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

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)]])

System applied rule normalize

And obtained the following new goals

Proof step 2:
zbrar[n].child = r1, zh[r].zbranches = zbrar, n < # zbrar, btree-sub-clean(r, n, zh) ⊦ zh[r1].dirty, btree-sub-clean(r, n + 1, zh[r, zh[r].zbranches:= zbrar[n, mkzbranch(key, adr, r1)]])

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

System applied rule normalize

And obtained the following new goals

Rule argument

Additional information