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Proof step 4 from proof F-ext (previous step)

∀ ino. (ino ∈ files ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory) ∧ (ino ∈ files → files[ino] = mkfile(fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, abs-content(ino, fs, ri))) ⊦ ∀ ino. (ino ∈ files ↔ ino ∈ abs-files(fs, ri)) ∧ (ino ∈ files → files[ino] = abs-files(fs, ri)[ino])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: in-files: ⊦ ino ∈ abs-files(fs, ri) ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory;