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Proof step 99 from proof reachable-addnew-rev (previous step)

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

User applied rule exists right

And closed the goal!

Rule argument

pos: right 5 terms: H[r0].nxt + ce.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);%reachable-notnullinH: ⊦ reachable(r, r1, H) → (r1 ∈ H ↔ true);%null-not-reachable: ⊦ ¬ reachable(r, null, H);% ⊦ r + x0 = r ' + x0; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ r ∈ H ∧ ¬ r0 ∈ H → H[r0, ce][r] = H[r]; (s)% ⊦ r ∈ H[r, ce]; (s)% ⊦ H[r, ce][r] = ce; (s)% ⊦ (r ' + r0 ' + x0).last = (r0 ' + x0).last; (s) Used terms: H[r0].nxt + ce.nxt + x