[Imprint][Data Privacy Statement][E-Mail]

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Proof step 8 from proof btree-sub-clean-next (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ btree-sub-clean(r, n, zh) ↔ 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))
Proof step 10:
zh[zbrar[n].child] = mkznode(r1, zbrar0, boolvar1, boolvar2, m0), zh[r] = mkznode(r0, zbrar, boolvar, boolvar0, m), 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) ⊦ r ∈ zh ∧ (¬ boolvar → (∀ n0. n0 < m ∧ ¬ n < n0 ∧ zbrar[n0].branch? ∧ zbrar[n0].child ∈ zh → ¬ zh[zbrar[n0].child].dirty)) ↔ ¬ boolvar ∧ n < m ∧ zbrar[n].branch? ∧ zbrar[n].child ∈ zh → ¬ boolvar2

Rule argument

spec: <toplevel> name: btree-sub-clean seq: ⊦ btree-sub-clean(r, n, zh) ↔ 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)) subst: [zh, n, r] → [zh, n, r] flags: <all paths>

Additional information

Used terms: zh, n, r