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Proof step 8 from proof del-del-again (previous step)

inodekey(m) ∈ ks, key ∈ ri, key.data? → key.ino ≠ m, key.data? → ¬ inodekey(key.ino) ∈ ks ⊦ # ks = 0, ((ri ⊖ ks) ⊖ inodekey(m))[key] = (ri ⊖ ks)[key], ks = ∅, key ∈ ks

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ key ∈ ri ∧ key ≠ key0 ∧ ¬ key.data? → (ri ⊖ key0)[key] = ri[key]
Proof step 10:
key ∈ ri, inodekey(m) ∈ ks, key.data? → ¬ inodekey(key.ino) ∈ ks, key.data? → key.ino ≠ m ⊦ # ks = 0, ((ri ⊖ ks) ⊖ inodekey(m))[key] = (ri ⊖ ks)[key], ks = ∅, key ∈ ks, key ∈ ri ⊖ ks ∧ key ≠ inodekey(m) ∧ ¬ key.data?

Rule argument

spec: <toplevel> name: at-del-ro-nodata seq: ⊦ key ∈ ri ∧ key ≠ key0 ∧ ¬ key.data? → (ri ⊖ key0)[key] = ri[key] subst: [key, key0, ri] → [key, inodekey(m), ri ⊖ ks] flags: <all paths>

Additional information

Used terms: key, inodekey(m), ri ⊖ ks