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Proof step 11 from proof btree-sub-clean-next (previous step)

zh[r] = mkznode(r0, zbrar, false, boolvar0, m), zh[zbrar[n].child] = mkznode(r1, zbrar0, boolvar1, boolvar2, m0), r ∈ zh, ∀ n0. n0 < m ∧ n0 < n ∧ zbrar[n0].branch? ∧ zbrar[n0].child ∈ zh → ¬ zh[zbrar[n0].child].dirty ⊦ (∀ n0. n0 < m ∧ ¬ n < n0 ∧ zbrar[n0].branch? ∧ zbrar[n0].child ∈ zh → ¬ zh[zbrar[n0].child].dirty) ↔ n < m ∧ zbrar[n].branch? ∧ zbrar[n].child ∈ zh → ¬ boolvar2

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 1

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