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Proof step 1 from proof btree-sub-clean-next (conclusion)

⊦ btree-sub-clean(r, n, zh) → ( btree-sub-clean(r, n + 1, zh) ↔ ¬ zh[r].leaf ∧ n < zh[r].usedsize ∧ zh[r].zbranches[n].branch? ∧ zh[r].zbranches[n].child ∈ zh → ¬ zh[zh[r].zbranches[n].child].dirty)

System applied rule normalize

And obtained the following new goals

Proof step 2:
btree-sub-clean(r, n, zh) ⊦ btree-sub-clean(r, n + 1, zh) ↔ ¬ zh[r].leaf ∧ n < zh[r].usedsize ∧ zh[r].zbranches[n].branch? ∧ zh[r].zbranches[n].child ∈ zh → ¬ zh[zh[r].zbranches[n].child].dirty

Proof step 1 from proof btree-sub-clean-next (conclusion)

System applied rule normalize

And obtained the following new goals

Rule argument

Additional information