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Proof step 138 from proof rem-stays-reachable-aux2 (previous step)

path(r1 ' + H[r0].nxt ', H), H[H[r0].nxt].nxt = r0, path(r ' + (x2 + r1 ') + H[r0].nxt ', H), H[r0].nxt ∈ H, r0 ∈ H, path(r0 ' + x + r1 ', H), r1 ∈ H, path(r ' + x2 + r1 ', H) ⊦ H[r0].nxt = null, r0 = r, r = H[r0].nxt, H[r0].nxt = r0, r0 = null, r0 = r1, r = r1, H[r0].nxt = r1, r0 ∈ x, r1 ∈ x, dups(x), r ∈ x2, H[r0].nxt ∈ x2, r0 ∈ x2, r1 ∈ x2, dups(x2)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 139:
H[H[r0].nxt].nxt = r0, H[r1].nxt = H[r0].nxt, path(r ' + (x2 + r1 ') + H[r0].nxt ', H), H[r0].nxt ∈ H, r0 ∈ H, path(r0 ' + x + r1 ', H), r1 ∈ H, path(r ' + x2 + r1 ', H) ⊦ H[r0].nxt = null, r0 = r, r = H[r0].nxt, H[r0].nxt = r0, r0 = null, r0 = r1, r = r1, H[r0].nxt = r1, r1 = null, r0 ∈ x, r1 ∈ x, dups(x), r ∈ x2, H[r0].nxt ∈ x2, r0 ∈ x2, r1 ∈ x2, dups(x2)

Rule argument

Additional information

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