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Proof step 31 from proof rem-stays-reachable-aux (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
ce.nxt = H[H[r0].nxt].nxt, path(r ' + x2 + H[r0].nxt ', H[r0, ce]), path(r ' + x1 + r0 ', H), H[r0].nxt ∈ H, r0 ∈ H, H[r0].nxt ∈ H[r0, ce] ⊦ H[r0].nxt = ce.nxt, H[r0].nxt = null, r = r0, r = H[r0].nxt, r ∈ x1, r0 ∈ x1, dups(x1), r ∈ x2, H[r0].nxt ∈ x2, dups(x2), ∃ x0. path(H[r0].nxt ' + x0 + H[r0].nxt ', H) ∧ ¬ r0 ∈ x0, ∃ x. path(r ' + 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]