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Proof step 5 from proof path-new-irrelevant-strong (previous step)

r ∈ H, H[r].nxt ∈ H → (path(H[r].nxt ' + x0, H[r2, ce]) ↔ path(H[r].nxt ' + x0, H)) ∨ r2 ∈ x0 ∨ r2 ∈ H, ∀ r, H, r2, ce. r ∈ H → (path(r ' + x0, H[r2, ce]) ↔ path(r ' + x0, H)) ∨ r2 ∈ x0 ∨ r2 ∈ H ⊦ r2 = H[r].nxt, r = null, r ∈ H[r2, ce] ∧ path(H[r].nxt ' + x0, H[r2, ce]) ↔ path(H[r].nxt ' + x0, H), r2 ∈ x0, r2 ∈ H

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
r ∈ H, ∀ r, H, r2, ce. r ∈ H → (path(r ' + x0, H[r2, ce]) ↔ path(r ' + x0, H)) ∨ r2 ∈ x0 ∨ r2 ∈ H, H[r].nxt ∈ H → (path(H[r].nxt ' + x0, H[r2, ce]) ↔ path(H[r].nxt ' + x0, H)) ⊦ r2 = H[r].nxt, r = null, r ∈ H[r2, ce] ∧ path(H[r].nxt ' + x0, H[r2, ce]) ↔ path(H[r].nxt ' + x0, H), r2 ∈ x0, r2 ∈ H

Proof step 5 from proof path-new-irrelevant-strong (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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