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Proof step 51 from proof rem-stays-reachable-aux2 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 52:
r0 = H[r0].nxt, (r ' + x1).last = x.last, (r0 ' + x0).last = x.last, x.last ∈ H, path(r0 ' + x0, H), r0 ∈ H, path(r ' + x + r0 ', H), path(r ' + x1, H) ⊦ r0 = r, r0 = null, x = [], dups(x), r ∈ x, dups(x1), r ∈ x1, dups(x0), r0 ∈ x0, r0 ∈ x

Proof step 51 from proof rem-stays-reachable-aux2 (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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