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Proof step 178 from proof rem-stays-reachable-aux2 (previous step)

x0 = x + r ', H[r].nxt = H[r1].nxt, r ∈ H, H[r1].nxt ∈ H, path(H[H[r1].nxt].nxt ' + x3 + r1 ', H), path(r1 ' + x0, H), r1 ∈ H ⊦ r = null, H[r1].nxt = r1, r1 = r, r1 = H[H[r1].nxt].nxt, H[r1].nxt = H[H[r1].nxt].nxt, r = H[H[r1].nxt].nxt, H[r1].nxt = null, x0 = [], dups(x3), r1 ∈ x3, H[r1].nxt ∈ x3, r ∈ x3, dups(x0), r1 ∈ x0, H[H[r1].nxt].nxt ∈ x3

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 179:
H[r].nxt = H[r1].nxt, r ∈ H, H[r1].nxt ∈ H, path(H[H[r1].nxt].nxt ' + x3 + r1 ', H), path(r1 ' + x + r ', H), r1 ∈ H ⊦ r = null, H[r1].nxt = r1, r1 = r, r1 = H[H[r1].nxt].nxt, H[r1].nxt = H[H[r1].nxt].nxt, r = H[H[r1].nxt].nxt, H[r1].nxt = null, H[H[r1].nxt].nxt ∈ x3, dups(x3), r1 ∈ x3, H[r1].nxt ∈ x3, r ∈ x3, r ∈ x, dups(x), r1 ∈ 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]