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Proof step 98 from proof reachable-addnew-rev (previous step)

reachable(ce.nxt, (ce.nxt ' + x).last, H), path(ce.nxt ' + x, 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], (ce.nxt ' + x).last ∈ H[H[r0].nxt, ce], (ce.nxt ' + x).last ∈ H ⊦ H[r0].nxt = null, reachable(r, (ce.nxt ' + x).last, H[H[r0].nxt, ce]), reachable(r, (ce.nxt ' + x).last, H), 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 ↔ false);%null-not-reachable: ⊦ ¬ reachable(r, null, H);%c: ⊦ r + x0 = r ' + x0; from specification list[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%At-in-out: ⊦ r ∈ H ∧ ¬ r0 ∈ H → H[r0, ce][r] = H[r]; from specification store[linheap]%insin: ⊦ r ∈ H[r, ce]; from specification store[linheap]%At-same: ⊦ H[r, ce][r] = ce; from specification store[linheap]%l-05: ⊦ (r ' + r0 ' + x0).last = (r0 ' + x0).last; from specification list-last[reflist]%in-neq: ⊦ r ≠ r0 → (r ∈ H[r0, ce] ↔ r ∈ H); from specification store[linheap] Used terms: H[r0].nxt + ce.nxt + x