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Proof step 13 from proof replay-orphans-del (previous step)

datakey(m, m0) ∈ ri ⊦ ri[datakey(m, m0)] = ((ri -- key) ⊖ ro)[datakey(m, m0)], datakey(m, m0) = key, key ∈ 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 -- key] flags: <all paths>

Additional information

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