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Proof step 19 from proof reach-reachnext (previous step)

(H[r].nxt ' + x).last = H[(H[r].nxt ' + x1).last].nxt, path(H[r].nxt ' + x, H), path(H[r].nxt ' + x1, H), (H[r].nxt ' + x1).last ∈ H, r ∈ H, ∀ r, x0, H. (r ' + x0).last = H[(r ' + x1).last].nxt ∧ path(r ' + x0, H) ∧ path(r ' + x1, H) ∧ (r ' + x1).last ∈ H → (r ' + x0).last ≠ null ∧ (r ' + x0).last ∈ H ⊦ r = null, (H[r].nxt ' + x).last ≠ null ∧ (H[r].nxt ' + x).last ∈ H

User applied rule all left

And closed the goal!

Rule argument

pos: left 6 terms: H[r].nxt, x, H abort: F discard: T computed: T

Additional information

Used simplifier rules: path-last: ⊦ path(r ' + x, H) → ((r ' + x).last ∈ H ↔ true);%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist] Used terms: H[r].nxt, x, H