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Proof step 69 from proof inv-truncate (previous step)

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

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 70:
# buf-opt.buf = VFS_PAGE_SIZE, fs0[ri0[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO ↔ inodekey(m) ∈ ro, VFS_PAGE_SIZE = n0 + m3 % VFS_PAGE_SIZE, fs0[ri0[inodekey(m)]].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), inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, m3 ≤ n1, ro ⊆ dom ri0, adr = adr1 ∨ adr = adr2 ∨ adr = adr3 ⊦ m3 % VFS_PAGE_SIZE = 0, 0 = m, adr = adr1, adr1 = adr2, adr1 = adr3, adr2 = adr3, fs0[ri0[inodekey(m)]].directory, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, adr ∈ log0, (adr = adr3 ∨ adr = adr2 ∨ adr = adr1 ∨ adr ∈ fs0) ∧ ( (adr3 = adr ⊃ datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ;(adr2 = adr ⊃ inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n1) ;(adr1 = adr ⊃ truncnode(inodekey(m), m3);fs0[adr]) ) ) .inode? → (adr3 = adr ⊃ datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ;(adr2 = adr ⊃ inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n1) ;(adr1 = adr ⊃ truncnode(inodekey(m), m3);fs0[adr]) ) ) .key .inode? ∧ (adr3 = adr ⊃ datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ;(adr2 = adr ⊃ inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n1) ;(adr1 = adr ⊃ truncnode(inodekey(m), m3);fs0[adr]) ) ) .key .ino ≠ 0) ∧ ( (adr3 = adr ⊃ datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ;(adr2 = adr ⊃ inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n1) ;(adr1 = adr ⊃ truncnode(inodekey(m), m3);fs0[adr]) ) ) .dentry? → (adr3 = adr ⊃ datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ;(adr2 = adr ⊃ inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n1) ;(adr1 = adr ⊃ truncnode(inodekey(m), m3);fs0[adr]) ) ) .key .dentry?) ∧ ( (adr3 = adr ⊃ datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ;(adr2 = adr ⊃ inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n1) ;(adr1 = adr ⊃ truncnode(inodekey(m), m3);fs0[adr]) ) ) .data? → (adr3 = adr ⊃ datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ;(adr2 = adr ⊃ inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n1) ;(adr1 = adr ⊃ truncnode(inodekey(m), m3);fs0[adr]) ) ) .key .data?) ∧ ( (adr3 = adr ⊃ datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ;(adr2 = adr ⊃ inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n1) ;(adr1 = adr ⊃ truncnode(inodekey(m), m3);fs0[adr]) ) ) .trunc? → (adr3 = adr ⊃ datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ;(adr2 = adr ⊃ inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n1) ;(adr1 = adr ⊃ truncnode(inodekey(m), m3);fs0[adr]) ) ) .key .inode?)

Rule argument

fma: adr = adr1

Additional information

Used simplifier rules: ⊦ ¬ truncnode(key, m).inode?; (s)% ⊦ ¬ truncnode(key, m).dentry?; (s)% ⊦ ¬ truncnode(key, m).data?; (s)% ⊦ truncnode(key, m).trunc?; (s)% ⊦ truncnode(key, m).key = key; (s)% ⊦ inodekey(m).inode?; (s) Used formulas: adr = adr1