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Proof step 3 from proof abs-dirs-del-dir (previous step)

fs[ri[inodekey(ino)]].directory, fs[ri[inodekey(ino0)]].directory, inodekey(ino) ∈ ri, inodekey(ino0) ∈ ri, dentrykey(ino0, str) ∈ ri ⊦ abs-children(ino0, fs, ri -- inodekey(ino))[str] = fs[ri[dentrykey(ino0, str)]].ino, ino0 = ino

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: dentrykey(ino0, str) ∈ ri -- inodekey(ino)

Additional information

Used simplifier rules: at-children: ⊦ dentrykey(ino, str) ∈ ri → abs-children(ino, fs, ri)[str] = fs[ri[dentrykey(ino, str)]].ino;% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)% ⊦ inodekey(m) ≠ dentrykey(m0, str); (s)%key ≠ key0 ⊦ (ri -- key0)[key] = ri[key]; (s) Used formulas: dentrykey(ino0, str) ∈ ri -- inodekey(ino)