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Proof step 9 from proof add-preserves-reachable-rev (previous step)

H[r1].nxt = H[ce.nxt].nxt, (H[r1, ce][r].nxt ' + x0).last ∈ H[r1, ce], r1 ∈ H, path(H[r1, ce][r].nxt ' + x0, H[r1, ce]), r ∈ H[r1, ce], reachable(r, r1, H), ce.nxt ∈ H, reachable(H[r1, ce][r].nxt, r1, H) → reachable(H[r1, ce][r].nxt, ce.nxt, H) ∨ reachable(H[r1, ce][r].nxt, (H[r1, ce][r].nxt ' + x0).last, H) ⊦ r = null, (H[r1, ce][r].nxt ' + x0).last = ce.nxt, ce.nxt = null, reachable(r, (H[r1, ce][r].nxt ' + x0).last, H), reachable(r, ce.nxt, 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, H[r1].nxt = H[ce.nxt].nxt, (H[r1, ce][r].nxt ' + x0).last ∈ H[r1, ce], r1 ∈ H, path(H[r1, ce][r].nxt ' + x0, H[r1, ce]), r ∈ H[r1, ce], reachable(r, r1, H), ce.nxt ∈ H, reachable(H[r1, ce][r].nxt, r1, H) → reachable(H[r1, ce][r].nxt, ce.nxt, H) ∨ reachable(H[r1, ce][r].nxt, (H[r1, ce][r].nxt ' + x0).last, H) ⊦ r = null, (H[r1, ce][r].nxt ' + x0).last = ce.nxt, ce.nxt = null, reachable(r, (H[r1, ce][r].nxt ' + x0).last, H), reachable(r, ce.nxt, H)
Proof step 58:
r ≠ r1, H[r1].nxt = H[ce.nxt].nxt, (H[r].nxt ' + x0).last ∈ H[r1, ce], r1 ∈ H, path(H[r].nxt ' + x0, H[r1, ce]), r ∈ H[r1, ce], reachable(r, r1, H), ce.nxt ∈ H, reachable(H[r].nxt, r1, H) → reachable(H[r].nxt, ce.nxt, H) ∨ reachable(H[r].nxt, (H[r].nxt ' + x0).last, H) ⊦ r = null, (H[r].nxt ' + x0).last = ce.nxt, ce.nxt = null, reachable(r, (H[r].nxt ' + x0).last, H), reachable(r, ce.nxt, 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