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Proof step 16 from proof reachable-modbehind (previous step)

(H[r1].nxt ' + x0).last ∈ H, reachable((H[r1].nxt ' + x0).last, r1, H), path(H[r1].nxt ' + x0, H), r1 ∈ H, ∀ r2, H0, r3, ce0. path(r2 ' + x0, H0) ∧ reachable((r2 ' + x0).last, r3, H0) → reachable(r3, (r2 ' + x0).last, H0) ∨ path(r2 ' + x0, H0[r3, ce0]) ⊦ r1 = null, ∃ x. path(r1 ' + x, H) ∧ (r1 ' + x).last = (H[r1].nxt ' + x0).last, path(ce.nxt ' + x0, H[r1, ce]) ∧ ce.nxt = H[r1].nxt

User applied rule exists right

And closed the goal!

Rule argument

pos: right 2 terms: H[r1].nxt + x0 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));%reachable-notnullinH: ⊦ reachable(r, r1, H) → (¬ r1 ∈ H ↔ false);%c: ⊦ r + x0 = r ' + x0; from specification list[reflist]%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[r1].nxt + x0