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Proof step 48 from proof inv-link (previous step)

fs0[ri0[dentrykey(ino, str)]].ino = fs0[ri0[dentrykey(ino0, str)]].ino, fs0[ri0[dentrykey(ino0, str)]].dentry?, fs0[ri0[inodekey(ino0)]].directory, fs0[ri0[inodekey(m3)]].directory, fs0[ri0[inodekey(ino)]].directory, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].inode?, fs0[ri0[inodekey(m3)]].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), dentrykey(ino0, str) ∈ ri0, inodekey(m3) ∈ ri0, inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) ∈ ri0, ri0[dentrykey(ino0, str)] ∈ fs0, dentrykey(ino, str) ∈ ri0, inodekey(ino0) ∈ ri0, inodekey(ino) ∈ ri0, ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)] ∈ fs0, ri0[inodekey(m3)] ∈ fs0, key ∈ ri0 → ri0[key] ∈ fs0 ∧ (key.inode? → fs0[ri0[key]].inode? ∧ key.ino ≠ 0) ∧ ( key.dentry? → fs0[ri0[key]].dentry? ∧ inodekey(key.ino) ∈ ri0 ∧ inodekey(fs0[ri0[key]].ino) ∈ ri0 ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey(fs0[ri0[key]].ino) ∈ ro ∧ fs0[ri0[inodekey(key.ino)]].directory) ∧ (key.data? → fs0[ri0[key]].data? ∧ inodekey(key.ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(key.ino)]].directory ∧ # fs0[ri0[key]].data = VFS_PAGE_SIZE), key = dentrykey(m3, str0) ∨ key ∈ ri0, fs0[ri0[inodekey(ino0)]].nlink ≠ 0 ∨ ino0 = ROOT_INO, fs0[ri0[inodekey(m3)]].nlink ≠ 0 ∨ m3 = ROOT_INO, fs0[ri0[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO ⊦ fs0[ri0[dentrykey(ino0, str)]].ino = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, m3 = 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].directory, inodekey(ino0) ∈ ro, inodekey(m3) ∈ ro, dentrykey(m3, str0) ∈ ri0, inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) ∈ ro, inodekey(ino) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, ( (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) = adr3 ∨ (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) = adr2 ∨ (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) = adr1 ∨ (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ∈ fs0) ∧ (adr3 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;(adr2 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[(inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key])))] ) ) ) .key = key ∧ ( key.inode? → (adr3 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;(adr2 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[(inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key])))] ) ) ) .inode? ∧ key.ino ≠ 0) ∧ ( key.dentry? → (adr3 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;(adr2 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[(inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key])))] ) ) ) .dentry? ∧ (key.ino = fs0[ri0[dentrykey(ino0, str)]].ino ∨ inodekey(key.ino) ∈ ri0) ∧ ( ( adr3 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;( adr2 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;( adr1 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0 [(inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ] ) ) ) .ino = fs0[ri0[dentrykey(ino0, str)]].ino ∨ ( adr3 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;( adr2 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;( adr1 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0 [(inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ] ) ) ) .ino = m3 ∨ inodekey (( adr3 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;( adr2 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;( adr1 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3 ;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key])) ) ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0 [(inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ] ) ) ) .ino) ∈ ri0) ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey (( adr3 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;( adr2 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;( adr1 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0 [(inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ] ) ) ) .ino) ∈ ro ∧ (adr3 = (fs0[ri0[dentrykey(ino0, str)]].ino = key.ino ⊃ adr3;(m3 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;(adr2 = (fs0[ri0[dentrykey(ino0, str)]].ino = key.ino ⊃ adr3;(m3 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = (fs0[ri0[dentrykey(ino0, str)]].ino = key.ino ⊃ adr3;(m3 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[(fs0[ri0[dentrykey(ino0, str)]].ino = key.ino ⊃ adr3;(m3 = key.ino ⊃ adr1;ri0[inodekey(key.ino)]))] ) ) ) .directory) ∧ ( key.data? → (adr3 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;(adr2 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[(inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key])))] ) ) ) .data? ∧ (key.ino = fs0[ri0[dentrykey(ino0, str)]].ino ∨ inodekey(key.ino) ∈ ri0) ∧ ¬ (adr3 = (fs0[ri0[dentrykey(ino0, str)]].ino = key.ino ⊃ adr3;(m3 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;(adr2 = (fs0[ri0[dentrykey(ino0, str)]].ino = key.ino ⊃ adr3;(m3 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = (fs0[ri0[dentrykey(ino0, str)]].ino = key.ino ⊃ adr3;(m3 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[(fs0[ri0[dentrykey(ino0, str)]].ino = key.ino ⊃ adr3;(m3 = key.ino ⊃ adr1;ri0[inodekey(key.ino)]))] ) ) ) .directory ∧ # (adr3 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;( adr2 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;( adr1 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[(inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key])))] ) ) ) .data = VFS_PAGE_SIZE)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 49:
