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Proof step 28 from proof inv-fsync (previous step)

# links(m, dirs) = m4, files[m] = mkfile(m1, md1, m4, content0), files0[m] = mkfile(m0, md0, m4, content), files0[m] = mkfile(m3, md2, m4, content1), err0 = ESUCCESS, inode = mkinode(m, md, false, m4, 0, m2), afs-cons(dirs, files), afs-cons(dirs, files0), dcache-cons(dcache, dirs, files), dcache-cons(dcache, dirs, files0), icache-cons(icache, dirs, files), icache-cons(icache, dirs, files0), pcache-cons(pcache, dirs, files), pcache-cons(pcache0, dirs, files0), synced(dirs, icache, pcache), synced(dirs, icache, pcache0), m ∈ files0, m ∈ files ⊦ [cache_fsync-inode#(; inode, err0, dirs, files0, icache, asynced)] ( icache-cons(icache, dirs, files0) ∧ dcache-cons(dcache, dirs, files0) ∧ pcache-cons(pcache0, dirs, files0) ∧ afs-cons(dirs, files0) ∧ synced(dirs, icache, pcache0) ∧ inode.ino ∈ files0 ∧ inode.nlink = files0[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory → ⟪if err0 = ESUCCESS then afs_fsync#(inode, false, dirs, files0; ; asynced, err0)⟫ true)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
files0[m] = mkfile(m3, md2, # links(m, dirs), content1), files[m] = mkfile(m1, md1, # links(m, dirs), content0), err0 = ESUCCESS, inode = mkinode(m, md, false, # links(m, dirs), 0, m2), afs-cons(dirs, files0), afs-cons(dirs, files), dcache-cons(dcache, dirs, files0), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files0), icache-cons(icache, dirs, files), pcache-cons(pcache0, dirs, files0), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache0), synced(dirs, icache, pcache), m ∈ files, m ∈ files0 ⊦ [cache_fsync-inode#(; inode, err0, dirs, files0, icache, asynced)] ( icache-cons(icache, dirs, files0) ∧ dcache-cons(dcache, dirs, files0) ∧ pcache-cons(pcache0, dirs, files0) ∧ afs-cons(dirs, files0) ∧ synced(dirs, icache, pcache0) ∧ inode.ino ∈ files0 ∧ inode.nlink = files0[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory → ⟪if err0 = ESUCCESS then afs_fsync#(inode, false, dirs, files0; ; asynced, err0)⟫ true)

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)