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

∀ r, y, H. path(x0 + r ' + y, H) → path(r ' + y, H), path((r0 + x0) + r ' + y, H) ⊦ path(r ' + y, H)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
path((r0 ' + x0) + r ' + y, H), ∀ r, y, H. path(x0 + r ' + y, H) → path(r ' + y, H) ⊦ path(r ' + 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]