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Proof step 19 from proof modified-stays-reachable (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
(H[r].nxt ' + x).last = r, r = (H[r].nxt ' + x0).last, path(H[r].nxt ' + x0, H), path(H[r].nxt ' + x, H[r, ce]), r ∈ H[r, ce], r ∈ H ⊦ ce.nxt = H[r].nxt, r = null, ∃ x. path(r ' + x, H[(r ' + x).last, ce]) ∧ (r ' + x).last = r

Rule argument

Additional information

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