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Proof step 45 from proof rem-stays-reachable-aux2 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 46:
⊦ x0 ≠ [] → (x1 + x0).last = x0.last
Proof step 47:
x0 ≠ [], x0.last = r, H[r].nxt = H[H[r].nxt].nxt, H[r].nxt ∈ H, path(H[r].nxt ' + x0, H), r ∈ H ⊦ r = null, H[r].nxt = null, H[r].nxt = r, H[r].nxt ∈ x0, dups(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: rewrite

Additional information

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