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

∀ H, r. path(x0, H) → path(x0, H -- r) ∨ r ∈ x0, path(r0 + x0, H) ⊦ path(r0 + x0, H -- r), r ∈ r0 + x0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
path(r0 ' + x0, H), ∀ H, r. path(x0, H) → path(x0, H -- r) ∨ r ∈ x0 ⊦ r = r0, path(r0 ' + x0, H -- r), r ∈ x0

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%in-06: ⊦ ¬ r ∈ r0 ' + x0 ↔ r ≠ r0 ∧ ¬ r ∈ x0; from specification list[reflist]%c: ⊦ r + x0 = r ' + x0; from specification list[reflist]