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Proof step 23 from proof in-ri-update-in-ri (previous step)

# ax1 = # ax0, key-cons(key, fs[ri[key]]), key ∈ ri, ri[key] ∈ fs, ax1.toSet ⊆ range ri ⊦ fs[ri[key]].key ∈ keys(fs, ax1), fs[ri[key]].key ∈ ri

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
⊦ key-cons(key, nd) ↔ nd.key = key ∧ (key.inode? → nd.inode? ∧ key.ino ≠ 0) ∧ (key.dentry? → nd.dentry?) ∧ (key.data? → nd.data?)

Rule argument

spec: <toplevel> name: key-cons seq: ⊦ key-cons(key, nd) ↔ nd.key = key ∧ (key.inode? → nd.inode? ∧ key.ino ≠ 0) ∧ (key.dentry? → nd.dentry?) ∧ (key.data? → nd.data?) subst: [nd, key] → [fs[ri[key]], key] flags: <all paths>

Additional information

Used terms: fs[ri[key]], key