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Proof step 9 from proof rem-stays-reachable-aux2 (previous step)

H[r0].nxt = H[(r ' + x).last].nxt, path(r ' + x, H), reachable(r, r0, H), H[r0].nxt ∈ H, (r ' + x).last ∈ H, r0 ∈ H ⊦ H[r0].nxt = null, reachable(r0, (r ' + x).last, H), (path(r ' + x, H) ∧ H[(r ' + x).last].nxt = H[r0].nxt ∧ H[r0].nxt ∈ H ∧ H[r0].nxt ≠ null) ∧ ¬ r0 ∈ x

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
H[r0].nxt = H[x.last].nxt, r0 ∈ H, r0 ∈ x, path(r ' + x, H), reachable(r, r0, H), H[r0].nxt ∈ H, x.last ∈ H ⊦ H[r0].nxt = null, reachable(r0, x.last, H)

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%l-in: ⊦ r ∈ x0 → (r0 ' + x0).last = x0.last; from specification list-last[reflist]