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Proof step 23 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, inodekey(m) ∈ ro, datakey(m, m0) ∈ ro, inodekey(m) ∈ ro ++ inodekey(ino), datakey(m, m0) ∈ ro ++ inodekey(ino)

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

Rule argument

Additional information

Used simplifier rules: ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)% ⊦ inodekey(m) ≠ datakey(m0, m1); (s)% ⊦ ¬ key ∈ ks → (key ∈ ks ++ key0 ↔ key = key0); (s)