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Proof step 569 from proof inv-rename-overwrite-keep-parent (previous step)

fs0[ri0[key]].key = key, fs0[ri0[inodekey(m)]] = inodenode(key2, md2, true, m1, m2, m4), fs0[ri0[dentrykey(m, str0)]] = dentrynode(key0, m8), fs0[ri0[inodekey(m8)]] = inodenode(key1, md0, boolvar0, m0, m9, m10), 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-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), key ∈ ri0, ri0[key] ∈ fs0, ri0[inodekey(m8)] ∈ fs0, ri0[dentrykey(m, str0)] ∈ fs0, inodekey(m8) ∈ ri0, dentrykey(m, str0) ∈ ri0, inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, 1 ≤ m4, 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, boolvar0 → dentrykeys(inodekey(m8), ri0) = ∅, m0 = 1 → links(m8, fs0, ri0) = ∅ ++ dentrykey(m, str0), boolvar3 → 1 ≤ m2, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar0 ∧ boolvar2 ∧ m6 = m10, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, m1 ≠ 0 ∨ m = ROOT_INO ⊦ 0 = m8, 0 = m, adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, inodekey(m) = key, inodekey(m8) = key, m0 = 0, m4 = 0, m8 = ROOT_INO, adr2 ∈ ri0 -- dentrykey(m, str0), adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m) ∈ ro, ( (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) = adr4 ∨ (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) = adr3 ∨ (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) = adr2 ∨ (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) = adr1 ∨ (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ∈ fs0) ∧ (adr4 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), 0);fs0[(dentrykey(m, str0) = key ⊃ adr2;ri0[key])]) ) ) ) .key = key ∧ ( key.inode? → (adr4 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), 0);fs0[(dentrykey(m, str0) = key ⊃ adr2;ri0[key])]) ) ) ) .inode? ∧ key.ino ≠ 0) ∧ ( key.dentry? → (adr4 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), 0);fs0[(dentrykey(m, str0) = key ⊃ adr2;ri0[key])]) ) ) ) .dentry? ∧ inodekey(key.ino) ∈ ri0 ∧ ( (adr4 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), 0) ;fs0[(dentrykey(m, str0) = key ⊃ adr2;ri0[key])] ) ) ) ) .ino = m8 ∨ (adr4 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), 0) ;fs0[(dentrykey(m, str0) = key ⊃ adr2;ri0[key])] ) ) ) ) .ino = m ∨ inodekey ((adr4 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), 0) ;fs0[(dentrykey(m, str0) = key ⊃ adr2;ri0[key])] ) ) ) ) .ino) ∈ ri0) ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey ((adr4 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), 0);fs0[(dentrykey(m, str0) = key ⊃ adr2;ri0[key])]) ) ) ) .ino) ∈ ro ∧ (adr4 = (m8 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (m8 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (m8 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (m8 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m, str0), 0) ;fs0[(m8 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)]))] ) ) ) ) .directory) ∧ ( key.data? → (adr4 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), 0);fs0[(dentrykey(m, str0) = key ⊃ adr2;ri0[key])]) ) ) ) .data? ∧ inodekey(key.ino) ∈ ri0 ∧ ¬ (adr4 = (m8 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (m8 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (m8 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (m8 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m, str0), 0) ;fs0[(m8 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)]))] ) ) ) ) .directory ∧ # (adr4 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), 0);fs0[(dentrykey(m, str0) = key ⊃ adr2;ri0[key])]) ) ) ) .data = VFS_PAGE_SIZE)

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Proof step 570:
fs0[ri0[key]].key = key, fs0[ri0[inodekey(m8)]] = inodenode(key1, md0, boolvar0, m0, m9, m10), fs0[ri0[dentrykey(m, str0)]] = dentrynode(key0, m8), fs0[ri0[inodekey(m)]] = inodenode(key2, md2, true, m1, m2, m4), 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-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, dentrykey(m, str0) ∈ ri0, inodekey(m8) ∈ ri0, ri0[dentrykey(m, str0)] ∈ fs0, ri0[inodekey(m8)] ∈ fs0, ri0[key] ∈ fs0, key ∈ ri0, 1 ≤ m4, boolvar3 → 1 ≤ m2, m0 = 1 → links(m8, fs0, ri0) = ∅ ++ dentrykey(m, str0), boolvar0 → dentrykeys(inodekey(m8), ri0) = ∅, key.data? → fs0[ri0[key]].data? ∧ inodekey(key.ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(key.ino)]].directory ∧ # fs0[ri0[key]].data = VFS_PAGE_SIZE, 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.inode? → fs0[ri0[key]].inode? ∧ key.ino ≠ 0, m1 ≠ 0 ∨ m = ROOT_INO, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar0 ∧ boolvar2 ∧ m6 = m10 ⊦ (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) = adr4, (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) = adr3, (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) = adr2, (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) = adr1, 0 = m, 0 = m8, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, inodekey(m8) = key, inodekey(m) = key, m0 = 0, m4 = 0, m8 = ROOT_INO, inodekey(m) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str0), (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ∈ fs0
