[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 91 from proof inv-truncate-buff-none-uncached (previous step)

asynced4 ↔ true, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files1[m0] = mkfile(m1, md1, # links(m0, dirs), content0), err = ESUCCESS, files = files1 [m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ], ino = m0, ino0 = m0, inode0 = mkinode(m0, md, false, # links(m0, dirs), 0, m), n = m, pcache = truncate(ino0, min(n, size), pcache0), size = m2, afs-cons (dirs, files1 [m0, mkfile(m, md, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]), afs-cons(dirs, files1), dcache-cons(dcache, dirs, files1), icache-cons(icache, dirs, files1), pcache-cons(pcache0, dirs, files1), synced(dirs, icache, pcache0), m0 ∈ files1, m2 / VFS_PAGE_SIZE ∈ content0, m2 ≤ m, m2 % VFS_PAGE_SIZE + n0 ≤ # content0[m2 / VFS_PAGE_SIZE], asynced2 → synced(files1, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ ⟪pcache_set# ((m0 ∈ dirs ⊃ mkinode(m0, dirs[m0].meta, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size) ;mkinode (m0, (m0 = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode0.size).meta:= inode0.meta;files[m0]).meta, false, (m0 = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode0.size).meta:= inode0.meta;files[m0]).nlink, 0, (m0 = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode0.size).meta:= inode0.meta;files[m0]).size) ) .ino, m2 / VFS_PAGE_SIZE, some(fill(files1[m0].content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)).buf, false ; err, pcache); if ¬ asynced4 ∨ err ≠ ESUCCESS then buf-opt := none⟫ ( icache-cons (icache[m0, mkientry(false, mkinode(m0, md, false, # links(m0, dirs), 0, m))], dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode0.size;files[ino]).meta:= inode0.meta]) ∧ dcache-cons(dcache, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode0.size;files[ino]).meta:= inode0.meta]) ∧ pcache-cons(pcache, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode0.size;files[ino]).meta:= inode0.meta]) ∧ synced(dirs, icache[m0, mkientry(false, mkinode(m0, md, false, # links(m0, dirs), 0, m))], pcache) ∧ ( asynced2 → synced (files[ino, (ino ∈ files ⊃ files[ino].size:= inode0.size;files[ino]).meta:= inode0.meta], icache[m0, mkientry(false, mkinode(m0, md, false, # links(m0, dirs), 0, m))], pcache))), m2 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0, datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 92:
VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files1[m0] = mkfile(m1, md1, # links(m0, dirs), content0), err = ESUCCESS, pcache = truncate(m0, m2, pcache0), m2 % VFS_PAGE_SIZE ≠ 0, afs-cons (dirs, files1 [m0, mkfile(m, md, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]), afs-cons(dirs, files1), dcache-cons(dcache, dirs, files1), icache-cons(icache, dirs, files1), pcache-cons(pcache0, dirs, files1), synced(dirs, icache, pcache0), m0 ∈ files1, m2 / VFS_PAGE_SIZE ∈ content0, m2 ≤ m, ¬ datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, asynced2 → synced(files1, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ ⟪pcache_set# (mkinode (m0, ( m0 ∈ files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] ⊃ ( files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m0 ] .size:= m) .meta:= md ;files1 [m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m0 ] ) .meta, false, ( m0 ∈ files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] ⊃ ( files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m0 ] .size:= m) .meta:= md ;files1 [m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m0 ] ) .nlink, 0, ( m0 ∈ files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] ⊃ ( files1 [m0, mkfile (m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m0 ] .size:= m) .meta:= md ;files1 [m0, mkfile(m1, md1, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [m0 ] ) .size) .ino, m2 / VFS_PAGE_SIZE, some(fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)).buf, false ; err, pcache); if err ≠ ESUCCESS then buf-opt := none⟫ ( icache-cons (icache[m0, mkientry(false, mkinode(m0, md, false, # links(m0, dirs), 0, m))], dirs, files1 [m0, mkfile(m, md, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]) ∧ dcache-cons (dcache, dirs, files1 [m0, mkfile(m, md, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]) ∧ pcache-cons (pcache, dirs, files1 [m0, mkfile(m, md, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]) ∧ synced(dirs, icache[m0, mkientry(false, mkinode(m0, md, false, # links(m0, dirs), 0, m))], pcache) ∧ ( asynced2 → synced (files1 [m0, mkfile (m, md, # links(m0, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ], icache[m0, mkientry(false, mkinode(m0, md, false, # links(m0, dirs), 0, m))], pcache)))

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).content = content; (s)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ m ≤ m; (s)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ files[ino, af][ino, af0] = files[ino, af0]; (s)% ⊦ mkfile(m, md, m0, content).meta:= md0 = mkfile(m, md0, m0, content); (s)% ⊦ mkfile(m, md, m0, content).size:= m1 = mkfile(m1, md, m0, content); (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)%⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)%min-comm: ⊦ min(n0, n1) = min(n1, n0); from specification min-max% ⊦ n0 ≤ n1 → min(n0, n1) = n0; (s)