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Proof step 79 from proof inv-truncate-buff-none-cached (previous step)

# buf0 = VFS_PAGE_SIZE, pcache[datakey(m, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), files0[m] = mkfile(m1, md1, # links(m, dirs), content0), files = files0 [m, mkfile (m1, md1, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE - m2 % VFS_PAGE_SIZE)] upto m2) ], inode = mkinode(m, md, false, # links(m, dirs), 0, m2), m2 % VFS_PAGE_SIZE ≠ 0, afs-cons(dirs, files0), dcache-cons(dcache, dirs, files0), icache-cons(icache, dirs, files0), pcache-cons(pcache, dirs, files0), synced(dirs, icache, pcache), datakey(m, m2 / VFS_PAGE_SIZE) ∈ pcache, m ∈ files0, m2 ≤ n, asynced2 → synced(files0, icache, pcache) ⊦ [afs_inode_sync#(mkinode(m, md, false, # links(m, dirs), 0, n); dirs, files); inode0 := (inode.ino ∈ dirs ⊃ mkinode(inode.ino, dirs[inode.ino].meta, true, dirs[inode.ino].nlink, dirs[inode.ino].nsubdirs, dirs[inode.ino].size) ;mkinode(inode.ino, files[inode.ino].meta, false, files[inode.ino].nlink, 0, files[inode.ino].size) ); err := ESUCCESS; asynced := ?] ( afs-cons(dirs, files) → ⟪asynced4 := true; if err = ESUCCESS then let asynced = false in {icache_set#(inode0, asynced; err, icache); pcache_truncate#(inode0.ino, m2, n; err, pcache); if asynced4 then pcache_set# (inode0.ino, m2 / VFS_PAGE_SIZE, some(fill(some(buf0).buf, zero, inode.size % VFS_PAGE_SIZE, VFS_PAGE_SIZE - inode.size % VFS_PAGE_SIZE)).buf, asynced ; err, pcache)}; if ¬ asynced4 ∨ err ≠ ESUCCESS then buf-opt0 := 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 80:
# buf0 = VFS_PAGE_SIZE, files0[m] = mkfile(m1, md1, # links(m, dirs), content0), pcache[datakey(m, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), files = files0 [m, mkfile (m1, md1, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE - m2 % VFS_PAGE_SIZE)] upto m2) ], inode = mkinode(m, md, false, # links(m, dirs), 0, m2), inode = mkinode(m0, md0, boolvar0, m3, m4, m5), afs-cons(dirs, files0), dcache-cons(dcache, dirs, files0), icache-cons(icache, dirs, files0), pcache-cons(pcache, dirs, files0), synced(dirs, icache, pcache), m ∈ files0, datakey(m, m2 / VFS_PAGE_SIZE) ∈ pcache, m2 ≤ n, asynced2 → synced(files0, icache, pcache) ⊦ [afs_inode_sync#(mkinode(m, md, false, # links(m, dirs), 0, n); dirs, files); inode0 := (m0 ∈ dirs ⊃ mkinode(m0, dirs[m0].meta, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size) ;mkinode(m0, files[m0].meta, false, files[m0].nlink, 0, files[m0].size) ); err := ESUCCESS; asynced := ?] ( afs-cons(dirs, files) → ⟪asynced4 := true; if err = ESUCCESS then let asynced = false in {icache_set#(inode0, asynced; err, icache); pcache_truncate#(inode0.ino, m2, n; err, pcache); if asynced4 then pcache_set# (inode0.ino, m2 / VFS_PAGE_SIZE, some(fill(some(buf0).buf, zero, m5 % VFS_PAGE_SIZE, VFS_PAGE_SIZE - m5 % VFS_PAGE_SIZE)).buf, asynced ; err, pcache)}; if ¬ asynced4 ∨ err ≠ ESUCCESS then buf-opt0 := 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)))), m2 % VFS_PAGE_SIZE = 0

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [inode, m0, md0, boolvar0, m3, m4, m5]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: inode, m0, md0, boolvar0, m3, m4, m5