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

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Proof step 3 from proof btree-sub-clean-next (previous step)

btree-sub-clean(r, n, zh) ⊦ btree-sub-clean(r, n + 1, zh) ↔ ¬ zh[r].leaf ∧ n < zh[r].usedsize ∧ zh[r].zbranches[n].branch? ∧ zh[r].zbranches[n].child ∈ zh → ¬ zh[zh[r].zbranches[n].child].dirty

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ 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 5:
btree-sub-clean(r, n, zh) ⊦ r ∈ zh ∧ ( ¬ zh[r].leaf → (∀ n0. n0 < zh[r].usedsize ∧ n0 < n + 1 ∧ zh[r].zbranches[n0].branch? ∧ zh[r].zbranches[n0].child ∈ zh → ¬ zh[zh[r].zbranches[n0].child].dirty)) ↔ ¬ zh[r].leaf ∧ n < zh[r].usedsize ∧ zh[r].zbranches[n].branch? ∧ zh[r].zbranches[n].child ∈ zh → ¬ zh[zh[r].zbranches[n].child].dirty

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 + 1, r] flags: <all paths>

Additional information

Used terms: zh, n + 1, r