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Proof step 21 from proof count-entries (previous step)

str0 = str ∨ str0 ∈ entries0 ↔ str0 ∈ sdt0[str, tree], ∀ entries1, sdt. # entries1 < # entries0[str, ino] → (∀ str. str ∈ entries1 ↔ str ∈ sdt) → # entries1 = # sdt ⊦ # entries0 = # sdt0, str0 ∈ entries0 ↔ str0 ∈ sdt0, str ∈ entries0, str ∈ sdt0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ str ∈ sdt[str0, tree] ↔ str = str0 ∨ str ∈ sdt

Rule argument

spec: store, inst: directory-tree-inst name: In-insert seq: ⊦ str ∈ sdt[str0, tree] ↔ str = str0 ∨ str ∈ sdt subst: [tree, str0, sdt, str] → [tree, str, sdt0, str0] flags: <all paths>

Additional information

Used terms: tree, str, sdt0, str0