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Proof step 15 from proof repalyone-monotonic (previous step)

datanode(key0, buf) = 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 16:
datanode(key0, buf) = fs[adr], key ∈ (inodekey(key0.ino) ∈ ri0 ⊃ ri0[key0, adr];ri0), key ∈ ri0 → key ∈ ri1, ∀ key. key ∈ ri0 → key ∈ ri1 ⊦ key ∈ (inodekey(key0.ino) ∈ ri1 ⊃ ri1[key0, adr];ri1)

Rule argument

Additional information

Used simplifier rules: replay-data: ⊦ replay-one(adr, datanode(key, buf), ri) = (inodekey(key.ino) ∈ ri ⊃ ri[key, adr];ri);