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Proof step 6 from proof abs-dirs-deldatakeys-2 (previous step)

inodekey(ino) ∈ ri ⊦ (fs[ri[inodekey(ino)]].directory ↔ fs[(ri \ datakeys(key, n, ri))[inodekey(ino)]].directory) ∧ ( fs[ri[inodekey(ino)]].directory → mkdir (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, fs[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri)) = mkdir (fs[(ri \ datakeys(key, n, ri))[inodekey(ino)]].size, fs[(ri \ datakeys(key, n, ri))[inodekey(ino)]].meta, fs[(ri \ datakeys(key, n, ri))[inodekey(ino)]].nlink, fs[(ri \ datakeys(key, n, ri))[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri \ datakeys(key, n, ri))))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store+set, inst: node-index name: Diff-get seq: ⊦ ¬ key ∈ ks → (ri \ ks)[key] = ri[key] subst: [key, ks, ri] → [inodekey(ino), datakeys(key, n, ri), ri] flags: <all paths>

Additional information

Used simplifier rules: ⊦ key ∈ datakeys(key0, n, ri) ↔ key ∈ datakeys(key0, ri) ∧ n ≤ key.part * VFS_PAGE_SIZE; (s)%⊦ key ∈ datakeys(key0, ri) ↔ key ∈ ri ∧ key.data? ∧ key0.inode? ∧ key.ino = key0.ino; (s)% ⊦ ¬ inodekey(m).data?; (s) Used terms: inodekey(ino), datakeys(key, n, ri), ri