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Proof step 26 from proof inv-fsync (previous step)

files[m] = mkfile(m1, md1, # links(m, dirs), content0), files0[m] = mkfile(m0, md0, # links(m, dirs), content), dcache0 = dcache, err0 = ESUCCESS, inode = mkinode(m, md, false, # links(m, dirs), 0, m2), pcache1 = pcache0, 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), valid-file-inode(inode, dirs, files0), m ∈ files0, m ∈ files ⊦ [cache_fsync-inode#(; inode, err0, dirs, files0, icache, asynced)] ( icache-cons(icache, dirs, files0) ∧ dcache-cons(dcache0, dirs, files0) ∧ pcache-cons(pcache1, dirs, files0) ∧ afs-cons(dirs, files0) ∧ synced(dirs, icache, pcache1) ∧ valid-file-inode(inode, dirs, files0) → ⟪if err0 = ESUCCESS then afs_fsync#(inode, false, dirs, files0; ; asynced, err0)⟫ ( icache-cons(icache, dirs, files0) ∧ dcache-cons(dcache, dirs, files0) ∧ pcache-cons(pcache0, dirs, files0) ∧ synced(dirs, icache, pcache0) ∧ afs-cons(dirs, files0)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
# links(m, dirs) = files0[m].nlink, files0[m] = mkfile(m0, md0, files0[m].nlink, content), files[m] = mkfile(m1, md1, files0[m].nlink, content0), err0 = ESUCCESS, inode = mkinode(m, md, false, files0[m].nlink, 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: ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (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)