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Proof step 23 from proof replay-cons-add-page (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
log-cons(log, fs), replay-safe(log, fs, fi ⊖ fo), datakey(m, m0) ∈ ri ⊦ (ri ⊖ (ro ++ datakey(ino, n)))[datakey(m, m0)] = ri[datakey(m, m0)], datakey(m, m0) = datakey(ino, n), datakey(m, m0) ∈ ro, inodekey(m) ∈ ro

Rule argument

Additional information

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