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Proof step 1 from proof abs-files-del-orphans (conclusion)

⊦ abs-files(fs, ri ⊖ orphans(fs, ri)) = abs-files(fs, ri) \ abs-keys(orphans(fs, ri))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ ( 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) ∧ ( inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory ∧ (fs[ri[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO) → (abs-files(fs, ri) \ abs-keys(orphans(fs, ri)))[ino] = 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))))

Rule argument

Additional information

Used simplifier rules: F-ext: ⊦ files = abs-files(fs, ri) ↔ (∀ ino. ( ino ∈ files ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory) ∧ (ino ∈ files → files[ino] = abs-file(ino, fs, ri)));%in-files: ⊦ ino ∈ abs-files(fs, ri) ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory;%abs-keys: ⊦ n ∈ abs-keys(ks) ↔ inodekey(n) ∈ ks;%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));% ⊦ 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)% ⊦ ino ∈ files \ ns ↔ ino ∈ files ∧ ¬ ino ∈ ns; (s)