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Proof step 4 from proof path-trans (previous step)

path(r ' + x0, H), path((r ' + x0).last ' + y, H), ∀ H, y. path(x0, H) ∧ path(x0.last ' + y, H) → path(x0 + y, H) ⊦ path((r ' + x0) + y, H)

User applied rule constructor cut

And obtained the following new goals

Proof step 5:
x0 = r0 + x, path(r ' + x0, H), path((r ' + x0).last ' + y, H), ∀ H, y. path(x0, H) ∧ path(x0.last ' + y, H) → path(x0 + y, H) ⊦ path((r ' + x0) + y, H)

Rule argument

var: x0

Additional information

Used simplifier rules: path-one: ⊦ path(r ', H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null);%reflist freely generated by [], +;;%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]%Nil: ⊦ [] + x0 = x0; from specification list[reflist]