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Proof step 30 from proof rem-stays-reachable-aux (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
x0.last = H[r0].nxt, ce.nxt = H[x0.last].nxt, path(r ' + x0, H[r0, ce]), path(r ' + x1 + r0 ', H), x0.last ∈ H, r0 ∈ H, x0.last ∈ H[r0, ce] ⊦ x0.last = ce.nxt, x0.last = null, r = r0, r = x0.last, x0 = [], dups(x0), dups(x1), r ∈ x1, r ∈ x0, r0 ∈ x1, ∃ x0. path(H[r0].nxt ' + x0 + H[r0].nxt ', H) ∧ ¬ r0 ∈ x0, ∃ x. path(r ' + x + x0.last ', H) ∧ ¬ r0 ∈ x

Proof step 30 from proof rem-stays-reachable-aux (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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