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Proof step 9 from proof btree-sub-clean-write-branches (previous step)

zh[r] = mkznode(r0, zbrar, boolvar, boolvar0, m), zh[zbrar[n].child] = mkznode(r1, zbrar0, boolvar1, false, m0), n < # zbrar, r ∈ zh, ¬ zh[r].leaf → (∀ n0. n0 < zh[r].usedsize ∧ n0 < n ∧ zh[r].zbranches[n0].branch? ∧ zh[r].zbranches[n0].child ∈ zh → ¬ zh[zh[r].zbranches[n0].child].dirty) ⊦ btree-sub-clean(r, n + 1, zh[r, mkznode(r0, zbrar[n, mkzbranch(key, adr, zbrar[n].child)], boolvar, boolvar0, m)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
zh[r] = mkznode(r0, zbrar, boolvar, boolvar0, m), zh[zbrar[n].child] = mkznode(r1, zbrar0, boolvar1, false, m0), n < # zbrar, r ∈ zh, ¬ boolvar → (∀ n0. n0 < m ∧ n0 < n ∧ zbrar[n0].branch? ∧ zbrar[n0].child ∈ zh → ¬ zh[zbrar[n0].child].dirty) ⊦ btree-sub-clean(r, n + 1, zh[r, mkznode(r0, zbrar[n, mkzbranch(key, adr, zbrar[n].child)], boolvar, boolvar0, m)])

Rule argument

Additional information

Used simplifier rules: ⊦ mkznode(r, zbrar, boolvar, boolvar0, m).zbranches = zbrar; (s)% ⊦ mkznode(r, zbrar, boolvar, boolvar0, m).usedsize = m; (s)% ⊦ mkznode(r, zbrar, boolvar, boolvar0, m).leaf ↔ boolvar; (s)