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Proof step 21 from proof replay-orphans-data (previous step)

datakey(m, m0) ∈ ri ⊦ ri[datakey(m, m0)] = (ri[datakey(ino, n), adr] ⊖ ro)[datakey(m, m0)], datakey(m, m0) = datakey(ino, n), datakey(ino, n) ∈ ro, inodekey(ino) ∈ ro, datakey(m, m0) ∈ ro, inodekey(m) ∈ ro

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: aubifs-base name: at-dels-ro-data seq: ⊦ datakey(ino, n) ∈ ri ∧ ¬ datakey(ino, n) ∈ ks ∧ ¬ inodekey(ino) ∈ ks → (ri ⊖ ks)[datakey(ino, n)] = ri[datakey(ino, n)] subst: [n, ino, ks, ri] → [m0, m, ro, ri[datakey(ino, n), adr]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ key ≠ key0 → ri[key0, adr][key] = ri[key]; (s)% ⊦ key ≠ key0 → (key ∈ ri[key0, adr] ↔ key ∈ ri); (s) Used terms: m0, m, ro, ri[datakey(ino, n), adr]