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Proof step 7 from proof inv-write_inode (previous step)

dirs[m] = mkdir(m5, md1, m6, m7, entries), files[m] = mkfile(m3, md0, m4, content), inode = mkinode(m, md, boolvar, m0, m1, m2), afs-cons(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 nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 8:
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)

Rule argument

fma: pre-write-inode(inode, dirs, files)

Additional information

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