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Proof step 7 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, ∀ ce0, H0, r2, r3. ce0.nxt = H0[H0[r2].nxt].nxt ∧ path(r3 ' + x0, H0) ∧ H0[r2].nxt ∈ H0 ∧ r2 ∈ H0 → r2 = null ∨ H0[r2].nxt = null ∨ (r3 ' + x0).last = H0[r2].nxt ∨ reachable(r3, (r3 ' + x0).last, H0[r2, ce0]) ⊦ 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 all left

And obtained the following new goals

Proof step 8:
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, ce.nxt = H[H[r1].nxt].nxt ∧ path(H[r].nxt ' + x0, H) ∧ H[r1].nxt ∈ H ∧ r1 ∈ H → r1 = null ∨ H[r1].nxt = null ∨ (H[r].nxt ' + x0).last = H[r1].nxt ∨ reachable(H[r].nxt, (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

pos: left 7 terms: ce, H, r1, H[r].nxt abort: F discard: T computed: T

Additional information

Used terms: ce, H, r1, H[r].nxt