[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 8 from proof inv-write_inode (previous step)

files[m] = mkfile(m3, md0, m4, content), dirs[m] = mkdir(m5, md1, m6, m7, entries), inode = mkinode(m, md, boolvar, m0, m1, m2), afs-cons(dirs, files), pre-write-inode(inode, dirs, files), m ∈ dirs ∧ m0 = m6 ∧ m2 = m5 ∧ m1 = m7 ∧ boolvar ∨ m ∈ files ∧ m0 = m4 ∧ m1 = 0 ∧ ¬ boolvar ⊦ ⟪if pre-write-inode(inode, dirs, files) then { {if inode.directory then dirs[inode.ino].meta := inode.meta else {files[inode.ino].meta := inode.meta; files[inode.ino].size := inode.size}; err := ESUCCESS} or fail#(; ; err); asynced := ?} else abort⟫ afs-cons(dirs, files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
files[m] = mkfile(m3, md0, m4, content), dirs[m] = mkdir(m5, md1, m6, m7, entries), afs-cons(dirs, files), m ∈ dirs ∧ m0 = m6 ∧ m2 = m5 ∧ m1 = m7 ∧ boolvar ∨ m ∈ files ∧ m0 = m4 ∧ m1 = 0 ∧ ¬ boolvar ⊦ ⟪ {if mkinode(m, md, boolvar, m0, m1, m2).directory then dirs[mkinode(m, md, boolvar, m0, m1, m2).ino].meta := mkinode(m, md, boolvar, m0, m1, m2).meta else {files[mkinode(m, md, boolvar, m0, m1, m2).ino].meta := mkinode(m, md, boolvar, m0, m1, m2).meta; files[mkinode(m, md, boolvar, m0, m1, m2).ino].size := mkinode(m, md, boolvar, m0, m1, m2).size}; err := ESUCCESS} or fail#(; ; err); asynced := ?⟫ afs-cons(dirs, files)

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkdir(m, md, m0, m1, entries).nsubdirs = m1; (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (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)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ valid-dir-inode(inode, dirs, files) ↔ valid-dir-ino(inode.ino, dirs, files) ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory; (s)%⊦ valid-wb-inode(inode, dirs, files) ↔ valid-dir-inode(inode, dirs, files) ∨ valid-file-inode(inode, dirs, files); (s)%⊦ pre-write-inode(inode, dirs, files) ↔ valid-wb-inode(inode, dirs, files); (s)