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Proof step 71 from proof acyclic-rem-not-reachable (previous step)

x0 = r2 + x2, ce.nxt = H[H[r0].nxt].nxt, r1 ' + x = x0 + r0 ', r0 ∈ H, path(r ' + x1 + H[r0].nxt ', H), path(r ' + (x1 + H[r0].nxt ' + x0) + r0 ', H), H[r0].nxt ∈ H, r1 ∈ x0 ∨ r1 = r0, ∀ r1. ¬ reachable(H[r1].nxt, r1, H), r0 = r1 ∨ r0 ∈ x ⊦ H[r0].nxt = null, r = H[r0].nxt, r0 = r, r0 = H[r0].nxt, r0 ∈ x1, r ∈ x1, H[r0].nxt ∈ x1, r ∈ x0, r0 ∈ x0, H[r0].nxt ∈ x0, dups(x1 + x0), dups(x1), dups(x0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 72:
ce.nxt = H[H[r0].nxt].nxt, path(r ' + x1 + H[r0].nxt ' + (r2 ' + x2) + r0 ', H), path(r ' + x1 + H[r0].nxt ', H), r0 ∈ H, H[r0].nxt ∈ H, ∀ r1. ¬ reachable(H[r1].nxt, r1, H) ⊦ H[r0].nxt = r2, r0 = r2, r = r2, r0 = H[r0].nxt, r0 = r, r = H[r0].nxt, H[r0].nxt = null, dups(x2), dups(x1), dups(x1 + x2), r2 ∈ x2, r2 ∈ x1, H[r0].nxt ∈ x2, r0 ∈ x2, r ∈ x2, H[r0].nxt ∈ x1, r ∈ x1, r0 ∈ x1

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]%a: ⊦ ¬ dups(x0 + x1) → ¬ dups(x0) ∧ ¬ dups(x1); (forward) from specification list-dup[reflist]%in-15: ⊦ x0 + r ' = x1 → r ∈ x1; (forward) from specification list[reflist]%in-rec: ⊦ r ∈ r0 ' + x0 ↔ ¬ ¬(r = r0 ∨ r ∈ x0); from specification list[reflist]%c-02: ⊦ ¬ r ∈ x0 → (dups(r ' + x0) ↔ dups(x0)); from specification list-dup[reflist]%f-01: ⊦ dups(x0 + r ' + x1) ↔ r ∈ x0 ∨ r ∈ x1 ∨ dups(x0 + x1); from specification list-dup[reflist]%in-06: ⊦ ¬ r ∈ r0 ' + x0 ↔ r ≠ r0 ∧ ¬ r ∈ x0; from specification list[reflist]%c-06: ⊦ r ' + x0 = r0 ' + x1 ↔ r = r0 ∧ x0 = x1; from specification list[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%c: ⊦ r + x0 = r ' + x0; from specification list[reflist]