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Proof step 13 from proof fsync-others-unchanged (previous step)

# links(m, dirs) = m3, files0[m] = mkfile(m0, md0, m3, content), files0[m] = mkfile(m1, md1, m3, 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, m3, 0, m2), dirs; err, files, pcache, asynced); 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 14:
files0[m] = mkfile(m1, md1, # links(m, dirs), 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, # links(m, dirs), 0, m2), dirs; err, files, pcache, asynced); 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: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)