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Proof step 13 from proof rem-reachable (previous step)

ce.nxt = H[H[r1].nxt].nxt, (H[r].nxt ' + x0).last ∈ H[r1, ce], reachable(H[r].nxt, (H[r].nxt ' + x0).last, H[r1, ce]), r ∈ H, path(H[r].nxt ' + x0, H), H[r1].nxt ∈ H, r1 ∈ H, (H[r].nxt ' + x0).last ∈ H, r ∈ H[r1, ce] ⊦ reachable(H[r1, ce][r].nxt, (H[r].nxt ' + x0).last, H[r1, ce]), r1 = null, H[r1].nxt = null, (H[r].nxt ' + x0).last = H[r1].nxt, r = null, reachable(r, (H[r].nxt ' + x0).last, H[r1, ce])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ r ≠ r0 → H[r0, ce][r] = H[r]
Proof step 15:
¬ r ≠ r1, ce.nxt = H[H[r1].nxt].nxt, (H[r].nxt ' + x0).last ∈ H[r1, ce], reachable(H[r].nxt, (H[r].nxt ' + x0).last, H[r1, ce]), r ∈ H, path(H[r].nxt ' + x0, H), H[r1].nxt ∈ H, r1 ∈ H, (H[r].nxt ' + x0).last ∈ H, r ∈ H[r1, ce] ⊦ reachable(H[r1, ce][r].nxt, (H[r].nxt ' + x0).last, H[r1, ce]), r1 = null, H[r1].nxt = null, (H[r].nxt ' + x0).last = H[r1].nxt, r = null, reachable(r, (H[r].nxt ' + x0).last, H[r1, ce])

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, r1, H] flags: rewrite

Additional information

Used terms: r, ce, r1, H