fs0[ri0[dentrykey(ino, str)]].ino = fs0[ri0[dentrykey(ino0, str)]].ino, fs0[ri0[dentrykey(ino0, str)]].dentry?, fs0[ri0[inodekey(ino)]].directory, fs0[ri0[inodekey(m3)]].directory, fs0[ri0[inodekey(ino0)]].directory, fs0[ri0[inodekey(m3)]].inode?, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].inode?, fo.inodes?, ro.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(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m3)] ∈ fs0, ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)] ∈ fs0, inodekey(ino) ∈ ri0, inodekey(ino0) ∈ ri0, dentrykey(ino, str) ∈ ri0, ri0[dentrykey(ino0, str)] ∈ fs0, inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) ∈ ri0, inodekey(m3) ∈ ri0, dentrykey(ino0, str) ∈ ri0, key ∈ ri0, key ∈ ri0 → ri0[key] ∈ fs0 ∧ (key.inode? → fs0[ri0[key]].inode? ∧ key.ino ≠ 0) ∧ ( key.dentry? → fs0[ri0[key]].dentry? ∧ inodekey(key.ino) ∈ ri0 ∧ inodekey(fs0[ri0[key]].ino) ∈ ri0 ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey(fs0[ri0[key]].ino) ∈ ro ∧ fs0[ri0[inodekey(key.ino)]].directory) ∧ (key.data? → fs0[ri0[key]].data? ∧ inodekey(key.ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(key.ino)]].directory ∧ # fs0[ri0[key]].data = VFS_PAGE_SIZE), fs0[ri0[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO, fs0[ri0[inodekey(m3)]].nlink ≠ 0 ∨ m3 = ROOT_INO, fs0[ri0[inodekey(ino0)]].nlink ≠ 0 ∨ ino0 = ROOT_INO, key = dentrykey(m3, str0) ∨ key ∈ ri0 ⊦ fs0[ri0[dentrykey(ino0, str)]].ino = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, m3 = 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].directory, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(ino) ∈ ro, inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) ∈ ro, dentrykey(m3, str0) ∈ ri0, inodekey(m3) ∈ ro, inodekey(ino0) ∈ ro, ( (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) = adr3 ∨ (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) = adr2 ∨ (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) = adr1 ∨ (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ∈ fs0) ∧ (adr3 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;(adr2 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[(inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key])))] ) ) ) .key = key ∧ ( key.inode? → (adr3 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;(adr2 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[(inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key])))] ) ) ) .inode? ∧ key.ino ≠ 0) ∧ ( key.dentry? → (adr3 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;(adr2 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[(inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key])))] ) ) ) .dentry? ∧ (key.ino = fs0[ri0[dentrykey(ino0, str)]].ino ∨ inodekey(key.ino) ∈ ri0) ∧ ( ( adr3 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;( adr2 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;( adr1 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0 [(inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ] ) ) ) .ino = fs0[ri0[dentrykey(ino0, str)]].ino ∨ ( adr3 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;( adr2 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;( adr1 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0 [(inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ] ) ) ) .ino = m3 ∨ inodekey (( adr3 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;( adr2 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;( adr1 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3 ;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key])) ) ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0 [(inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ] ) ) ) .ino) ∈ ri0) ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey (( adr3 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;( adr2 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;( adr1 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0 [(inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ] ) ) ) .ino) ∈ ro ∧ (adr3 = (fs0[ri0[dentrykey(ino0, str)]].ino = key.ino ⊃ adr3;(m3 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;(adr2 = (fs0[ri0[dentrykey(ino0, str)]].ino = key.ino ⊃ adr3;(m3 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = (fs0[ri0[dentrykey(ino0, str)]].ino = key.ino ⊃ adr3;(m3 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[(fs0[ri0[dentrykey(ino0, str)]].ino = key.ino ⊃ adr3;(m3 = key.ino ⊃ adr1;ri0[inodekey(key.ino)]))] ) ) ) .directory) ∧ ( key.data? → (adr3 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;(adr2 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[(inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key])))] ) ) ) .data? ∧ (key.ino = fs0[ri0[dentrykey(ino0, str)]].ino ∨ inodekey(key.ino) ∈ ri0) ∧ ¬ (adr3 = (fs0[ri0[dentrykey(ino0, str)]].ino = key.ino ⊃ adr3;(m3 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;(adr2 = (fs0[ri0[dentrykey(ino0, str)]].ino = key.ino ⊃ adr3;(m3 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;(adr1 = (fs0[ri0[dentrykey(ino0, str)]].ino = key.ino ⊃ adr3;(m3 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[(fs0[ri0[dentrykey(ino0, str)]].ino = key.ino ⊃ adr3;(m3 = key.ino ⊃ adr1;ri0[inodekey(key.ino)]))] ) ) ) .directory ∧ # (adr3 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ;( adr2 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ;( adr1 = (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key]))) ⊃ inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1) ;fs0[(inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) = key ⊃ adr3;(dentrykey(m3, str0) = key ⊃ adr2;(inodekey(m3) = key ⊃ adr1;ri0[key])))] ) ) ) .data = VFS_PAGE_SIZE)

Rule argument

fma: key ∈ ri0

Additional information

Used simplifier rules: ⊦ dentrynode(key, m).key = key; (s)% ⊦ ¬ dentrynode(key, m).inode?; (s)% ⊦ dentrynode(key, m).dentry?; (s)% ⊦ dentrynode(key, m).ino = m; (s)% ⊦ ¬ dentrynode(key, m).data?; (s)% ⊦ ¬ dentrykey(m, str).inode?; (s)% ⊦ dentrykey(m, str).dentry?; (s)% ⊦ dentrykey(m, str).ino = m; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).directory ↔ boolvar; (s)% ⊦ ¬ dentrykey(m, str).data?; (s) Used formulas: key ∈ ri0