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Proof step 124 from proof rem-stays-reachable-aux2 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 125:
⊦ x0 ≠ [] → (x1 + x0).last = x0.last

Rule argument

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

Additional information

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