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Proof step 19 from proof fsync-others-unchanged (previous step)

files0[m] = mkfile(m1, md1, # links(m, dirs), content0), dcache0 = dcache, dirs0 = dirs, err = ESUCCESS, files = files0, icache1 = icache0, inode0 = mkinode(m, md, false, # links(m, dirs), 0, m2), pcache = pcache0, afs-cons(dirs, files0), afs-cons(dirs, files), dcache-cons(dcache, dirs, files0), dcache-cons(dcache, dirs, files), icache-cons(icache0, dirs, files0), icache-cons(icache0, dirs, files), pcache-cons(pcache0, dirs, files0), pcache-cons(pcache, dirs, files), synced(dirs, icache0, pcache0), synced(dirs, icache0, pcache), valid-file-inode(mkinode(m, md, false, # links(m, dirs), 0, m2), dirs, files), m ∈ files0 ⊦ [cache_fsync-pages#(mkinode(m, md, false, # links(m, dirs), 0, m2), dirs; err, files, pcache, asynced)] ( icache-cons(icache1, dirs0, files) ∧ dcache-cons(dcache0, dirs0, files) ∧ pcache-cons(pcache, dirs0, files) ∧ afs-cons(dirs0, files) ∧ synced(dirs0, icache1, pcache) ∧ valid-file-inode(inode0, dirs0, files) → (∀ ino. ino ≠ m ∧ ino ∈ files0 → ino ∈ files ∧ mkfile(files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)) = mkfile(files0[ino].size, files0[ino].meta, files0[ino].nlink, files0[ino].content ⊕ mkcontent(ino, pcache0))) → [inode := mkinode(m, md, false, # links(m, dirs), 0, m2); icache := icache0; 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)] ∀ ino. ino ≠ m ∧ 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 20:
# links(m, dirs) = files0[m].nlink, files0[m] = mkfile(m1, md1, files0[m].nlink, content0), err = ESUCCESS, files = files0, 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), m ∈ files0 ⊦ [cache_fsync-pages#(mkinode(m, md, false, files0[m].nlink, 0, m2), dirs; err, files, pcache, asynced)] ( icache-cons(icache0, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache0, pcache) ∧ m ∈ files ∧ # links(m, dirs) = files[m].nlink → (∀ ino. ino ≠ m ∧ ino ∈ files0 → ino ∈ files ∧ mkfile(files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)) = mkfile(files0[ino].size, files0[ino].meta, files0[ino].nlink, files0[ino].content ⊕ mkcontent(ino, pcache0))) → [inode := mkinode(m, md, false, # links(m, dirs), 0, m2); icache := icache0; 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)] ∀ ino. ino ≠ m ∧ ino ∈ files0 → ino ∈ files ∧ ((files ⊕ pcache) ⊕ icache)[ino] = ((files0 ⊕ pcache0) ⊕ icache0)[ino])

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)