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Proof step 24 from proof inv-fsync (previous step)

files0[m] = mkfile(m0, md0, # links(m, dirs), content), files[m] = mkfile(m1, md1, # links(m, dirs), content0), err0 = ESUCCESS, inode = mkinode(m, md, false, # links(m, dirs), 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 ∈ files, m ∈ files0 ⊦ ⟪cache_fsync-inode#(; inode, err0, dirs, files0, icache, asynced); 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))

User applied rule insert program lemma

And obtained the following new goals

Proof step 25:
valid-file-inode(inode, dirs, files), icache-cons(icache, dirs, files), dcache-cons(dcache, dirs, files), pcache-cons(pcache, dirs, files), afs-cons(dirs, files), synced(dirs, icache, pcache) ⊦ ⟪cache_fsync-inode#(; inode, err, dirs, files, icache, asynced)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache, pcache) ∧ valid-file-inode(inode, dirs, files))
Proof step 26:
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)))

Rule argument

spec: <toplevel> name: fsync-inode-inv seq: valid-file-inode(inode, dirs, files), icache-cons(icache, dirs, files), dcache-cons(dcache, dirs, files), pcache-cons(pcache, dirs, files), afs-cons(dirs, files), synced(dirs, icache, pcache) ⊦ ⟪cache_fsync-inode# (; inode, err, dirs, files, icache, asynced)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache, pcache) ∧ valid-file-inode(inode, dirs, files)) subst: [asynced, icache, files, dirs, err, inode, dcache, pcache] → [asynced, icache, files0, dirs, err0, inode, dcache, pcache0] flags: List([[1,0,0]])

Additional information

Used simplifier rules: ⊦ 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)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)