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

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

Rule argument

spec: inst: name: fromnext-reachable-rev seq: ⊦ reachable(H[r].nxt, r0, H) ∧ r ≠ r0 ∧ r ≠ null ∧ r ∈ H → (¬ reachable(r, r0, H) ↔ false) subst: [H, r0, r] → [H[r1, ce], (H[r].nxt ' + x0).last, r] flags: rewrite, current

Additional information

Used terms: H[r1, ce], (H[r].nxt ' + x0).last, r