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Proof step 19 from proof reachable-addnew-rev (previous step)

H[r1, ce][(r ' + x1).last].nxt = r1, path(r ' + x1, H[r1, ce]), r ∈ H, r1 ∈ H[r1, ce] ⊦ r1 = null, dups(x1), r ∈ x1, r1 ∈ H, r1 ∈ x1, reachable(r, (r ' + x1).last, H) ∧ H[(r ' + x1).last].nxt = r1 ∧ H[(r ' + x1).last].nxt ≠ null

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
H[r1, ce][(r ' + x1).last].nxt = r1, path(r ' + x1, H), r ∈ H ⊦ r1 = null, dups(x1), r1 ∈ x1, r1 ∈ H, r ∈ x1, reachable(r, (r ' + x1).last, H) ∧ H[(r ' + x1).last].nxt = r1

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)