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Proof step 20 from proof fsync-keep-abs (previous step)

files[m] = mkfile(m1, md1, # links(m, dirs), content0), err = ESUCCESS, files0 = (files ⊕ pcache) ⊕ icache, 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 ⊦ ∀ 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) ∧ m ∈ files ∧ # links(m, dirs) = files[m].nlink → files0 = (files ⊕ pcache) ⊕ icache → [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)] (files0 = (files ⊕ pcache) ⊕ icache)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
# links(m, dirs) = files1[m].nlink, files[m] = mkfile(m1, md1, files1[m].nlink, content0), files0 = (files ⊕ pcache) ⊕ icache, (files1 ⊕ pcache0) ⊕ icache = (files ⊕ pcache) ⊕ icache, afs-cons(dirs, files1), afs-cons(dirs, files), dcache-cons(dcache, dirs, files1), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files1), icache-cons(icache, dirs, files), pcache-cons(pcache0, dirs, files1), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache0), synced(dirs, icache, pcache), m ∈ files1, m ∈ files ⊦ [inode := mkinode(m, md, false, files1[m].nlink, 0, m2); if err0 = ESUCCESS ∧ ¬ asynced1 then cache_fsync-inode#(; inode, err0, dirs, files1, icache, asynced); if err0 = ESUCCESS then afs_fsync#(inode, asynced1, dirs, files1; ; asynced, err0)] (files0 = (files1 ⊕ pcache0) ⊕ icache)

Rule argument

Additional information

Used simplifier rules: afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base