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Proof step 5 from proof path-modify-strong (previous step)

r0 ∈ H, ∀ r0, H, r1, ce. r0 ∈ H → (path(x0 + r1 ', H[r0, ce]) ↔ path(x0 + r1 ', H)) ∨ r0 ∈ x0 ⊦ path((r ' + x0) + r1 ', H[r0, ce]) ↔ path((r ' + x0) + r1 ', H), r0 = r, r0 ∈ x0

User applied rule constructor cut

And obtained the following new goals

Proof step 6:
x0 = r2 + x, r0 ∈ H, ∀ r0, H, r1, ce. r0 ∈ H → (path(x0 + r1 ', H[r0, ce]) ↔ path(x0 + r1 ', H)) ∨ r0 ∈ x0 ⊦ path((r ' + x0) + r1 ', H[r0, ce]) ↔ path((r ' + x0) + r1 ', H), r0 = r, r0 ∈ x0

Rule argument

var: x0

Additional information

Used simplifier rules: path-two: ⊦ path(r ' + r0 ', H) ↔ r ∈ H ∧ r0 ∈ H ∧ r ≠ null ∧ r0 ≠ null ∧ H[r].nxt = r0;%reflist freely generated by [], +;;% ⊦ [] + x0 = x0; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ r ≠ r0 → (r ∈ H[r0, ce] ↔ r ∈ H); (s)% ⊦ r ≠ r0 → H[r0, ce][r] = H[r]; (s)% ⊦ r ∈ H[r0, ce] ↔ r = r0 ∨ r ∈ H; (ws)% ⊦ ¬ r ∈ []; (s)