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Proof step 9 from proof ri-cons-inj (previous step)

fs[ri[key0]].key = key, ri[key] = ri[key0], key-cons(key0, fs[ri[key0]]), ri[key0] ∈ fs, key0 ∈ ri, key ∈ ri, key.inode? → fs[ri[key0]].inode? ∧ key.ino ≠ 0, key.dentry? → fs[ri[key0]].dentry?, key.data? → fs[ri[key0]].data? ⊦ key = key0

User applied rule insert rewrite lemma

And obtained the following new goals

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[key0]], key0] flags: <all paths>

Additional information

Used terms: fs[ri[key0]], key0