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Proof step 91 from proof reachable-addnew-rev (previous step)

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

User applied rule exists right

And closed the goal!

Rule argument

pos: right 2 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 ↔ false);%null-not-reachable: ⊦ ¬ reachable(r, null, H);%At-in-out: ⊦ r ∈ H ∧ ¬ r0 ∈ H → H[r0, ce][r] = H[r]; from specification store[linheap]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%last-def: ⊦ (x0 + r ').last = r; from specification list-last[reflist] Used terms: H[r0].nxt '