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Proof step 9 from proof abs-files-orphans (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
inodekey(ino) ∈ ri ⊦ fs[ri[inodekey(ino)]].directory, fs[ri[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO, (¬ fs[(ri \ orphans(fs, ri))[inodekey(ino)]].directory ↔ fs[ri[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO) ∧ ( inodekey(ino) ∈ ri \ orphans(fs, ri) ∧ ¬ fs[(ri \ orphans(fs, ri))[inodekey(ino)]].directory → mkfile (fs[(ri \ orphans(fs, ri))[inodekey(ino)]].size, fs[(ri \ orphans(fs, ri))[inodekey(ino)]].meta, fs[(ri \ orphans(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: in-files: ⊦ ino ∈ abs-files(fs, ri) ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory;%abs-keys: ⊦ n ∈ abs-keys(ks) ↔ inodekey(n) ∈ ks;%at-files: ⊦ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory → abs-files(fs, ri)[ino] = abs-file(ino, fs, ri);%file: ⊦ abs-file(ino, fs, ri) = mkfile (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, abs-content(ino, fs, ri));% ⊦ key ∈ ri \ ks ↔ key ∈ ri ∧ ¬ key ∈ ks; (ws)% ⊦ 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)