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Proof step 8 from proof path-new-irrelevant-strong (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
path(H[r].nxt ' + x0, H[r2, ce]), r ∈ H[r2, ce], r ∈ H, ∀ r, H, r2, ce. r ∈ H → (path(r ' + x0, H[r2, ce]) ↔ path(r ' + x0, H)) ∨ r2 ∈ H ∨ r2 ∈ x0 ⊦ r = null, r2 = H[r].nxt, path(H[r].nxt ' + x0, H), r2 ∈ x0, r2 ∈ H, H[r].nxt ∈ H

Proof step 8 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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