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Theorem btree-sub-clean-write-branches

n < # zbrar ⊦ zh[r].zbranches = zbrar ∧ zbrar[n].child = r1 ∧ ¬ zh[r1].dirty ∧ btree-sub-clean(r, n, zh) → btree-sub-clean(r, n + 1, zh[r, zh[r].zbranches:= zbrar[n, mkzbranch(key, adr, r1)]])

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