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Proof step 63 from proof rem-stays-reachable-aux2 (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 64:
r0 = H[r0].nxt, x0 = x1 + r1 ', path(r ' + x + r1 ', H), path(r0 ' + x0, H), path(r ' + (x2 + r1 ') + r0 ', H), r0 ∈ H, r1 ∈ H ⊦ r = r1, r0 = r1, r0 = r, r0 = null, x0 = [], dups(x), dups(x2), dups(x0), r1 ∈ x, r1 ∈ x2, r0 ∈ x2, r0 ∈ x0, r ∈ x, 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] → [x0, r1, x1]

Additional information

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