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Proof step 21 from proof repalyone-monotonic (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
datanode(key0, buf) = fs[adr], inodekey(key0.ino) ∈ ri0, ∀ key. key ∈ ri0 → key ∈ ri1 ⊦ key0 ∈ ri0, key0 ∈ ri1, inodekey(key0.ino) ∈ ri1

Rule argument

Additional information

Used simplifier rules: ⊦ key ∈ ri[key0, adr] ↔ key = key0 ∨ key ∈ ri; (ws)