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Proof step 18 from proof modified-stays-reachable (previous step)

¬ r ≠ (H[r].nxt ' + x0).last, (H[r].nxt ' + x).last = (H[r].nxt ' + x0).last, path(H[r].nxt ' + x, H[(H[r].nxt ' + x0).last, ce]), r ∈ H, path(H[r].nxt ' + x0, H), (H[r].nxt ' + x0).last ∈ H, r ∈ H[(H[r].nxt ' + x0).last, ce] ⊦ r = null, H[(H[r].nxt ' + x0).last, ce][r].nxt = H[r].nxt, ∃ 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 19:
(H[r].nxt ' + x).last = r, r = (H[r].nxt ' + x0).last, path(H[r].nxt ' + x0, H), r ∈ H, path(H[r].nxt ' + x, H[r, ce]) ⊦ 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: insin: ⊦ r ∈ H[r, ce]; from specification store[linheap]%k-At-same: ⊦ r = r0 → H[r0, ce][r] = ce; from specification store[linheap]