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Proof step 9 from proof rem-reachable-rev-weak (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ r ≠ r0 → H[r0, ce][r] = H[r]
Proof step 11:
¬ r ≠ r1, ce.nxt = H[H[r1].nxt].nxt, (H[r1, ce][r].nxt ' + x0).last ∈ H[r1, ce], r1 ∈ H, H[r1].nxt ∈ H, path(H[r1, ce][r].nxt ' + x0, H[r1, ce]), r ∈ H[r1, ce], reachable(H[r1, ce][r].nxt, (H[r1, ce][r].nxt ' + x0).last, H), (H[r1, ce][r].nxt ' + x0).last ∈ H ⊦ r = null, (H[r1, ce][r].nxt ' + x0).last = H[r1].nxt, H[r1].nxt = null, r1 = null, reachable(r, (H[r1, ce][r].nxt ' + x0).last, H)
Proof step 18:
r ≠ r1, ce.nxt = H[H[r1].nxt].nxt, (H[r].nxt ' + x0).last ∈ H[r1, ce], r1 ∈ H, H[r1].nxt ∈ H, path(H[r].nxt ' + x0, H[r1, ce]), r ∈ H[r1, ce], reachable(H[r].nxt, (H[r].nxt ' + x0).last, H), (H[r].nxt ' + x0).last ∈ H ⊦ r = null, (H[r].nxt ' + x0).last = H[r1].nxt, H[r1].nxt = null, r1 = null, reachable(r, (H[r].nxt ' + x0).last, H)

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