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

inodekey(m) ∈ ks, key ∈ ri[inodekey(m), adr], key ∈ ri, key.data? → ¬ inodekey(key.ino) ∈ ks ⊦ # ks = 0, (ri[inodekey(m), adr] ⊖ ks)[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 ∈ ks ∧ ¬ key.data? → (ri ⊖ ks)[key] = ri[key]
Proof step 10:
key ∈ ri, key ∈ ri[inodekey(m), adr], inodekey(m) ∈ ks, key.data? → ¬ inodekey(key.ino) ∈ ks ⊦ # ks = 0, (ri[inodekey(m), adr] ⊖ ks)[key] = (ri ⊖ ks)[key], ks = ∅, key ∈ ks, key ∈ ri[inodekey(m), adr] ∧ ¬ key ∈ ks ∧ ¬ key.data?
Proof step 15:
key ∈ ri, inodekey(m) ∈ ks, key ∈ ri[inodekey(m), adr], key.data? → ¬ inodekey(key.ino) ∈ ks ⊦ # ks = 0, ri[inodekey(m), adr][key] = (ri ⊖ ks)[key], ks = ∅, key.data?, key ∈ ks

Rule argument

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

Additional information

Used terms: key, ks, ri[inodekey(m), adr]