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Proof step 135 from proof rem-stays-reachable-aux2 (previous step)

H[H[r0].nxt].nxt = r0, path(r ' + x1 + H[r0].nxt ', H), H[r0].nxt ∈ H, r0 ∈ H, path(r0 ' + x + x1.last ', H), x1.last ∈ H, path(r ' + x1, H) ⊦ H[r0].nxt = null, r0 = r, r = H[r0].nxt, H[r0].nxt = r0, r0 = null, r0 = x1.last, x1 = [], r ∈ x1, H[r0].nxt ∈ x1, r0 ∈ x1, dups(x1), r0 ∈ x, x1.last ∈ x, dups(x)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 136:
x1 = x2 + r1 ', H[H[r0].nxt].nxt = r0, path(r ' + x1 + H[r0].nxt ', H), H[r0].nxt ∈ H, r0 ∈ H, path(r0 ' + x + r1 ', H), r1 ∈ H, path(r ' + x1, H) ⊦ H[r0].nxt = null, r0 = r, r = H[r0].nxt, H[r0].nxt = r0, r0 = null, r0 = r1, x1 = [], r ∈ x1, H[r0].nxt ∈ x1, r0 ∈ x1, dups(x1), r0 ∈ x, r1 ∈ x, dups(x)

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, r1, x0] flags: []

Additional information

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