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Proof step 19 from proof abs-files-orphans (previous step)

datakey(ino, n) ∈ ri, inodekey(ino) ∈ ri ⊦ fs[ri[datakey(ino, n)]].data = fs[(ri \ orphans(fs, ri))[datakey(ino, n)]].data, fs[ri[inodekey(ino)]].directory, fs[ri[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO, (fs[ri[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO) ∧ ( inodekey(ino) ∈ ri \ orphans(fs, ri) → mkfile(fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, abs-content(ino, fs, ri \ orphans(fs, ri))) = mkfile(fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, abs-content(ino, fs, ri)))

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: datakey(ino, n) ∈ orphans(fs, ri)

Additional information

Used simplifier rules: ⊦ ¬ key ∈ ks → (ri \ ks)[key] = ri[key]; (s)% ⊦ key ∈ ks → (ri \ ks)[key] = (∅)[key]; (s)%⊦ key ∈ orphans(fs, ri) ↔ key.inode? ∧ key ∈ ri ∧ fs[ri[key]].nlink = 0 ∧ key.ino ≠ ROOT_INO; (s)% ⊦ ¬ datakey(m, m0).inode?; (s) Used formulas: datakey(ino, n) ∈ orphans(fs, ri)