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Proof step 79 from proof rem-stays-reachable-aux2 (previous step)

(x2.last ' + x0).last = (r ' + x).last, (r1 ' + y0).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 + r1 ' + y0, H), path(r ' + x2, H), (r ' + x).last ∈ H, x2.last ∈ H, H[x2.last].nxt ∈ H ⊦ x2.last = r, H[x2.last].nxt = null, r = r1, x2 = [], dups(x0), dups(x2 + y0), dups(x2), dups(y0), r ∈ x2, r ∈ y0, x2.last ∈ x0, x2.last ∈ x, r1 ∈ x2, r1 ∈ y0

User applied rule insert elim lemma

And obtained the following new goals

Proof step 80:
(r1 ' + y0).last = (r ' + x).last, (r2 ' + x0).last = (r ' + x).last, x2 = (x + H[r2].nxt ') + r0 ' + y, x2 = x1 + r2 ', path(r ' + x2, H), path(r ' + x2 + r1 ' + y0, H), path(r2 ' + x0, H), path(r ' + x + H[r2].nxt ', H), H[r2].nxt ∈ H, r2 ∈ H, (r ' + x).last ∈ H ⊦ H[r2].nxt = null, r = r1, r2 = r, x2 = [], dups(y0), dups(x2), dups(x2 + y0), dups(x0), r1 ∈ y0, r1 ∈ x2, r2 ∈ x, r2 ∈ x0, r ∈ y0, 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, r2, x1]

Additional information

Used simplifier rules: x0 ≠ [] ⊦ r = x0.last ∧ x1 = x0.butlast ↔ x0 = x1 + r '; (elim) Used terms: x2, r2, x1