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Proof step 13 from proof repalyone-monotonic (previous step)

dentrynode(key0, ino) = fs[adr], key ∈ replay-one(adr, fs[adr], ri0), key ∈ ri0 → key ∈ ri1, ∀ key. key ∈ ri0 → key ∈ ri1 ⊦ key ∈ replay-one(adr, fs[adr], ri1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
dentrynode(key0, ino) = fs[adr], key ∈ (ino ≠ 0 ⊃ ri0[key0, adr];ri0 -- key0), key ∈ ri0 → key ∈ ri1, ∀ key. key ∈ ri0 → key ∈ ri1 ⊦ key ∈ (ino ≠ 0 ⊃ ri1[key0, adr];ri1 -- key0)

Rule argument

Additional information

Used simplifier rules: replay-dentry: ⊦ replay-one(adr, dentrynode(key, ino), ri) = (ino ≠ 0 ⊃ ri[key, adr];ri -- key);