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Proof step 12 from proof reachable-addnew (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
(H[r].nxt ' + x0).last ∈ H, path(H[r].nxt ' + x0, H), r ∈ H, r ∈ H[r2, ce], ∀ r, H, r2, ce. path(r ' + x0, H) ∧ x0.last ∈ H → x0 = [] ∨ r2 ∈ H ∨ path(r ' + x0, H[r2, ce]) ⊦ r = null, r2 ∈ H, path(H[r].nxt ' + x0, H[r2, ce])

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));%In-insert: ⊦ r ∈ H[r0, ce] ↔ r = r0 ∨ r ∈ H; from specification store[linheap]%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]%e-01: ⊦ r ' + x0 ≠ []; from specification list[reflist]%c: ⊦ r + x0 = r ' + x0; from specification list[reflist]