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Proof step 21 from proof add-preserves-reachable-rev (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
H[r1].nxt = H[ce.nxt].nxt, reachable(r1, H[r].nxt, H), r1 ∈ H, ce.nxt ∈ H, path(H[r].nxt ' + x, H[r1, ce]), r ∈ H, ∀ H, r1, ce, r. H[r1].nxt = H[ce.nxt].nxt ∧ reachable(r1, H[r].nxt, H) ∧ path(r ' + x, H[r1, ce]) ∧ ce.nxt ∈ H ∧ r1 ∈ H → ce.nxt = null ∨ r1 = null ∨ (ce.nxt ' + x).last = ce.nxt ∨ reachable(r1, ce.nxt, H) ∨ reachable(r1, (r ' + x).last, H) ⊦ r = null, (H[r].nxt ' + x).last = ce.nxt, r1 = null, ce.nxt = null, r = r1, reachable(r1, (H[r].nxt ' + x).last, H), reachable(r1, ce.nxt, H)

Rule argument

Additional information

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