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Proof step 178 from proof rem-stays-reachable-aux2 (previous step)

H[x0.last].nxt = H[r1].nxt, path(r1 ' + x0, H), path(H[H[r1].nxt].nxt ' + x3 + r1 ', H), H[r1].nxt ∈ H, x0.last ∈ H, r1 ∈ H ⊦ x0.last = null, x0.last = H[H[r1].nxt].nxt, H[r1].nxt = null, H[r1].nxt = H[H[r1].nxt].nxt, H[r1].nxt = r1, r1 = H[H[r1].nxt].nxt, r1 = x0.last, x0 = [], dups(x0), dups(x3), H[H[r1].nxt].nxt ∈ x3, x0.last ∈ x3, r1 ∈ x0, H[r1].nxt ∈ x3, r1 ∈ x3

User applied rule insert elim lemma

And obtained the following new goals

Proof step 179:
H[r].nxt = H[r1].nxt, x0 = x + r ', path(H[H[r1].nxt].nxt ' + x3 + r1 ', H), path(r1 ' + x0, H), r1 ∈ H, r ∈ H, H[r1].nxt ∈ H ⊦ H[r1].nxt = r1, H[r1].nxt = H[H[r1].nxt].nxt, H[r1].nxt = null, r = H[H[r1].nxt].nxt, r = null, r1 = r, r1 = H[H[r1].nxt].nxt, x0 = [], dups(x3), dups(x0), r1 ∈ x3, H[r1].nxt ∈ x3, r1 ∈ x0, r ∈ x3, H[H[r1].nxt].nxt ∈ x3

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, r, x]

Additional information

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