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Proof step 7 from proof inv-truncate-buff-none-cached (previous step)

files[m] = mkfile(m0, md0, # links(m, dirs), content), buf-opt = none, inode = mkinode(m, md, false, # links(m, dirs), 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, asynced → synced(files, icache, pcache) ⊦ ⟪cache_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt, inode, asynced0, err, dirs, files, asynced1, icache, pcache)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)))

User applied rule call right

And obtained the following new goals

Proof step 8:
asynced4 ↔ asynced0, asynced3 ↔ asynced1, files[m] = mkfile(m0, md0, # links(m, dirs), content), buf-opt = none, inode = mkinode(m, md, false, # links(m, dirs), 0, m2), pageno = m2 / VFS_PAGE_SIZE, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), datakey(m, m2 / VFS_PAGE_SIZE) ∈ pcache, m ∈ files, asynced → synced(files, icache, pcache) ⊦ ⟪if pre-truncate(inode, n, pageno, buf-opt, dirs, files) then let ino = inode.ino, size = inode.size, asynced2 = buf-opt.some?, asynced1 = false, asynced0 = false in {err := ESUCCESS; if buf-opt.none? then let buf = ? in {pcache_check_page#(ino, pageno, pcache; asynced1, asynced0, err); if err = ESUCCESS ∧ asynced1 then pcache_get#(ino, pageno, pcache; asynced1, buf, err); if err = ESUCCESS ∧ asynced1 then buf-opt := some(buf)}; if err = ESUCCESS then afs_truncate#(n, pageno; buf-opt, inode, asynced4, err, dirs, files, asynced3); if err = ESUCCESS then let asynced = false in {icache_set#(inode, asynced; err, icache); pcache_truncate#(inode.ino, size, n; err, pcache); if asynced4 then pcache_set#(inode.ino, pageno, buf-opt.buf, asynced; err, pcache)}; if (¬ asynced4 ∨ err ≠ ESUCCESS) ∧ ¬ asynced2 then buf-opt := none} else abort⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache))), VFS_PAGE_SIZE = 0

Rule argument

pos: right 1

Additional information

Used simplifier rules: truncate: ⊦ ;% ⊦ VFS_PAGE_SIZE ≠ 0; (s)