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Proof step 16 from proof modified-stays-reachable (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
(H[r].nxt ' + x).last = (H[r].nxt ' + x0).last, path(H[r].nxt ' + x, H[(H[r].nxt ' + x0).last, ce]), path(H[r].nxt ' + x0, H), r ∈ H, r ∈ H[(H[r].nxt ' + x0).last, ce] ⊦ 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

Rule argument

Additional information

Used simplifier rules: path-cons: ⊦ path(r ' + r0 ' + x, H) ↔ r ∈ H ∧ r ≠ null ∧ H[r].nxt = r0 ∧ path(r0 ' + x, H);% ⊦ ¬ r ∈ H → H[r] = (∅)[r]; (s)% ⊦ r ∈ H[r0, ce] ↔ r = r0 ∨ r ∈ H; (ws)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ (r ' + r0 ' + x0).last = (r0 ' + x0).last; (s)