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Proof step 6 from proof path-delnonmember (previous step)

path(r0 ' + x0, H), path(x0, H) → path(x0, H -- r) ⊦ r = r0, path(r0 ' + x0, H -- r), r ∈ x0

User applied rule constructor cut

And closed the goal!

Rule argument

var: x0

Additional information

Used simplifier rules: path-one: ⊦ path(r ', H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null);%path-cons: ⊦ path(r ' + r0 ' + x, H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null ∧ H[r].nxt = r0 ∧ path(r0 ' + x, H));%reflist freely generated by [], +;;%c: ⊦ r + x0 = r ' + x0; from specification list[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%Del-in: ⊦ r ∈ H -- r0 ↔ r ≠ r0 ∧ r ∈ H; from specification store[linheap]%Del-at: ⊦ r ≠ r0 → (H -- r0)[r] = H[r]; from specification store[linheap]%in-06: ⊦ ¬ r ∈ r0 ' + x0 ↔ r ≠ r0 ∧ ¬ r ∈ x0; from specification list[reflist]%app: ⊦ x0 + [] = x0; from specification list[reflist]