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Proof step 19 from proof add-preserves-reachable-rev (previous step)

¬ r ≠ r1, H[r1].nxt = H[ce.nxt].nxt, path(H[r1, ce][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[r1, ce][r].nxt ' + x).last = ce.nxt, r1 = null, ce.nxt = null, reachable(r1, (H[r1, ce][r].nxt ' + x).last, H), reachable(r1, ce.nxt, H)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
H[r1].nxt = H[ce.nxt].nxt, reachable(r1, H[r1].nxt, H), r1 ∈ H, ce.nxt ∈ H, path(ce.nxt ' + x, H[r1, ce]), H[r1].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) ⊦ r1 = null, ce.nxt = null, (ce.nxt ' + x).last = ce.nxt, reachable(r1, ce.nxt, H), reachable(r1, (ce.nxt ' + x).last, H)

Rule argument

Additional information

Used simplifier rules: reach-alloc: ⊦ reachable(r, r1, H) → r1 ∈ H;%insin: ⊦ r ∈ H[r, ce]; from specification store[linheap]%At-same: ⊦ H[r, ce][r] = ce; from specification store[linheap]