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Proof step 605 from proof inv-truncate (previous step)

fs0[ri0[inodekey(m0)]].nlink = 0 ∧ m0 ≠ ROOT_INO ↔ inodekey(m0) ∈ ro, adr2 = (m0 = key0.ino ⊃ adr2;ri0[inodekey(key0.ino)]), m0 = key0.ino, fs0[ri0[inodekey(m0)]].inode?, ro.inodes?, fo.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), inodekey(m0) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, ri0[key0] ∈ fs0, key0 ∈ ri0, inodekey(key0.ino) ∈ ri0, m4 ≤ n0, ro ⊆ dom ri0, key0.data? → fs0[ri0[key0]].data? ∧ ¬ fs0[ri0[inodekey(key0.ino)]].directory ∧ # fs0[ri0[key0]].data = VFS_PAGE_SIZE, key0.dentry? → fs0[ri0[key0]].dentry? ∧ inodekey(fs0[ri0[key0]].ino) ∈ ri0 ∧ ¬ inodekey(key0.ino) ∈ ro ∧ ¬ inodekey(fs0[ri0[key0]].ino) ∈ ro ∧ fs0[ri0[inodekey(key0.ino)]].directory, key0.inode? → fs0[ri0[key0]].inode?, ¬ key0.data? ∨ key0.ino ≠ m0 ∨ ¬ m4 ≤ key0.part * VFS_PAGE_SIZE ⊦ m4 % VFS_PAGE_SIZE = 0, key0.ino = 0, adr1 = adr2, inodekey(m0) = key0, m0 = 0, fs0[ri0[inodekey(m0)]].directory, buf-opt.some?, adr2 ∈ fs0, adr1 ∈ fs0, datakey(m0, m4 / VFS_PAGE_SIZE) ∈ ri0, ( (key0.data? ∧ key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0]) = adr2 ∨ (key0.data? ∧ key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0]) = adr1 ∨ (key0.data? ∧ key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0]) ∈ fs0) ∧ (adr2 = (key0.data? ∧ key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0]) ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ;(adr1 = (key0.data? ∧ key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0]) ⊃ truncnode(inodekey(m0), m4) ;fs0[(key0.data? ∧ key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0])] ) ) .key = key0 ∧ ¬ key0.dentry? ∧ ( key0.data? → (adr2 = (key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0]) ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ;(adr1 = (key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0]) ⊃ truncnode(inodekey(m0), m4) ;fs0[(key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0])] ) ) .data? ∧ # (adr2 = (key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0]) ⊃ inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ;(adr1 = (key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0]) ⊃ truncnode(inodekey(m0), m4) ;fs0[(key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0])] ) ) .data = VFS_PAGE_SIZE)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 606:
fs0[ri0[inodekey(key0.ino)]].nlink = 0 ∧ key0.ino ≠ ROOT_INO ↔ inodekey(key0.ino) ∈ ro, fs0[ri0[inodekey(key0.ino)]].inode?, ro.inodes?, fo.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(key0.ino)] ∈ fs0, ri0[key0] ∈ fs0, key0 ∈ ri0, inodekey(key0.ino) ∈ ri0, m4 ≤ n0, ro ⊆ dom ri0, key0.data? → fs0[ri0[key0]].data? ∧ # fs0[ri0[key0]].data = VFS_PAGE_SIZE, ¬ key0.data? ∨ ¬ m4 ≤ key0.part * VFS_PAGE_SIZE ⊦ m4 % VFS_PAGE_SIZE = 0, key0.ino = 0, adr1 = adr2, inodekey(key0.ino) = key0, key0.dentry?, fs0[ri0[inodekey(key0.ino)]].directory, key0.inode?, buf-opt.some?, adr2 ∈ fs0, adr1 ∈ fs0, datakey(key0.ino, m4 / VFS_PAGE_SIZE) ∈ ri0, ( (key0.data? ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0]) = adr2 ∨ (key0.data? ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0]) = adr1 ∨ (key0.data? ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0]) ∈ fs0) ∧ (adr2 = (key0.data? ∧ m4 ≤ 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, n0) ;(adr1 = (key0.data? ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0]) ⊃ truncnode(inodekey(key0.ino), m4) ;fs0[(key0.data? ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0])] ) ) .key = key0 ∧ ( key0.data? → (adr2 = (m4 ≤ 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, n0) ;(adr1 = (m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0]) ⊃ truncnode(inodekey(key0.ino), m4) ;fs0[(m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0])] ) ) .data? ∧ # (adr2 = (m4 ≤ 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, n0) ;(adr1 = (m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0]) ⊃ truncnode(inodekey(key0.ino), m4) ;fs0[(m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];ri0[key0])] ) ) .data = VFS_PAGE_SIZE)

Rule argument

Additional information

Used simplifier rules: ⊦ key.inode? → inodekey(key.ino) = key; (s)