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Proof step 23 from proof fsync-others-unchanged (previous step)

files0[m] = mkfile(m0, md0, # links(m, dirs), content), 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 ⊦ ∀ 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]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
# links(m, dirs) = files1[m].nlink, files0[m] = mkfile(m0, md0, files1[m].nlink, content), afs-cons(dirs, files1), afs-cons(dirs, files0), dcache-cons(dcache, dirs, files1), dcache-cons(dcache, dirs, files0), icache-cons(icache0, dirs, files1), icache-cons(icache0, dirs, files0), pcache-cons(pcache1, dirs, files1), pcache-cons(pcache0, dirs, files0), synced(dirs, icache0, pcache1), synced(dirs, icache0, pcache0), m ∈ files1, m ∈ files0, ∀ ino. ino ≠ m ∧ ino ∈ files0 → ino ∈ files1 ∧ mkfile(files1[ino].size, files1[ino].meta, files1[ino].nlink, files1[ino].content ⊕ mkcontent(ino, pcache1)) = mkfile(files0[ino].size, files0[ino].meta, files0[ino].nlink, files0[ino].content ⊕ mkcontent(ino, pcache0)) ⊦ [inode := mkinode(m, md, false, files1[m].nlink, 0, m2); icache := icache0; 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)] ∀ ino. ino ≠ m ∧ ino ∈ files0 → ino ∈ files1 ∧ ((files1 ⊕ pcache1) ⊕ icache)[ino] = ((files0 ⊕ pcache0) ⊕ icache0)[ino]

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