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Proof step 78 from proof rem-stays-reachable-aux2 (previous step)

(r ' + x1).last = (r ' + x).last, (x2.last ' + x0).last = (r ' + x).last, x1 = x2 + r1 ' + y0, x2 = (x + H[x2.last].nxt ') + r0 ' + y, path(r ' + x2, H), path(r ' + x1, H), path(x2.last ' + x0, H), path(r ' + x + H[x2.last].nxt ', H), H[x2.last].nxt ∈ H, x2.last ∈ H, (r ' + x).last ∈ H ⊦ x2.last = r, H[x2.last].nxt = null, x2 = [], dups(x0), dups(x1), dups(x2), x2.last ∈ x, x2.last ∈ x0, r ∈ x1, r ∈ x2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 79:
(x2.last ' + x0).last = (r ' + x).last, (r1 ' + y0).last = (r ' + x).last, x2 = (x + H[x2.last].nxt ') + r0 ' + y, path(r ' + x + H[x2.last].nxt ', H), path(x2.last ' + x0, H), path(r ' + x2 + r1 ' + y0, H), path(r ' + x2, H), (r ' + x).last ∈ H, x2.last ∈ H, H[x2.last].nxt ∈ H ⊦ x2.last = r, H[x2.last].nxt = null, r = r1, x2 = [], dups(x0), dups(x2 + y0), dups(x2), dups(y0), r ∈ x2, r ∈ y0, x2.last ∈ x0, x2.last ∈ x, r1 ∈ x2, r1 ∈ y0

Rule argument

Additional information

Used simplifier rules: a: ⊦ ¬ dups(x0 + x1) → ¬ dups(x0) ∧ ¬ dups(x1); (forward) from specification list-dup[reflist]% ⊦ dups(x0 + r ' + x1) ↔ r ∈ x0 ∨ r ∈ x1 ∨ dups(x0 + x1); (ws)% ⊦ r ∈ r0 ' ↔ r = r0; (s)% ⊦ r ∈ x0 + x1 ↔ r ∈ x0 ∨ r ∈ x1; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ (x0 + r ' + x1).last = (r ' + x1).last; (s)