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Proof step 10 from proof reachable-addnewtonull-rev (previous step)

∀ ce, r, H, r2. ce.nxt = null ∧ path(r ' + x0, H[r2, ce]) ∧ (r ' + x0).last ∈ H ∧ (r ' + x0).last ∈ H[r2, ce] → r2 ∈ H ∨ path(r ' + x0, H), ce.nxt = null, path(r ' + (r0 + x0), H[r2, ce]), (r ' + (r0 + x0)).last ∈ H, (r ' + (r0 + x0)).last ∈ H[r2, ce] ⊦ r2 ∈ H, path(r ' + (r0 + x0), H)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

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);%At-in-out: ⊦ r ∈ H ∧ ¬ r0 ∈ H → H[r0, ce][r] = H[r]; 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]