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Proof step 17 from proof abs-files-orphans (previous step)

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))), (datakey(ino, n) ∈ ri \ orphans(fs, ri) → datakey(ino, n) ∈ ri) ∧ (datakey(ino, n) ∈ ri → fs[ri[datakey(ino, n)]].data = fs[(ri \ orphans(fs, ri))[datakey(ino, n)]].data)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 18:
inodekey(ino) ∈ ri, datakey(ino, n) ∈ ri ⊦ fs[ri[inodekey(ino)]].directory, (datakey(ino, n) ∈ ri \ orphans(fs, ri) → datakey(ino, n) ∈ ri) ∧ (datakey(ino, n) ∈ ri → fs[ri[datakey(ino, n)]].data = fs[(ri \ orphans(fs, ri))[datakey(ino, n)]].data), (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

Rule argument

fma: datakey(ino, n) ∈ ri

Additional information

Used simplifier rules: ⊦ key ∈ ri \ ks ↔ key ∈ ri ∧ ¬ key ∈ ks; (ws) Used formulas: datakey(ino, n) ∈ ri