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Proof step 37 from proof rem-stays-reachable-aux1 (previous step)

(H[H[r0].nxt].nxt ' + x).last = r0, path(H[H[r0].nxt].nxt ' + x, H), path(H[H[r0].nxt].nxt ' + x0 + H[r0].nxt ', H), H[r0].nxt ∈ H, r0 ∈ H ⊦ H[r0].nxt = null, H[r0].nxt = H[H[r0].nxt].nxt, r0 = H[H[r0].nxt].nxt, dups(x), r0 ∈ x0, H[H[r0].nxt].nxt ∈ x

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 38:
⊦ x0 ≠ [] → (x1 + x0).last = x0.last
Proof step 39:
x.last = r0, path(H[H[r0].nxt].nxt ' + x0 + H[r0].nxt ', H), path(H[H[r0].nxt].nxt ' + x, H), r0 ∈ H, H[r0].nxt ∈ H ⊦ H[r0].nxt = H[H[r0].nxt].nxt, H[r0].nxt = null, r0 = H[H[r0].nxt].nxt, x = [], dups(x), H[H[r0].nxt].nxt ∈ x, r0 ∈ x0

Rule argument

spec: list-last, inst: reflist name: lapp seq: ⊦ x0 ≠ [] → (x1 + x0).last = x0.last subst: [x0, x1] → [x, H[H[r0].nxt].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: x, H[H[r0].nxt].nxt '