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Proof step 27 from proof replay-cons-add-orphan (previous step)

log-cons(log, fs), replay-safe(log, fs, fi ⊖ fo), datakey(m, m0) ∈ ri ⊦ ri[datakey(m, m0)] = ((ri ⊖ inodekey(ino)) ⊖ ro)[datakey(m, m0)], m = ino, datakey(m, m0) ∈ ro, inodekey(m) ∈ ro, datakey(m, m0) ∈ ri ⊖ inodekey(ino)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: aubifs-base name: in-del-ro seq: ⊦ key ∈ ri ⊖ key0 ↔ key ∈ ri ∧ key ≠ key0 ∧ (key.data? → inodekey(key.ino) ≠ key0) subst: [key0, ri, key] → [inodekey(ino), ri, datakey(m, m0)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ inodekey(m) ≠ datakey(m0, m1); (s)% ⊦ datakey(m, m0).data?; (s)% ⊦ datakey(m, m0).ino = m; (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s) Used terms: inodekey(ino), ri, datakey(m, m0)