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Proof step 87 from proof rem-stays-reachable-aux2 (previous step)

x1 + r2 ' + x3 = x + H[(r2 ' + x3).last].nxt ' + r0 ' + y, ((r2 ' + x3).last ' + x0).last = (r ' + x).last, (r ' + x1).last = (r ' + x).last, x3 = [], path((r2 ' + x3).last ' + x0, H), path(r ' + x + H[(r2 ' + x3).last].nxt ', H), path(r ' + x1 + r2 ' + x3, H), path(r ' + x1, H), H[(r2 ' + x3).last].nxt ∈ H, (r2 ' + x3).last ∈ H, (r ' + x).last ∈ H ⊦ (r2 ' + x3).last = r, H[(r2 ' + x3).last].nxt = null, r = r2, dups(x3), dups(x1), dups(x1 + x3), dups(x0), r2 ∈ x3, r2 ∈ x1, (r2 ' + x3).last ∈ x, (r2 ' + x3).last ∈ x0, r ∈ x1, r ∈ x3

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 88:
x1 + r2 ' = x + H[r2].nxt ' + r0 ' + y, (r2 ' + x0).last = (r ' + x).last, (r ' + x1).last = (r ' + x).last, path(r2 ' + x0, H), path(r ' + x + H[r2].nxt ', H), path(r ' + x1 + r2 ', H), path(r ' + x1, H), H[r2].nxt ∈ H, r2 ∈ H, (r ' + x).last ∈ H, r2 = H[r2].nxt ∨ r2 = r0 ∨ r2 ∈ y ⊦ H[r2].nxt = null, r = r2, dups(x0), dups(x1), r2 ∈ x1, r2 ∈ x, r2 ∈ x0, r ∈ x1

Rule argument

Additional information

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