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Proof step 10 from proof changenonnxt-reachable (previous step)

∀ ce, H, r1, r. ce.nxt = H[r1].nxt ∧ path(r ' + x0, H) ∧ (r ' + x0).last ∈ H → path(r ' + x0, H[r1, ce]), ce.nxt = H[r1].nxt, path(r ' + (r0 + x0), H), (r ' + (r0 + x0)).last ∈ H ⊦ path(r ' + (r0 + x0), H[r1, ce])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
ce.nxt = H[r1].nxt, (H[r].nxt ' + x0).last ∈ H, path(H[r].nxt ' + x0, H), r ∈ H, r ∈ H[r1, ce], ∀ ce0, H0, r2, r3. ce0.nxt = H0[r2].nxt ∧ path(r3 ' + x0, H0) → path(r3 ' + x0, H0[r2, ce0]) ⊦ r = null, path(H[r1, ce][r].nxt ' + x0, H[r1, ce]) ∧ H[r1, ce][r].nxt = H[r].nxt

Rule argument

Additional information

Used simplifier rules: path-cons: ⊦ path(r ' + r0 ' + x, H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null ∧ H[r].nxt = r0 ∧ path(r0 ' + x, H));%path-last: ⊦ path(r ' + x, H) → (¬ (r ' + x).last ∈ H ↔ false);%In-insert: ⊦ r ∈ H[r0, ce] ↔ r = r0 ∨ r ∈ H; from specification store[linheap]%l-05: ⊦ (r ' + r0 ' + x0).last = (r0 ' + x0).last; from specification list-last[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%c: ⊦ r + x0 = r ' + x0; from specification list[reflist]