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Proof step 57 from proof rem-stays-reachable-aux1 (previous step)

path(H[H[r].nxt].nxt ' + x0 + H[r].nxt ', H), H[r].nxt ∈ H, r ∈ H, path(H[H[r].nxt].nxt ' + x0 + H[r].nxt ' + r1 ' + x1 + r ', H) ⊦ r = H[r].nxt, r = H[H[r].nxt].nxt, H[r].nxt = null, H[r].nxt = H[H[r].nxt].nxt, H[H[r].nxt].nxt = r1, r = r1, H[r].nxt = r1, H[r].nxt ∈ x0, r ∈ x0, r1 ∈ x1, H[H[r].nxt].nxt ∈ x1, H[H[r].nxt].nxt ∈ x0, r ∈ x1, r1 ∈ x0, dups(x0 + x1), H[r].nxt ∈ x1, dups(x0), dups(x1)

User applied rule cut formula

And closed the goal!

Rule argument

fma: path(H[r].nxt ' + r1 ' + x1 + r ', H)

Additional information

Used simplifier rules: path-cons: ⊦ path(r ' + r0 ' + x, H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null ∧ H[r].nxt = r0 ∧ path(r0 ' + x, H));%path-postfix: ⊦ path(x + r ' + y, H) → (¬ path(r ' + y, H) ↔ false);%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist] Used formulas: path(H[r].nxt ' + r1 ' + x1 + r ', H)