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Proof step 3 from proof path-trans (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
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

Additional information

Used simplifier rules: a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%c: ⊦ r + x0 = r ' + x0; from specification list[reflist]