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Proof step 399 from proof inv-truncate-buff-none-cached (previous step)

# buf0 = VFS_PAGE_SIZE, pcache0[datakey(m0, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino] = mkientry(boolvar1, mkinode(m, md, boolvar0, m3, m4, m6)), afs-cons(dirs, files0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), synced(dirs, icache, pcache0), ino ∈ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))], datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, m0 ∈ files0, asynced2 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data?, ∀ ino. ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ valid-file-inode(icache[ino].inode, dirs, files0) ;valid-ino(ino, dirs, files0) ∧ valid-inode(icache[ino].inode, dirs, files0) ) ⊦ m = ino ∧ (boolvar1 ⊃ ino ∈ files0 ∧ m3 = (ino = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[ino]).nlink ∧ m4 = 0 ∧ ¬ boolvar0 ; (ino ∈ dirs ∨ ino ∈ files0) ∧ mkinode(ino, md, boolvar0, m3, m4, m6) = (ino ∈ dirs ⊃ mkinode(ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, (ino = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[ino]).meta, false, (ino = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[ino]).nlink, 0, (ino = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[ino]).size) ) ), m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 400:
# buf0 = VFS_PAGE_SIZE, icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino] = mkientry(boolvar1, mkinode(m, md, boolvar0, m3, m4, m6)), files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), pcache0[datakey(m0, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), afs-cons(dirs, files0), synced(dirs, icache, pcache0), m0 ∈ files0, datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, ino ∈ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))], asynced2 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data?, ∀ ino0. ino0 ∈ icache → icache[ino0].inode.ino = ino0 ∧ (icache[ino0].dirty ⊃ icache[ino0].inode.ino ∈ files0 ∧ icache[ino0].inode.nlink = files0[icache[ino0].inode.ino].nlink ∧ icache[ino0].inode.nsubdirs = 0 ∧ ¬ icache[ino0].inode.directory ; (ino0 ∈ dirs ∨ ino0 ∈ files0) ∧ icache[ino0].inode = (icache[ino0].inode.ino ∈ dirs ⊃ mkinode (icache[ino0].inode.ino, dirs[icache[ino0].inode.ino].meta, true, dirs[icache[ino0].inode.ino].nlink, dirs[icache[ino0].inode.ino].nsubdirs, dirs[icache[ino0].inode.ino].size) ;mkinode (icache[ino0].inode.ino, files0[icache[ino0].inode.ino].meta, false, files0[icache[ino0].inode.ino].nlink, 0, files0[icache[ino0].inode.ino].size) ) ) ⊦ m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0, m = ino ∧ (boolvar1 ⊃ ino ∈ files0 ∧ m3 = (ino = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[ino]).nlink ∧ m4 = 0 ∧ ¬ boolvar0 ; (ino ∈ dirs ∨ ino ∈ files0) ∧ mkinode(ino, md, boolvar0, m3, m4, m6) = (ino ∈ dirs ⊃ mkinode(ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, (ino = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[ino]).meta, false, (ino = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[ino]).nlink, 0, (ino = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[ino]).size) ) )

Rule argument

Additional information

Used simplifier rules: ⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)%⊦ valid-inode(inode, dirs, files) ↔ inode = getinode(inode.ino, dirs, files); (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)