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Proof step 6 from proof fsync-pages-inv (previous step)

files[m] = mkfile(m1, md0, m3, content), m0 = m3, 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, m3, 0, m2), 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) ∧ m ∈ files ∧ m0 = files[m].nlink)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
files[m] = mkfile(m1, md0, # links(m, dirs), content), 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)⟫ ( 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)

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