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Proof step 181 from proof rem-stays-reachable-aux2 (previous step)

H[r].nxt = H[r1].nxt, x = r0 + x0, path(H[H[r1].nxt].nxt ' + x3 + r1 ', H), path(r1 ' + x + r ', H), r1 ∈ H, r ∈ H, H[r1].nxt ∈ H ⊦ H[r1].nxt = r1, H[r1].nxt = H[H[r1].nxt].nxt, H[r1].nxt = null, r = H[H[r1].nxt].nxt, r = null, r1 = r, r1 = H[H[r1].nxt].nxt, dups(x), dups(x3), r ∈ x, r1 ∈ x3, H[r1].nxt ∈ x3, r1 ∈ x, r ∈ x3, H[H[r1].nxt].nxt ∈ x3

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 182:
H[r].nxt = H[r1].nxt, path(H[r1].nxt ' + x0 + r ', H), path(H[H[r1].nxt].nxt ' + x3 + r1 ', H), r1 ∈ H, r ∈ H, H[r1].nxt ∈ H ⊦ H[r1].nxt = r1, H[r1].nxt = H[H[r1].nxt].nxt, H[r1].nxt = null, r = H[H[r1].nxt].nxt, r = null, r1 = null, r1 = r, r1 = H[H[r1].nxt].nxt, dups(x0), dups(x3), H[r1].nxt ∈ x0, r ∈ x0, r1 ∈ x3, H[r1].nxt ∈ x3, r1 ∈ x0, r ∈ x3, H[H[r1].nxt].nxt ∈ x3

Rule argument

Additional information

Used simplifier rules: path-cons: ⊦ path(r ' + r0 ' + x, H) ↔ r ∈ H ∧ r ≠ null ∧ H[r].nxt = r0 ∧ path(r0 ' + x, H);% ⊦ dups(r ' + x0) ↔ dups(x0) ∨ r ∈ x0; (ws)% ⊦ r ∈ r0 ' + x0 ↔ ¬(r ≠ r0 ∧ ¬ r ∈ x0); (ss)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ r + x0 = r ' + x0; (s)