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Proof step 17 from proof repalyone-monotonic (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
datanode(key0, buf) = fs[adr], inodekey(key0.ino) ∈ ri1, key ∈ (inodekey(key0.ino) ∈ ri0 ⊃ ri0[key0, adr];ri0), ∀ key. key ∈ ri0 → key ∈ ri1 ⊦ key = key0, key ∈ ri1, key ∈ ri0

Rule argument

Additional information

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