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Proof step 17 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 ∈ 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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ r ≠ r0 → H[r0, ce][r] = H[r]
Proof step 19:
(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

Rule argument

spec: store, inst: linheap name: At-other seq: ⊦ r ≠ r0 → H[r0, ce][r] = H[r] subst: [r, ce, r0, H] → [r, ce, (H[r].nxt ' + x0).last, H] flags: <all paths>

Additional information

Used terms: r, ce, (H[r].nxt ' + x0).last, H