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Proof step 90 from proof inv-truncate (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, fs0[ri0[key0]].key = key0, fs0[ri0[inodekey(key0.ino)]].nlink = 0 ∧ key0.ino ≠ ROOT_INO ↔ inodekey(key0.ino) ∈ ro, VFS_PAGE_SIZE = n0 + m3 % VFS_PAGE_SIZE, fs0[ri0[inodekey(key0.ino)]].inode?, fo.inodes?, ro.inodes?, buf-opt.some?, file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[key0] ∈ fs0, ri0[inodekey(key0.ino)] ∈ fs0, key0 ∈ ri0, inodekey(key0.ino) ∈ ri0, m3 ≤ n1, ro ⊆ dom ri0, key0.data? → fs0[ri0[key0]].data? ∧ # fs0[ri0[key0]].data = VFS_PAGE_SIZE, ¬ key0.data? ∨ ¬ m3 ≤ key0.part * VFS_PAGE_SIZE ⊦ m3 % VFS_PAGE_SIZE = 0, key0.ino = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, datakey(key0.ino, m3 / VFS_PAGE_SIZE) = key0, inodekey(key0.ino) = key0, key0.dentry?, fs0[ri0[inodekey(key0.ino)]].directory, key0.inode?, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, ( (key0.data? ∧ m3 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0]) = adr3 ∨ (key0.data? ∧ m3 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0]) = adr2 ∨ (key0.data? ∧ m3 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0]) = adr1 ∨ (key0.data? ∧ m3 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0]) ∈ fs0) ∧ (adr3 = (key0.data? ∧ m3 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0]) ⊃ datanode(datakey(key0.ino, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ;(adr2 = (key0.data? ∧ m3 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0]) ⊃ inodenode(inodekey(key0.ino), md0, false, fs0[ri0[inodekey(key0.ino)]].nlink, fs0[ri0[inodekey(key0.ino)]].nsubdirs, n1) ;(adr1 = (key0.data? ∧ m3 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0]) ⊃ truncnode(inodekey(key0.ino), m3) ;fs0[(key0.data? ∧ m3 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0])] ) ) ) .key = key0 ∧ ( key0.data? → (adr3 = (m3 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0]) ⊃ datanode(datakey(key0.ino, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ;(adr2 = (m3 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0]) ⊃ inodenode(inodekey(key0.ino), md0, false, fs0[ri0[inodekey(key0.ino)]].nlink, fs0[ri0[inodekey(key0.ino)]].nsubdirs, n1) ;(adr1 = (m3 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0]) ⊃ truncnode(inodekey(key0.ino), m3) ;fs0[(m3 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0])] ) ) ) .data? ∧ # (adr3 = (m3 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0]) ⊃ datanode(datakey(key0.ino, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ;(adr2 = (m3 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0]) ⊃ inodenode(inodekey(key0.ino), md0, false, fs0[ri0[inodekey(key0.ino)]].nlink, fs0[ri0[inodekey(key0.ino)]].nsubdirs, n1) ;(adr1 = (m3 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0]) ⊃ truncnode(inodekey(key0.ino), m3) ;fs0[(m3 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0])] ) ) ) .data = VFS_PAGE_SIZE)

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: key0.data?

Additional information

Used simplifier rules: elim-data: ⊦ key.data? ↔ (∃ ino, n. key = datakey(ino, n));%data-ubifs-cons: ⊦ datakey(ino, n) ∈ ri ∧ ri[datakey(ino, n)] ∈ fs ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[datakey(ino, n)]].data?;% ⊦ key ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → ri[key] ∈ fs; (ss)% ⊦ datakey(m, m0).ino = m; (s)% ⊦ inodekey(m) ≠ datakey(m0, m1); (s)% ⊦ ¬ datakey(m, m0).dentry?; (s)% ⊦ ¬ datakey(m, m0).inode?; (s)% ⊦ datakey(m, m0).data?; (s)%⊦ datakey(m, n) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → # fs[ri[datakey(m, n)]].data = VFS_PAGE_SIZE; (s)% ⊦ datakey(m, m0).part = m0; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s) Used formulas: key0.data?