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Proof step 36 from proof reachable-addnew-rev (previous step)

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)

User applied rule cut formula

And obtained the following new goals

Proof step 37:
path(r ' + x1 + r2 ', H[r2, ce]), 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)

Rule argument

fma: path(r ' + x1 + r2 ', H[r2, ce])

Additional information

Used simplifier rules: path-prefix: ⊦ path(r ' + x + y, H) → (¬ path(r ' + x, H) ↔ false);%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist] Used formulas: path(r ' + x1 + r2 ', H[r2, ce])