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Proof step 13 from proof replay-drop-data (previous step)

inodekey(ino) ∈ ro, key.data? → ¬ inodekey(key.ino) ∈ ro, key = datakey(ino, n) ∨ key ∈ ri ⊦ # ro = 0, (ri[datakey(ino, n), adr] ⊖ ro)[key] = (ri ⊖ ro)[key], ro = ∅, key ∈ ro

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ key ∈ ri ∧ ¬ key ∈ ks ∧ ¬ key.data? → (ri ⊖ ks)[key] = ri[key]
Proof step 15:
inodekey(ino) ∈ ro, key.data? → ¬ inodekey(key.ino) ∈ ro, key = datakey(ino, n) ∨ key ∈ ri ⊦ # ro = 0, (ri[datakey(ino, n), adr] ⊖ ro)[key] = (ri ⊖ ro)[key], ro = ∅, key ∈ ro, key ∈ ri[datakey(ino, n), adr] ∧ ¬ key ∈ ro ∧ ¬ key.data?

Rule argument

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

Additional information

Used simplifier rules: ⊦ ri[key, adr][key] = adr; (s)% ⊦ key ∈ ri[key, adr]; (s)% ⊦ datakey(m, m0).data?; (s)% ⊦ key ≠ key0 → ri[key0, adr][key] = ri[key]; (s)% ⊦ key ∈ ri ∧ ¬ key ∈ ks ∧ ¬ key.data? → (ri ⊖ ks)[key] = ri[key]; (s) Used terms: key, ro, ri[datakey(ino, n), adr]