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Proof step 5 from proof reachable-addnew (previous step)

path(r ' + x, H), (r ' + x).last ∈ H ⊦ r2 ∈ H, reachable(r, (r ' + x).last, H[r2, ce])

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 6:
path(r ' + x, H), (r ' + x).last ∈ H ⊦ x = [], r2 ∈ H, reachable(r, (r ' + x).last, H[r2, ce])

Rule argument

fma: x = []

Additional information

Used simplifier rules: path-one: ⊦ path(r ', H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null);%self-reachable: ⊦ reachable(r, r, H) ↔ ¬ ¬(r ≠ null ∧ r ∈ H);%app: ⊦ x0 + [] = x0; from specification list[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%l: ⊦ r '.last = r; from specification list-last[reflist]%In-insert: ⊦ r ∈ H[r0, ce] ↔ r = r0 ∨ r ∈ H; from specification store[linheap] Used formulas: x = []