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Proof step 32 from proof replay-cons-add-page (previous step)

log-cons(log, fs), replay-safe(log, fs, fi ⊖ fo) ⊦ key ∈ ri ⊖ (ro ++ datakey(ino, n)) ↔ key ∈ ri -- datakey(ino, n) ∧ ¬ key ∈ ro ∧ (key.data? → ¬ inodekey(key.ino) ∈ ro)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: aubifs-base name: in-dels-ro seq: ⊦ key ∈ ri ⊖ ks ↔ key ∈ ri ∧ ¬ key ∈ ks ∧ (key.data? → ¬ inodekey(key.ino) ∈ ks) subst: [ks, ri, key] → [ro ++ datakey(ino, n), ri, key] flags: <all paths>

Additional information

Used simplifier rules: ⊦ key ∈ ks ++ key0 ↔ key = key0 ∨ key ∈ ks; (s)% ⊦ inodekey(m) ≠ datakey(m0, m1); (s)% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)% ⊦ key ≠ key0 → (key ∈ ks ++ key0 ↔ key ∈ ks); (s) Used terms: ro ++ datakey(ino, n), ri, key