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Proof step 1 from proof F-ext (conclusion)

⊦ 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)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
∀ 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))) ⊦ files = abs-files(fs, ri)

Rule argument

Additional information

Used simplifier rules: 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));