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Proof step 46 from proof rem-stays-reachable-aux2 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 47:
⊦ x0 ≠ [] → (x1 + x0).last = x0.last
Proof step 48:
x0.last = r, H[r].nxt = H[H[r].nxt].nxt, path(H[r].nxt ' + x0, H), r ∈ H, H[r].nxt ∈ H ⊦ H[r].nxt = null, H[r].nxt = r, r = null, x0 = [], dups(x0), H[r].nxt ∈ x0

Rule argument

spec: list-last, inst: reflist name: lapp seq: ⊦ x0 ≠ [] → (x1 + x0).last = x0.last subst: [x0, x1] → [x0, H[r].nxt '] flags: <all paths>

Additional information

Used simplifier rules: ⊦ x0 + [] = x0; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ r '.last = r; (s) Used terms: x0, H[r].nxt '