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Proof step 14 from proof reachable-addnewtonull-rev (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
ce.nxt = null, path(H[r].nxt ' + x0, H[r2, ce]), (H[r].nxt ' + x0).last ∈ H, r ∈ H, ∀ ce, r, H, r2. ce.nxt = null ∧ path(r ' + x0, H[r2, ce]) ∧ (r ' + x0).last ∈ H → path(r ' + x0, H) ∨ r2 ∈ H ⊦ r = null, path(H[r].nxt ' + x0, H), r2 ∈ H

Rule argument

Additional information

Used simplifier rules: ⊦ r ∈ H[r0, ce] ↔ r = r0 ∨ r ∈ H; (ws)