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Proof step 65 from proof reachable-addnew-rev (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 66:
path(r ' + x + r0 ', H), path(r ' + (x + r0 ') + H[r0].nxt ' + x0, H[H[r0].nxt, ce]), path(H[r0].nxt ' + x0, H[H[r0].nxt, ce]), r ∈ H, (H[r0].nxt ' + x0).last ∈ H, r0 ∈ H ⊦ H[r0].nxt = null, r = r0, r0 = H[r0].nxt, r0 = null, dups(x + x0), dups(x), dups(x0), reachable(r, (H[r0].nxt ' + x0).last, H), reachable(ce.nxt, (H[r0].nxt ' + x0).last, H), H[r0].nxt ∈ H, r ∈ x, r ∈ x0, H[r0].nxt ∈ x, H[r0].nxt ∈ x0, r0 ∈ x, r0 ∈ x0

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);%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ r ≠ r0 → H[r0, ce][r] = H[r]; (s)% ⊦ r ≠ r0 → (r ∈ H[r0, ce] ↔ r ∈ H); (s)