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Proof step 14 from proof changenonnxt-reachable (previous step)

ce.nxt = H[r1].nxt, r = r1, path(H[r].nxt ' + x0, H), r ∈ H[r1, ce], r ∈ H, ∀ ce, H, r1, r. ce.nxt = H[r1].nxt ∧ path(r ' + x0, H) → path(r ' + x0, H[r1, ce]) ⊦ r = null, path(H[r1, ce][r].nxt ' + x0, H[r1, ce]) ∧ H[r1, ce][r].nxt = H[r].nxt

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
ce.nxt = H[r1].nxt, path(ce.nxt ' + x0, H), r1 ∈ H, r1 ∈ H[r1, ce], ∀ ce, H, r1, r. ce.nxt = H[r1].nxt ∧ path(r ' + x0, H) → path(r ' + x0, H[r1, ce]) ⊦ r1 = null, path(ce.nxt ' + x0, H[r1, ce])

Rule argument

Additional information

Used simplifier rules: ⊦ H[r, ce][r] = ce; (s)