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Proof step 92 from proof reachable-addnew-rev (previous step)

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

User applied rule exists right

And closed the goal!

Rule argument

pos: right 4 terms: H[r0].nxt ' abort: F discard: T computed: F

Additional information

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