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Proof step 5 from proof abs-dirs-drop (previous step)

⊦ ri[inodekey(ino)] ∈ ri, (inodekey(ino) ∈ ri → (fs[ri[inodekey(ino)]].directory ↔ nd.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(nd.size, nd.meta, nd.nlink, nd.nsubdirs, abs-children(ino, fs[ri[inodekey(ino)], nd], ri)))

User applied rule case distinction

And closed the goal!

Rule argument

pos: right 2

Additional information

Used simplifier rules: D-inj: ⊦ mkdir(n0, md0, m0, m1, entries0) = mkdir(n1, md1, m2, m3, entries1) ↔ ¬(md0 ≠ md1 ∨ n0 ≠ n1 ∨ m0 ≠ m2 ∨ m1 ≠ m3 ∨ entries0 ≠ entries1);%key ∈ ri ⊦ ri[key] ∈ ri; (s)