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Proof step 90 from proof rem-stays-reachable-aux2 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 91:
x1 + r2 ' = H[r2].nxt ' + r0 ' + y, ((r2 ' + x0).last ' + x1).last = (r2 ' + x0).last, H[(r2 ' + x0).last].nxt = H[r2].nxt, path(r2 ' + x0, H), path((r2 ' + x0).last ' + x1, H), path((r2 ' + x0).last ' + x1 + r2 ', H), (r2 ' + x0).last ∈ H, r2 ∈ H, H[r2].nxt ∈ H, r2 = H[r2].nxt ∨ r2 = r0 ∨ r2 ∈ y, H[r2].nxt ∈ x1 ∨ H[r2].nxt = r2 ⊦ (r2 ' + x0).last = null, (r2 ' + x0).last = r2, H[r2].nxt = null, dups(x1), dups(x0), (r2 ' + x0).last ∈ x1, r2 ∈ x0, r2 ∈ x1

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;% ⊦ r ∈ r0 ' ↔ r = r0; (s)% ⊦ r ∈ x0 + x1 ↔ r ∈ x0 ∨ r ∈ x1; (s)%in-14: ⊦ r ' + x0 = x1 → r ∈ x1; (forward) from specification list[reflist]%in-15: ⊦ x0 + r ' = x1 → r ∈ x1; (forward) from specification list[reflist]% ⊦ ¬ r ∈ []; (s)% ⊦ [] + x0 = x0; (s)% ⊦ r '.last = r; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ x0 + [] = x0; (s)