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Proof step 11 from proof rem-stays-reachable-aux1 (previous step)

x = x1 + r ', r = H[r0].nxt, path(H[r].nxt ' + x, H), r0 ∈ H, r ∈ H ⊦ r = H[r].nxt, r = null, x = [], reachable(H[r].nxt, r0, H), H[r].nxt ∈ x, dups(x), ∃ x. path(H[r0].nxt ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
path(H[H[r0].nxt].nxt ' + x1 + H[r0].nxt ', H), r0 ∈ H, H[r0].nxt ∈ H ⊦ H[r0].nxt = H[H[r0].nxt].nxt, H[r0].nxt = null, reachable(H[H[r0].nxt].nxt, r0, H), H[H[r0].nxt].nxt ∈ x1, H[r0].nxt ∈ x1, dups(x1), ∃ x. path(H[r0].nxt ' + x + H[r0].nxt ', H) ∧ ¬ 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]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%e-02: ⊦ x0 + r ' ≠ []; from specification list[reflist]