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Proof step 62 from proof inv-mkdir (previous step)

fs1[ri1[key]].key = key, fs1[ri1[inodekey(m)]].directory, fs1[ri1[inodekey(m)]].inode?, ro.inodes?, fo.inodes?, file-node-cons(fs1, ri1), log-cons(log0, fs1), orphans-cons(fs1, ri1, ro), replay-cons-strong(fs1, ri1, ro, fi, fo, log0), ri-inj(ri1), ri-inj(fi), ubifs-cons(fs1, ri1, ro, fi, fo, log0), key ∈ ri1, inodekey(m) ∈ ri1, ri1[inodekey(m)] ∈ fs1, ri1[key] ∈ fs1, key.inode? → fs1[ri1[key]].inode? ∧ key.ino ≠ 0, key.dentry? → fs1[ri1[key]].dentry? ∧ inodekey(key.ino) ∈ ri1 ∧ inodekey(fs1[ri1[key]].ino) ∈ ri1 ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey(fs1[ri1[key]].ino) ∈ ro ∧ fs1[ri1[inodekey(key.ino)]].directory, key.data? → fs1[ri1[key]].data? ∧ inodekey(key.ino) ∈ ri1 ∧ ¬ fs1[ri1[inodekey(key.ino)]].directory ∧ # fs1[ri1[key]].data = VFS_PAGE_SIZE, fs1[ri1[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ 0 = m, adr1 = adr2, adr1 = adr3, adr2 = adr3, n = 0, adr3 ∈ fs1, adr2 ∈ fs1, adr1 ∈ fs1, inodekey(n) ∈ ri1, inodekey(n) ∈ fo, dentrykey(m, str) ∈ ri1, inodekey(m) ∈ ro, ( (inodekey(m) = key ⊃ adr1;ri1[key]) = adr3 ∨ (inodekey(m) = key ⊃ adr1;ri1[key]) = adr2 ∨ (inodekey(m) = key ⊃ adr1;ri1[key]) = adr1 ∨ (inodekey(m) = key ⊃ adr1;ri1[key]) ∈ fs1) ∧ (adr3 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(inodekey(m) = key ⊃ adr1;ri1[key])] ) ) ) .key = key ∧ ( key.inode? → (adr3 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(inodekey(m) = key ⊃ adr1;ri1[key])] ) ) ) .inode? ∧ key.ino ≠ 0) ∧ ( key.dentry? → (adr3 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(inodekey(m) = key ⊃ adr1;ri1[key])] ) ) ) .dentry? ∧ (key.ino = n ∨ inodekey(key.ino) ∈ ri1) ∧ ( (adr3 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(inodekey(m) = key ⊃ adr1;ri1[key])] ) ) ) .ino = n ∨ (adr3 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(inodekey(m) = key ⊃ adr1;ri1[key])] ) ) ) .ino = m ∨ inodekey ((adr3 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(inodekey(m) = key ⊃ adr1;ri1[key])] ) ) ) .ino) ∈ ri1) ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey ((adr3 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(inodekey(m) = key ⊃ adr1;ri1[key])] ) ) ) .ino) ∈ ro ∧ (adr3 = (n = key.ino ⊃ adr3;(m = key.ino ⊃ adr1;ri1[inodekey(key.ino)])) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (n = key.ino ⊃ adr3;(m = key.ino ⊃ adr1;ri1[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (n = key.ino ⊃ adr3;(m = key.ino ⊃ adr1;ri1[inodekey(key.ino)])) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(n = key.ino ⊃ adr3;(m = key.ino ⊃ adr1;ri1[inodekey(key.ino)]))] ) ) ) .directory) ∧ ( key.data? → (adr3 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(inodekey(m) = key ⊃ adr1;ri1[key])] ) ) ) .data? ∧ (key.ino = n ∨ inodekey(key.ino) ∈ ri1) ∧ ¬ (adr3 = (n = key.ino ⊃ adr3;(m = key.ino ⊃ adr1;ri1[inodekey(key.ino)])) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (n = key.ino ⊃ adr3;(m = key.ino ⊃ adr1;ri1[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (n = key.ino ⊃ adr3;(m = key.ino ⊃ adr1;ri1[inodekey(key.ino)])) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(n = key.ino ⊃ adr3;(m = key.ino ⊃ adr1;ri1[inodekey(key.ino)]))] ) ) ) .directory ∧ # (adr3 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(inodekey(m) = key ⊃ adr1;ri1[key])] ) ) ) .data = VFS_PAGE_SIZE)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 63:
