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Proof step 38 from proof rem-stays-reachable-aux2 (previous step)

x2 = x3 + r0 ' ∧ x2 ≠ [], x2 = x + H[r0].nxt ', (r0 ' + x0).last = (r ' + x).last, (r ' + x1).last = (r ' + x).last, path(r ' + x1, H), path(r ' + x2, H), H[r0].nxt ∈ H, r0 ∈ H, path(r0 ' + x0, H), (r ' + x).last ∈ H, H[r0].nxt ∈ x2 ⊦ H[r0].nxt = null, r0 = r, r0 ∈ x, r0 ∈ x0, dups(x0), r ∈ x1, dups(x1), r ∈ x2, dups(x2)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 39:
r0 = H[r0].nxt, (r ' + x1).last = (r ' + x).last, (r0 ' + x0).last = (r ' + x).last, (r ' + x).last ∈ H, path(r0 ' + x0, H), r0 ∈ H, path(r ' + x + r0 ', H), path(r ' + x1, H) ⊦ r0 = r, r0 = null, dups(x), r ∈ x, dups(x1), r ∈ x1, dups(x0), r0 ∈ x0, r0 ∈ x

Rule argument

Additional information

Used simplifier rules: f: ⊦ dups(x0 + r ') ↔ r ∈ x0 ∨ dups(x0); from specification list-dup[reflist]%in-17: ⊦ r ∈ r0 ' ↔ r = r0; from specification list[reflist]%in-append: ⊦ r ∈ x0 + x1 ↔ ¬ ¬(r ∈ x0 ∨ r ∈ x1); from specification list[reflist]%e-02: ⊦ x0 + r ' ≠ []; from specification list[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%app-06: ⊦ x0 + r ' = x1 + r0 ' ↔ x0 = x1 ∧ r = r0; from specification list[reflist]