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Proof step 2 from proof C-ext (previous step)

∀ str. (str ∈ entries ↔ dentrykey(ino, str) ∈ ri) ∧ (str ∈ entries → entries[str] = fs[ri[dentrykey(ino, str)]].ino) ⊦ entries = abs-children(ino, fs, ri)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ entries = entries0 ↔ (∀ str. (str ∈ entries ↔ str ∈ entries0) ∧ (str ∈ entries → entries[str] = entries0[str]))
Proof step 4:
∀ str. (str ∈ entries ↔ dentrykey(ino, str) ∈ ri) ∧ (str ∈ entries → entries[str] = fs[ri[dentrykey(ino, str)]].ino) ⊦ ∀ str. (str ∈ entries ↔ str ∈ abs-children(ino, fs, ri)) ∧ (str ∈ entries → entries[str] = abs-children(ino, fs, ri)[str])

Rule argument

spec: store, inst: dir-entries name: k-Extension seq: ⊦ entries = entries0 ↔ (∀ str. (str ∈ entries ↔ str ∈ entries0) ∧ (str ∈ entries → entries[str] = entries0[str])) subst: [entries0, entries] → [abs-children(ino, fs, ri), entries] flags: <all paths>

Additional information

Used terms: abs-children(ino, fs, ri), entries