fs1[ri1[key]].key = key, fs1[ri1[inodekey(m)]].directory, fs1[ri1[inodekey(m)]].inode?, fo.inodes?, ro.inodes?, file-node-cons(fs1, ri1), log-cons(log0, fs1), orphans-cons(fs1, ri1, ro), replay-cons-strong(fs1, ri1, ro, fi, fo, log0), ri-inj(fi), ri-inj(ri1), ubifs-cons(fs1, ri1, ro, fi, fo, log0), ri1[key] ∈ fs1, ri1[inodekey(m)] ∈ fs1, inodekey(m) ∈ ri1, key ∈ ri1, key.data? → fs1[ri1[key]].data? ∧ inodekey(key.ino) ∈ ri1 ∧ ¬ fs1[ri1[inodekey(key.ino)]].directory ∧ # fs1[ri1[key]].data = VFS_PAGE_SIZE, key.dentry? → fs1[ri1[key]].dentry? ∧ inodekey(key.ino) ∈ ri1 ∧ inodekey(fs1[ri1[key]].ino) ∈ ri1 ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey(fs1[ri1[key]].ino) ∈ ro ∧ fs1[ri1[inodekey(key.ino)]].directory, key.inode? → fs1[ri1[key]].inode? ∧ key.ino ≠ 0, fs1[ri1[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ 0 = m, adr1 = adr3, adr1 = adr2, adr2 = adr3, inodekey(m) = key, n = 0, inodekey(m) ∈ ro, dentrykey(m, str) ∈ ri1, inodekey(n) ∈ fo, inodekey(n) ∈ ri1, adr1 ∈ fs1, adr2 ∈ fs1, adr3 ∈ fs1, ( (inodekey(m) = key ⊃ adr1;ri1[key]) = adr3 ∨ (inodekey(m) = key ⊃ adr1;ri1[key]) = adr2 ∨ (inodekey(m) = key ⊃ adr1;ri1[key]) = adr1 ∨ (inodekey(m) = key ⊃ adr1;ri1[key]) ∈ fs1) ∧ (adr3 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(inodekey(m) = key ⊃ adr1;ri1[key])] ) ) ) .key = key ∧ ( key.inode? → (adr3 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(inodekey(m) = key ⊃ adr1;ri1[key])] ) ) ) .inode? ∧ key.ino ≠ 0) ∧ ( key.dentry? → (adr3 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(inodekey(m) = key ⊃ adr1;ri1[key])] ) ) ) .dentry? ∧ (key.ino = n ∨ inodekey(key.ino) ∈ ri1) ∧ ( (adr3 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(inodekey(m) = key ⊃ adr1;ri1[key])] ) ) ) .ino = n ∨ (adr3 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(inodekey(m) = key ⊃ adr1;ri1[key])] ) ) ) .ino = m ∨ inodekey ((adr3 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(inodekey(m) = key ⊃ adr1;ri1[key])] ) ) ) .ino) ∈ ri1) ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey ((adr3 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(inodekey(m) = key ⊃ adr1;ri1[key])] ) ) ) .ino) ∈ ro ∧ (adr3 = (n = key.ino ⊃ adr3;(m = key.ino ⊃ adr1;ri1[inodekey(key.ino)])) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (n = key.ino ⊃ adr3;(m = key.ino ⊃ adr1;ri1[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (n = key.ino ⊃ adr3;(m = key.ino ⊃ adr1;ri1[inodekey(key.ino)])) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(n = key.ino ⊃ adr3;(m = key.ino ⊃ adr1;ri1[inodekey(key.ino)]))] ) ) ) .directory) ∧ ( key.data? → (adr3 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(inodekey(m) = key ⊃ adr1;ri1[key])] ) ) ) .data? ∧ (key.ino = n ∨ inodekey(key.ino) ∈ ri1) ∧ ¬ (adr3 = (n = key.ino ⊃ adr3;(m = key.ino ⊃ adr1;ri1[inodekey(key.ino)])) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (n = key.ino ⊃ adr3;(m = key.ino ⊃ adr1;ri1[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (n = key.ino ⊃ adr3;(m = key.ino ⊃ adr1;ri1[inodekey(key.ino)])) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(n = key.ino ⊃ adr3;(m = key.ino ⊃ adr1;ri1[inodekey(key.ino)]))] ) ) ) .directory ∧ # (adr3 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (inodekey(m) = key ⊃ adr1;ri1[key]) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(inodekey(m) = key ⊃ adr1;ri1[key])] ) ) ) .data = VFS_PAGE_SIZE)

Rule argument

fma: inodekey(m) = key

Additional information

Used simplifier rules: ⊦ inodekey(m).inode?; (s)% ⊦ inodekey(m).ino = m; (s)% ⊦ ¬ inodekey(m).dentry?; (s)% ⊦ ¬ inodekey(m).data?; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).key = key; (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).inode?; (s) Used formulas: inodekey(m) = key