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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
∀ H, r0, ce. (path(x0, H[r0, ce]) ↔ path(x0, H)) ∨ r0 ∈ x0 ⊦ path(r ' + x0, H[r0, ce]) ↔ path(r ' + x0, H), r0 = r, r0 ∈ x0

Rule argument

Additional information

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