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Proof step 2 from proof abs-files-unused-adrs (previous step)

range ri ∩ as = ∅ ⊦ abs-files(fs \ as, ri) = abs-files(fs, ri)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
range ri ∩ as = ∅ ⊦ (inodekey(ino) ∈ ri → (¬ fs[ri[inodekey(ino)]].directory ↔ ¬ (fs \ as)[ri[inodekey(ino)]].directory)) ∧ ( inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory → mkfile(fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, abs-content(ino, fs, ri)) = mkfile ((fs \ as)[ri[inodekey(ino)]].size, (fs \ as)[ri[inodekey(ino)]].meta, (fs \ as)[ri[inodekey(ino)]].nlink, abs-content(ino, fs \ as, 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;%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));