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Proof step 17 from proof reachable-modbehind (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
(H[r].nxt ' + x0).last ∈ H, reachable((H[r].nxt ' + x0).last, r1, H), path(H[r].nxt ' + x0, H), r1 ∈ H, r ∈ H, ∀ r2, H0, r3, ce0. path(r2 ' + x0, H0) ∧ reachable((r2 ' + x0).last, r3, H0) → reachable(r3, (r2 ' + x0).last, H0) ∨ path(r2 ' + x0, H0[r3, ce0]) ⊦ r = null, r = r1, reachable(r1, (H[r].nxt ' + x0).last, H), path(H[r].nxt ' + x0, H[r1, ce])

Rule argument

Additional information

Used simplifier rules: in-neq: ⊦ r ≠ r0 → (r ∈ H[r0, ce] ↔ r ∈ H); from specification store[linheap]