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Proof step 121 from proof rem-stays-reachable-aux2 (previous step)

(r0 ' + x0).last = (r ' + x1).last, H[H[r0].nxt].nxt = r0, path(r ' + x1 + H[r0].nxt ', H), path(r0 ' + x0, H), path(r ' + x1, H), r0 ∈ H, (r ' + x1).last ∈ H, H[r0].nxt ∈ H ⊦ H[r0].nxt = null, H[r0].nxt = r0, r = H[r0].nxt, r0 = null, r0 = r, dups(x1), dups(x0), H[r0].nxt ∈ x1, r0 ∈ x1, r ∈ x1, r0 ∈ x0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 122:
⊦ x0 ≠ [] → (x1 + x0).last = x0.last
Proof step 123:
(r0 ' + x0).last = (r ' + x1).last, H[H[r0].nxt].nxt = r0, x0 = [], path(r ' + x1, H), path(r0 ' + x0, H), path(r ' + x1 + H[r0].nxt ', H), H[r0].nxt ∈ H, (r ' + x1).last ∈ H, r0 ∈ H ⊦ H[r0].nxt = r0, H[r0].nxt = null, r = H[r0].nxt, r0 = r, r0 = null, dups(x0), dups(x1), r0 ∈ x0, r ∈ x1, r0 ∈ x1, H[r0].nxt ∈ x1
Proof step 126:
x0.last = (r ' + x1).last, H[H[r0].nxt].nxt = r0, path(r ' + x1, H), path(r0 ' + x0, H), path(r ' + x1 + H[r0].nxt ', H), H[r0].nxt ∈ H, (r ' + x1).last ∈ H, r0 ∈ H ⊦ H[r0].nxt = r0, H[r0].nxt = null, r = H[r0].nxt, r0 = r, r0 = null, x0 = [], dups(x0), dups(x1), r0 ∈ x0, r ∈ x1, r0 ∈ x1, H[r0].nxt ∈ x1

Rule argument

spec: list-last, inst: reflist name: lapp seq: ⊦ x0 ≠ [] → (x1 + x0).last = x0.last subst: [x0, x1] → [x0, r0 '] flags: <all paths>

Additional information

Used terms: x0, r0 '