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Proof step 5 from proof abs-dirs-del-dentry (previous step)

fs[ri[inodekey(ino)]].directory, fs[ri[inodekey(ino0)]].directory, inodekey(ino) ∈ ri, inodekey(ino0) ∈ ri ⊦ ino = 0, ino0 = ino, (dentrykey(ino0, str0) ∈ ri → dentrykey(ino0, str0) ≠ dentrykey(ino, str)) ∧ ( dentrykey(ino0, str0) ≠ dentrykey(ino, str) ∧ dentrykey(ino0, str0) ∈ ri → abs-children(ino0, fs, ri -- dentrykey(ino, str))[str0] = fs[ri[dentrykey(ino0, str0)]].ino)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 6:
fs[ri[inodekey(ino0)]].directory, fs[ri[inodekey(ino)]].directory, inodekey(ino0) ∈ ri, inodekey(ino) ∈ ri, dentrykey(ino0, str0) ∈ ri -- dentrykey(ino, str) ⊦ ino = 0, ino0 = ino, (dentrykey(ino0, str0) ∈ ri → dentrykey(ino0, str0) ≠ dentrykey(ino, str)) ∧ ( dentrykey(ino0, str0) ≠ dentrykey(ino, str) ∧ dentrykey(ino0, str0) ∈ ri → abs-children(ino0, fs, ri -- dentrykey(ino, str))[str0] = fs[ri[dentrykey(ino0, str0)]].ino)

Rule argument

fma: dentrykey(ino0, str0) ∈ ri -- dentrykey(ino, str)

Additional information

Used simplifier rules: ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)% ⊦ dentrykey(m, str) = dentrykey(m0, str0) ↔ m = m0 ∧ str = str0; (ws) Used formulas: dentrykey(ino0, str0) ∈ ri -- dentrykey(ino, str)