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Proof step 3 from proof path-modify-strong (previous step)

∀ r0, H, r1, ce. r0 ∈ H → (path(x0 + r1 ', H[r0, ce]) ↔ path(x0 + r1 ', H)) ∨ r0 ∈ x0, r0 ∈ H ⊦ path((r + x0) + r1 ', H[r0, ce]) ↔ path((r + x0) + r1 ', H), r0 ∈ r + x0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
r0 ∈ H, ∀ r0, H, r1, ce. r0 ∈ H → (path(x0 + r1 ', H[r0, ce]) ↔ path(x0 + r1 ', H)) ∨ r0 ∈ x0 ⊦ path((r ' + x0) + r1 ', H[r0, ce]) ↔ path((r ' + x0) + r1 ', H), r0 = r, r0 ∈ x0

Rule argument

Additional information

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