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Proof step 45 from proof rem-stays-reachable-aux (previous step)

ce.nxt = H[H[r0].nxt].nxt, path(r ' + x0 + r0 ' + (ce.nxt ' + x2) + H[r0].nxt ', H[r0, ce]), path(r ' + x0 + r0 ', H[r0, ce]), path((ce.nxt ' + x2) + H[r0].nxt ', H), path(r ' + x1 + r0 ', H), r0 ∈ H, H[r0].nxt ∈ H ⊦ H[r0].nxt = r0, H[r0].nxt = null, H[r0].nxt = ce.nxt, r = ce.nxt, r = r0, r = H[r0].nxt, r0 = ce.nxt, r0 = null, dups(x2), dups(x0), dups(x0 + x2), dups(x1), ce.nxt ∈ x2, ce.nxt ∈ x0, H[r0].nxt ∈ x2, H[r0].nxt ∈ x0, r0 ∈ x1, r ∈ x2, r ∈ x0, r ∈ x1, r0 ∈ x0, r0 ∈ x2, ∃ x. path(r ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x, ∃ x0. path(H[r0].nxt ' + x0 + H[r0].nxt ', H) ∧ ¬ r0 ∈ x0

User applied rule exists right

And closed the goal!

Rule argument

pos: right 24 terms: ce.nxt ' + x2 abort: F discard: T computed: F

Additional information

Used simplifier rules: path-cons: ⊦ path(r ' + r0 ' + x, H) ↔ r ∈ H ∧ r ≠ null ∧ H[r].nxt = r0 ∧ path(r0 ' + x, H);%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ r ≠ r0 → (r ∈ r0 ' + x0 ↔ r ∈ x0); (s) Used terms: ce.nxt ' + x2