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Proof step 95 from proof rem-stays-reachable-aux2 (previous step)

x1 + r2 ' = H[r2].nxt ' + r0 ' + y, (r ' + x1).last = r, H[r].nxt = H[r2].nxt, x0 = x + r ', path(r ' + x1 + r2 ', H), path(r ' + x1, H), path(r2 ' + x0, H), H[r2].nxt ∈ H, r2 ∈ H, r ∈ H, H[r2].nxt ∈ x1 ∨ H[r2].nxt = r2, r2 = H[r2].nxt ∨ r2 = r0 ∨ r2 ∈ y ⊦ H[r2].nxt = null, r = r2, r = null, x0 = [], dups(x0), dups(x1), r2 ∈ x1, r2 ∈ x0, r ∈ x1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 96:
x1 + r2 ' = H[r2].nxt ' + r0 ' + y, (r ' + x1).last = r, H[r].nxt = H[r2].nxt, path(r2 ' + x + r ', H), path(r ' + x1, H), path(r ' + x1 + r2 ', H), r ∈ H, r2 ∈ H, H[r2].nxt ∈ H, r2 = H[r2].nxt ∨ r2 = r0 ∨ r2 ∈ y, H[r2].nxt ∈ x1 ∨ H[r2].nxt = r2 ⊦ H[r2].nxt = null, r = null, r = r2, dups(x1), dups(x), r ∈ x1, r2 ∈ x, r2 ∈ x1, r ∈ x

Rule argument

Additional information

Used simplifier rules: ⊦ dups(x0 + r ') ↔ r ∈ x0 ∨ dups(x0); (ws)% ⊦ r ∈ r0 ' ↔ r = r0; (s)% ⊦ r ∈ x0 + x1 ↔ r ∈ x0 ∨ r ∈ x1; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ x0 + r ' ≠ []; (s)