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Proof step 79 from proof rem-stays-reachable-aux2 (previous step)

x2 = x1 + r2 ', x2 = (x + H[r2].nxt ') + r0 ' + y, (r2 ' + x0).last = (r ' + x).last, (r1 ' + y0).last = (r ' + x).last, path(r ' + x2 + r1 ' + y0, H), path(r ' + x + H[r2].nxt ', H), path(r ' + x2, H), H[r2].nxt ∈ H, r2 ∈ H, path(r2 ' + x0, H), (r ' + x).last ∈ H ⊦ H[r2].nxt = null, r2 = r, x2 = [], r = r1, r ∈ x2, r2 ∈ x, r2 ∈ x0, dups(x0), r ∈ y0, r1 ∈ x2, r1 ∈ y0, dups(x2 + y0), dups(x2), dups(y0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 80:
(r1 ' + y0).last = (r ' + x).last, (r2 ' + x0).last = (r ' + x).last, x1 + r2 ' = (x + H[r2].nxt ') + r0 ' + y, (r ' + x).last ∈ H, path(r2 ' + x0, H), r2 ∈ H, H[r2].nxt ∈ H, path(r ' + x1 + r2 ', H), path(r ' + x + H[r2].nxt ', H), path(r ' + (x1 + r2 ') + r1 ' + y0, H), r2 = H[r2].nxt ∨ r2 = r0 ∨ r2 ∈ y ⊦ r1 = r2, r = r1, r2 = r, H[r2].nxt = null, dups(y0), dups(x1), dups(x1 + y0), r2 ∈ y0, r2 ∈ x1, r1 ∈ y0, r1 ∈ x1, r ∈ y0, dups(x0), r2 ∈ x0, r2 ∈ x, r ∈ x1

Rule argument

Additional information

Used simplifier rules: in-rec: ⊦ r ∈ r0 ' + x0 ↔ ¬ ¬(r = r0 ∨ r ∈ x0); 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]%l-03: ⊦ ¬ r ∈ x0 → (dups(x0 + r ') ↔ 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-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]