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Proof step 76 from proof rem-stays-reachable-aux2 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 77:
⊦ 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] → [x, 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)% ⊦ [] + x0 = x0; (s) Used terms: x, r '