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

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 10 from proof entries-dom (previous step)

((abs(tree, ino) * abs(sdt0, sdi0) * D))(dirs), ∀ sdt1, sdi, D, dirs, str. # sdt1 < # sdt0[str0, tree] → ((abs(sdt1, sdi) * D))(dirs) → (str ∈ sdi ↔ str ∈ sdt1) ⊦ str ∈ sdi0[str0, ino] ↔ str = str0 ∨ str ∈ sdt0, str0 ∈ sdt0, str0 ∈ sdi0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ str ∈ entries[str0, ino] ↔ str = str0 ∨ str ∈ entries
Proof step 12:
((abs(tree, ino) * abs(sdt0, sdi0) * D))(dirs), ∀ sdt1, sdi, D, dirs, str. # sdt1 < # sdt0[str0, tree] → ((abs(sdt1, sdi) * D))(dirs) → (str ∈ sdi ↔ str ∈ sdt1) ⊦ str = str0 ∨ str ∈ sdi0 ↔ str = str0 ∨ str ∈ sdt0, str0 ∈ sdi0, str0 ∈ sdt0

Rule argument

spec: store, inst: dir-entries name: In-insert seq: ⊦ str ∈ entries[str0, ino] ↔ str = str0 ∨ str ∈ entries subst: [ino, str0, entries, str] → [ino, str0, sdi0, str] flags: <all paths>

Additional information

Used terms: ino, str0, sdi0, str