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Proof step 207 from proof inv-truncate-buff-none-uncached (previous step)

VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files1[m3] = mkfile(m1, md1, # links(m3, dirs), content0), afs-cons (dirs, files1 [m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]), afs-cons(dirs, files1), icache-cons(icache, dirs, files1), synced(dirs, icache, pcache0), ino ∈ icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))], m3 ∈ files1, m2 / VFS_PAGE_SIZE ∈ content0, m2 ≤ m, asynced2 → synced(files1, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ pcache0, icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.ino = ino ∧ (icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].dirty ⊃ icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.ino ∈ files1 ∧ icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.nlink = (icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.ino = m3 ⊃ mkfile (m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files1[icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.ino] ) .nlink ∧ icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.nsubdirs = 0 ∧ ¬ icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.directory ; (ino ∈ dirs ∨ ino ∈ files1) ∧ icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode = (icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.ino ∈ dirs ⊃ mkinode (icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.ino, dirs[icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.ino].meta, true, dirs[icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.ino].nlink, dirs[icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.ino].nsubdirs, dirs[icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.ino].size) ;mkinode (icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.ino, (icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.ino = m3 ⊃ mkfile (m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files1[icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.ino] ) .meta, false, (icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.ino = m3 ⊃ mkfile (m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files1[icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.ino] ) .nlink, 0, (icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.ino = m3 ⊃ mkfile (m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files1[icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.ino] ) .size) ) )

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 208:
icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode = mkinode(m0, md0, boolvar, m4, m5, m6), VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files1[m3] = mkfile(m1, md1, # links(m3, dirs), content0), afs-cons(dirs, files1), afs-cons (dirs, files1 [m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]), icache-cons(icache, dirs, files1), synced(dirs, icache, pcache0), m2 / VFS_PAGE_SIZE ∈ content0, m3 ∈ files1, ino ∈ icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))], m2 ≤ m, asynced2 → synced(files1, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ pcache0, m0 = ino ∧ (icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].dirty ⊃ m0 ∈ files1 ∧ m4 = (m0 = m3 ⊃ mkfile (m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files1[m0] ) .nlink ∧ m5 = 0 ∧ ¬ boolvar ; (ino ∈ dirs ∨ ino ∈ files1) ∧ icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode = (m0 ∈ dirs ⊃ mkinode(m0, dirs[m0].meta, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size) ;mkinode (m0, (m0 = m3 ⊃ mkfile (m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files1[m0] ) .meta, false, (m0 = m3 ⊃ mkfile (m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files1[m0] ) .nlink, 0, (m0 = m3 ⊃ mkfile (m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files1[m0] ) .size) ) )

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] → [icache [m3, mkientry (false, mkinode(m3, md, false, # links(m3, dirs), 0, m)) ] [ino ] .inode, m0, md0, boolvar, m4, m5, m6]

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: icache [m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m)) ] [ino ] .inode, m0, md0, boolvar, m4, m5, m6