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Proof step 39 from proof reachable-addnew-rev (previous step)

path(r ' + x1, H[r2, ce]) ∧ H[r2, ce][(r ' + x1).last].nxt = r2 ∧ r2 ∈ H[r2, ce] ∧ r2 ≠ null, path(r ' + x1 + r2 ' + x0, H[r2, ce]), r ∈ H, (r2 ' + x0).last ∈ H ⊦ r2 ∈ H, r ∈ x1, r ∈ x0, r2 ∈ x1, r2 ∈ x0, dups(x1 + x0), reachable(r, (r2 ' + x0).last, H), dups(x1), dups(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 40:
H[r2, ce][(r ' + x1).last].nxt = r2, path(r ' + x1 + r2 ' + x0, H[r2, ce]), r ∈ H, (r2 ' + x0).last ∈ H, path(r ' + x1, H) ⊦ r2 = null, r2 ∈ H, r ∈ x1, r ∈ x0, r2 ∈ x1, r2 ∈ x0, dups(x1 + x0), reachable(r, (r2 ' + x0).last, H), dups(x1), dups(x0), 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));%In-insert: ⊦ r ∈ H[r0, ce] ↔ r = r0 ∨ r ∈ H; from specification store[linheap]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]