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Proof step 14 from proof abs-files-orphans (previous step)

inodekey(ino) ∈ ri, inodekey(ino) ∈ ri \ orphans(fs, ri) ⊦ fs[ri[inodekey(ino)]].directory, (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))), fs[ri[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
inodekey(ino) ∈ ri ⊦ 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)))

Rule argument

Additional information

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