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Proof step 9 from proof modnotreachable-reachable-rev-weak (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
r0 ∈ H, path(H[r].nxt ' + x0, H[r0, ce]), r ∈ H, ∀ r0, H, r, ce. r0 ∈ H ∧ path(r ' + x0, H[r0, ce]) → r0 = null ∨ reachable(r, (r ' + x0).last, H) ∨ reachable(r, r0, H) ⊦ r = null, r0 = null, r = r0, reachable(r, (H[r].nxt ' + x0).last, H), reachable(r, r0, H)

Rule argument

Additional information

Used simplifier rules: In-insert: ⊦ r ∈ H[r0, ce] ↔ r = r0 ∨ r ∈ H; from specification store[linheap]