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Proof step 40 from proof reachable-addnew-rev (previous step)

H[r2, ce][(r ' + x1).last].nxt = r2, path(r ' + x1, H[r2, ce]), path(r ' + x1 + r2 ' + x0, H[r2, ce]), r ∈ H, (r2 ' + x0).last ∈ H, r2 ∈ H[r2, ce] ⊦ r2 = null, dups(x1 + x0), dups(x1), dups(x0), reachable(r, (r2 ' + x0).last, H), r2 ∈ H, r ∈ x1, r ∈ x0, r2 ∈ x1, r2 ∈ x0, reachable(r, (r ' + x1).last, H) ∧ H[(r ' + x1).last].nxt = r2 ∧ H[(r ' + x1).last].nxt ≠ null ∧ reachable(ce.nxt, (H[(r ' + x1).last].nxt ' + x0).last, H)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 41:
H[r2, ce][(r ' + x1).last].nxt = r2, path(r ' + x1 + r2 ' + x0, H[r2, ce]), path(r ' + x1, H), (r2 ' + x0).last ∈ H, r ∈ H ⊦ r2 = null, dups(x0), dups(x1), dups(x1 + x0), reachable(r, (r2 ' + x0).last, H), r2 ∈ x0, r2 ∈ x1, r ∈ x0, r ∈ x1, r2 ∈ H, reachable(r, (r ' + x1).last, H) ∧ H[(r ' + x1).last].nxt = r2 ∧ reachable(ce.nxt, (H[(r ' + x1).last].nxt ' + x0).last, H)

Rule argument

Additional information

Used simplifier rules: path-new-irrelevant-strong: ⊦ ¬ r2 ∈ H ∧ ¬ r2 ∈ x ∧ r ∈ H → (path(r ' + x, H[r2, ce]) ↔ path(r ' + x, H));%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ r ∈ H[r0, ce] ↔ r = r0 ∨ r ∈ H; (ws)