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Proof step 13 from proof reachable-addnew-rev (previous step)

r ∈ H, path(r ' + x, H[x.last, ce]) ⊦ x = [], r ∈ x, dups(x), x.last ∈ H, ∃ r0. reachable(r, r0, H) ∧ H[r0].nxt = x.last ∧ H[r0].nxt ≠ null

User applied rule insert elim lemma

And obtained the following new goals

Proof step 14:
x = x1 + r1 ', r ∈ H, path(r ' + x, H[r1, ce]) ⊦ x = [], r ∈ x, dups(x), r1 ∈ H, ∃ r0. reachable(r, r0, H) ∧ H[r0].nxt = r1 ∧ H[r0].nxt ≠ null

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] → [x, r1, x0] flags: []

Additional information

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