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Proof step 20 from proof ri-closed-gc-one (previous step)

fs[ri[key]] = dentrynode(key0, m), (∅)[ri[inodekey(key0.ino)]].directory, inodekey(m) ∈ ri[key, ri[inodekey(key0.ino)]], key ∈ ri, ri[key] ∈ fs, inodekey(key0.ino) ∈ ri, inodekey(m) ∈ ri, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ dentrynode(key0, m).directory, ri[inodekey(key0.ino)] ∈ fs, inodekey(m) ∈ ro, inodekey(key0.ino) ∈ ro

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 8 terms: inodekey(key0.ino)

Additional information

Used terms: inodekey(key0.ino)