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Proof step 8 from proof abs-dirs-unused-adrs (previous step)

ri[inodekey(ino)] ∈ as, ∀ adr. ¬ adr ∈ range ri ∩ as ⊦ # as = 0, as = ∅, (inodekey(ino) ∈ ri → (fs[ri[inodekey(ino)]].directory ↔ (∅)[ri[inodekey(ino)]].directory)) ∧ ( inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → mkdir (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, fs[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri)) = mkdir ((∅)[ri[inodekey(ino)]].size, (∅)[ri[inodekey(ino)]].meta, (∅)[ri[inodekey(ino)]].nlink, (∅)[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs \ as, ri)))

User applied rule all left

And obtained the following new goals

Proof step 9:
ri[inodekey(ino)] ∈ as, ∀ adr. ¬ adr ∈ range ri ∩ as ⊦ # as = 0, as = ∅, ri[inodekey(ino)] ∈ range ri ∩ as, (inodekey(ino) ∈ ri → (fs[ri[inodekey(ino)]].directory ↔ (∅)[ri[inodekey(ino)]].directory)) ∧ ( inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → mkdir (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, fs[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri)) = mkdir ((∅)[ri[inodekey(ino)]].size, (∅)[ri[inodekey(ino)]].meta, (∅)[ri[inodekey(ino)]].nlink, (∅)[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs \ as, ri)))

Rule argument

pos: left 2 terms: ri[inodekey(ino)] abort: F discard: F computed: T

Additional information

Used terms: ri[inodekey(ino)]