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Proof step 58 from proof rem-stays-reachable-aux2 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 59:
r0 = H[r0].nxt, (r0 ' + x0).last ∈ H, path(r0 ' + x0, H), r0 ∈ H, path(r ' + (x2 + (r0 ' + x0).last ') + r0 ', H), path(r ' + x + (r0 ' + x0).last ', H) ⊦ r0 = r, r0 = null, r = (r0 ' + x0).last, r0 = (r0 ' + x0).last, dups(x0), r0 ∈ x0, r0 ∈ x2, (r0 ' + x0).last ∈ x2, dups(x2), r ∈ x2, (r0 ' + x0).last ∈ x, dups(x), r ∈ x

Rule argument

Additional information

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