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Proof step 173 from proof rem-stays-reachable-aux2 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 174:
H[(r1 ' + x0).last].nxt = H[r1].nxt, (r1 ' + x0).last ∈ H, H[r1].nxt ∈ H, path(H[H[r1].nxt].nxt ' + x3 + r1 ', H), path(r1 ' + x0, H), r1 ∈ H ⊦ (r1 ' + x0).last = null, H[r1].nxt = r1, r1 = (r1 ' + x0).last, r1 = H[H[r1].nxt].nxt, H[r1].nxt = H[H[r1].nxt].nxt, (r1 ' + x0).last = H[H[r1].nxt].nxt, H[r1].nxt = null, dups(x3), r1 ∈ x3, H[r1].nxt ∈ x3, (r1 ' + x0).last ∈ x3, dups(x0), r1 ∈ x0, H[H[r1].nxt].nxt ∈ x3

Rule argument

Additional information

Used simplifier rules: path-one: ⊦ path(r ', H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null);%path-cons: ⊦ path(r ' + r0 ' + x, H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null ∧ H[r].nxt = r0 ∧ path(r0 ' + x, H));%in-empty: ⊦ ¬ r ∈ []; from specification list[reflist]%e-01: ⊦ ¬ dups([]); from specification list-dup[reflist]%Nil: ⊦ [] + x0 = x0; from specification list[reflist]%l: ⊦ r '.last = r; from specification list-last[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%app: ⊦ x0 + [] = x0; from specification list[reflist]