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Proof step 12 from proof inv-fsync (previous step)

files[m] = mkfile(m0, md0, # links(m, dirs), content), err = ESUCCESS, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ files ⊦ ⟪cache_fsync-pages#(mkinode(m, md, false, # links(m, dirs), 0, m2), dirs; err, files, pcache, asynced); inode := mkinode(m, md, false, # links(m, dirs), 0, m2); if err = ESUCCESS ∧ ¬ asynced1 then cache_fsync-inode#(; inode, err, dirs, files, icache, asynced); if err = ESUCCESS then afs_fsync#(inode, asynced1, dirs, files; ; asynced, err)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ afs-cons(dirs, files))

User applied rule insert program lemma

And obtained the following new goals

Proof step 13:
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-pages#(inode, dirs; err, files, pcache, 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 14:
files[m] = mkfile(m0, md0, # links(m, dirs), content), dcache0 = dcache, dirs0 = dirs, err = ESUCCESS, icache0 = icache, inode0 = mkinode(m, md, false, # links(m, dirs), 0, m2), 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(mkinode(m, md, false, # links(m, dirs), 0, m2), dirs, files), m ∈ files ⊦ [cache_fsync-pages#(mkinode(m, md, false, # links(m, dirs), 0, m2), dirs; err, files, pcache, asynced)] ( icache-cons(icache0, dirs0, files) ∧ dcache-cons(dcache0, dirs0, files) ∧ pcache-cons(pcache, dirs0, files) ∧ afs-cons(dirs0, files) ∧ synced(dirs0, icache0, pcache) ∧ valid-file-inode(inode0, dirs0, files) → ⟪inode := mkinode(m, md, false, # links(m, dirs), 0, m2); if err = ESUCCESS ∧ ¬ asynced1 then cache_fsync-inode#(; inode, err, dirs, files, icache, asynced); if err = ESUCCESS then afs_fsync#(inode, asynced1, dirs, files; ; asynced, err)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ afs-cons(dirs, files)))

Rule argument

spec: <toplevel> name: fsync-pages-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-pages# (inode, dirs; err, files, pcache, 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: [dirs, inode, asynced, pcache, files, err, icache, dcache] → [dirs, mkinode(m, md, false, # links(m, dirs), 0, m2), asynced, pcache, files, err, icache, dcache] 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)