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Proof step 36 from proof inv-truncate-buff-none-uncached (previous step)

# links(m, dirs) = files[m].nlink, files[m] = mkfile(m1, md1, files[m].nlink, content0), buf-opt = none, err = ESUCCESS, inode = mkinode(m, md, false, files[m].nlink, 0, m2), 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, ¬ datakey(m, m2 / VFS_PAGE_SIZE) ∈ pcache, asynced2 → synced(files, icache, pcache) ⊦ [afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt, inode, asynced4, err, dirs, files, asynced3)] ( afs-cons(dirs, files) → ⟪if err = ESUCCESS then let asynced = false in {icache_set#(inode, asynced; err, icache); pcache_truncate#(inode.ino, m2, n; err, pcache); if asynced4 then pcache_set#(inode.ino, m2 / VFS_PAGE_SIZE, buf-opt.buf, asynced; err, pcache)}; if ¬ asynced4 ∨ err ≠ ESUCCESS then buf-opt := none⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced2 → synced(files, icache, pcache))))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 37:
# links(m, dirs) = m3, files[m] = mkfile(m1, md1, m3, content0), files[m] = mkfile(m0, md0, m3, content), buf-opt = none, err = ESUCCESS, inode = mkinode(m, md, false, m3, 0, m2), 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, asynced2 → synced(files, icache, pcache) ⊦ [afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt, inode, asynced4, err, dirs, files, asynced3)] ( afs-cons(dirs, files) → ⟪if err = ESUCCESS then let asynced = false in {icache_set#(inode, asynced; err, icache); pcache_truncate#(inode.ino, m2, n; err, pcache); if asynced4 then pcache_set#(inode.ino, m2 / VFS_PAGE_SIZE, buf-opt.buf, asynced; err, pcache)}; if ¬ asynced4 ∨ err ≠ ESUCCESS then buf-opt := none⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced2 → synced(files, icache, pcache)))), datakey(m, m2 / VFS_PAGE_SIZE) ∈ pcache

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files[m], m0, md0, m3, content]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files[m], m0, md0, m3, content