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Proof step 2 from proof fsync-others-unchanged (previous step)

files = files0, icache = icache0, pcache = pcache0, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), valid-file-inode(inode, dirs, files) ⊦ [cache_fsync#(inode, bv, bv0; dirs, files, icache, pcache, asynced; err)] ∀ ino. ino ≠ inode.ino ∧ ino ∈ files0 → ino ∈ files ∧ ((files ⊕ pcache) ⊕ icache)[ino] = ((files0 ⊕ pcache0) ⊕ icache0)[ino]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
inode.nlink = files0[inode.ino].nlink, inode.nsubdirs = 0, files = files0, icache = icache0, pcache = pcache0, afs-cons(dirs, files0), dcache-cons(dcache, dirs, files0), icache-cons(icache0, dirs, files0), pcache-cons(pcache0, dirs, files0), synced(dirs, icache0, pcache0), inode.ino ∈ files0, ¬ inode.directory ⊦ [cache_fsync#(inode, bv, bv0; dirs, files, icache, pcache, asynced; err)] ∀ ino. ino ≠ inode.ino ∧ ino ∈ files0 → ino ∈ files ∧ ((files ⊕ pcache) ⊕ icache)[ino] = ((files0 ⊕ pcache0) ⊕ icache0)[ino]

Rule argument

Additional information

Used simplifier rules: ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)