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Proof step 12 from proof reachable-addnew-rev (previous step)

path(r ' + x, H[(r ' + x).last, ce]), r ∈ H ⊦ dups(x), (r ' + x).last ∈ H, r ∈ x, ∃ r0. reachable(r, r0, H) ∧ H[r0].nxt = (r ' + x).last ∧ H[r0].nxt ≠ null

User applied rule cut formula

And obtained the following new goals

Proof step 13:
path(r ' + x, H[(r ' + x).last, ce]), r ∈ H ⊦ x = [], dups(x), r ∈ x, (r ' + x).last ∈ H, ∃ r0. reachable(r, r0, H) ∧ H[r0].nxt = (r ' + x).last ∧ H[r0].nxt ≠ null

Rule argument

fma: x = []

Additional information

Used simplifier rules: path-one: ⊦ path(r ', H) ↔ r ∈ H ∧ r ≠ null;% ⊦ x0 + [] = x0; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ r '.last = r; (s)% ⊦ r ∈ H[r, ce]; (s) Used formulas: x = []