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Proof step 9 from proof tr-unfold (conclusion)

⊦ r ≠ null → (¬ ¬ (tr(r, t) * P)(H) ↔ (∃ t0, t1, a, r0, r1. t = branch(t0, a, t1) ∧ (r => mknode(r0, a, r1) * tr(r0, t0) * tr(r1, t1) * P)(H)))

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : tr-fold, , , ⊦ ( r => mknode(r0, a, r1) * tr(r0, t0) * tr(r1, t1) * P )(H) → ( ¬ ( tr (r, branch(t0, a, t1)) * P )(H) ↔ false)], [CSIMPSEQ : ⊦ P0 * P1 = P1 * P0], [CSIMPSEQ : ⊦ (P0 * P1) * P2 = P0 * P1 * P2])]]