + H[x2.last].nxt ', H), path(x2.last ' + x0, H), path(r ' + x2, H), x2.last ∈ H, H[x2.last].nxt ∈ H ⊦ x2.last = r, H[x2.last].nxt = null, x2 = [], dups(x2), dups(x0), r ∈ x2, x2.last ∈ x0, x2.last ∈ x

User applied rule insert elim lemma

And obtained the following new goals

Proof step 75:
(r1 ' + x0).last = r1, r1 = (r ' + x).last, x2 = (x + H[r1].nxt ') + r0 ' + y, x2 = x1 + r1 ', path(r ' + x2, H), path(r1 ' + x0, H), path(r ' + x + H[r1].nxt ', H), H[r1].nxt ∈ H, r1 ∈ H ⊦ H[r1].nxt = null, r1 = r, x2 = [], dups(x0), dups(x2), r1 ∈ x, r1 ∈ x0, r ∈ x2

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] → [x2, r1, x1]

Additional information

Used simplifier rules: x0 ≠ [] ⊦ r = x0.last ∧ x1 = x0.butlast ↔ x0 = x1 + r '; (elim) Used terms: x2, r1, x1