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Proof step 17 from proof modnotreachable-reachable-rev (previous step)

(H[r].nxt ' + x).last = (H[r].nxt ' + x0).last, r ∈ H, path(H[r].nxt ' + x0, H[r0, ce]), (H[r].nxt ' + x0).last ∈ H[r0, ce], r0 ∈ H, path(H[r].nxt ' + x, H), (H[r].nxt ' + x0).last ∈ H ⊦ r = r0, r = null, reachable(r, r0, H), ∃ x. path(r ' + x, H) ∧ (r ' + x).last = (H[r].nxt ' + x0).last, reachable(H[r].nxt, r0, H)

User applied rule exists right

And closed the goal!

Rule argument

pos: right 4 terms: H[r].nxt ' + x 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]%l-05: ⊦ (r ' + r0 ' + x0).last = (r0 ' + x0).last; from specification list-last[reflist] Used terms: H[r].nxt ' + x