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Proof step 61 from proof reachable-addnew-rev (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 62:
x1 = x + r0 ', path(r ' + x1 + H[r0].nxt ' + x0, H[H[r0].nxt, ce]), r ∈ H, (H[r0].nxt ' + x0).last ∈ H, path(r ' + x1, H) ⊦ H[r0].nxt = null, r0 = H[r0].nxt, x1 = [], reachable(ce.nxt, (H[r0].nxt ' + x0).last, H), H[r0].nxt ∈ H, r ∈ x1, r ∈ x0, H[r0].nxt ∈ x1, H[r0].nxt ∈ x0, dups(x1 + x0), reachable(r, (H[r0].nxt ' + x0).last, H), dups(x1), dups(x0)

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] → [x1, r0, x] flags: []

Additional information

Used simplifier rules: x0 ≠ [] ⊦ r = x0.last ∧ x1 = x0.butlast ↔ x0 = x1 + r '; (elim) Used terms: x1, r0, x