Proof step 571:
fs0[ri0[key]].key = key, fs0[ri0[inodekey(m8)]] = inodenode(key1, md0, boolvar0, m0, m9, m10), fs0[ri0[dentrykey(m, str0)]] = dentrynode(key0, m8), fs0[ri0[inodekey(m)]] = inodenode(key2, md2, true, m1, m2, m4), 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-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, dentrykey(m, str0) ∈ ri0, inodekey(m8) ∈ ri0, ri0[dentrykey(m, str0)] ∈ fs0, ri0[inodekey(m8)] ∈ fs0, ri0[key] ∈ fs0, key ∈ ri0, 1 ≤ m4, boolvar3 → 1 ≤ m2, m0 = 1 → links(m8, fs0, ri0) = ∅ ++ dentrykey(m, str0), boolvar0 → dentrykeys(inodekey(m8), ri0) = ∅, key.data? → fs0[ri0[key]].data? ∧ inodekey(key.ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(key.ino)]].directory ∧ # fs0[ri0[key]].data = VFS_PAGE_SIZE, 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.inode? → fs0[ri0[key]].inode? ∧ key.ino ≠ 0, m1 ≠ 0 ∨ m = ROOT_INO, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar0 ∧ boolvar2 ∧ m6 = m10 ⊦ (adr4 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), 0);fs0[(dentrykey(m, str0) = key ⊃ adr2;ri0[key])]) ) ) ) .key = key, 0 = m, 0 = m8, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, inodekey(m8) = key, inodekey(m) = key, m0 = 0, m4 = 0, m8 = ROOT_INO, inodekey(m) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str0)
Proof step 572:
fs0[ri0[key]].key = key, fs0[ri0[inodekey(m8)]] = inodenode(key1, md0, boolvar0, m0, m9, m10), fs0[ri0[dentrykey(m, str0)]] = dentrynode(key0, m8), fs0[ri0[inodekey(m)]] = inodenode(key2, md2, true, m1, m2, m4), key.dentry?, 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-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, dentrykey(m, str0) ∈ ri0, inodekey(m8) ∈ ri0, ri0[dentrykey(m, str0)] ∈ fs0, ri0[inodekey(m8)] ∈ fs0, ri0[key] ∈ fs0, key ∈ ri0, 1 ≤ m4, boolvar3 → 1 ≤ m2, m0 = 1 → links(m8, fs0, ri0) = ∅ ++ dentrykey(m, str0), boolvar0 → dentrykeys(inodekey(m8), ri0) = ∅, key.data? → fs0[ri0[key]].data? ∧ inodekey(key.ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(key.ino)]].directory ∧ # fs0[ri0[key]].data = VFS_PAGE_SIZE, 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.inode? → fs0[ri0[key]].inode? ∧ key.ino ≠ 0, m1 ≠ 0 ∨ m = ROOT_INO, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar0 ∧ boolvar2 ∧ m6 = m10 ⊦ 0 = m, 0 = m8, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, inodekey(m8) = key, inodekey(m) = key, m0 = 0, m4 = 0, m8 = ROOT_INO, inodekey(m) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str0), (adr4 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), 0);fs0[(dentrykey(m, str0) = key ⊃ adr2;ri0[key])]) ) ) ) .dentry? ∧ inodekey(key.ino) ∈ ri0 ∧ ( (adr4 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), 0);fs0[(dentrykey(m, str0) = key ⊃ adr2;ri0[key])]) ) ) ) .ino = m8 ∨ (adr4 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), 0);fs0[(dentrykey(m, str0) = key ⊃ adr2;ri0[key])]) ) ) ) .ino = m ∨ inodekey ((adr4 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), 0);fs0[(dentrykey(m, str0) = key ⊃ adr2;ri0[key])]) ) ) ) .ino) ∈ ri0) ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey ((adr4 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), 0);fs0[(dentrykey(m, str0) = key ⊃ adr2;ri0[key])]) ) ) ) .ino) ∈ ro ∧ (adr4 = (m8 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (m8 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (m8 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (m8 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m, str0), 0) ;fs0[(m8 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)]))] ) ) ) ) .directory
Proof step 594:
fs0[ri0[key]].key = key, fs0[ri0[inodekey(m8)]] = inodenode(key1, md0, boolvar0, m0, m9, m10), fs0[ri0[dentrykey(m, str0)]] = dentrynode(key0, m8), fs0[ri0[inodekey(m)]] = inodenode(key2, md2, true, m1, m2, m4), key.data?, 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-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, dentrykey(m, str0) ∈ ri0, inodekey(m8) ∈ ri0, ri0[dentrykey(m, str0)] ∈ fs0, ri0[inodekey(m8)] ∈ fs0, ri0[key] ∈ fs0, key ∈ ri0, 1 ≤ m4, boolvar3 → 1 ≤ m2, m0 = 1 → links(m8, fs0, ri0) = ∅ ++ dentrykey(m, str0), boolvar0 → dentrykeys(inodekey(m8), ri0) = ∅, key.data? → fs0[ri0[key]].data? ∧ inodekey(key.ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(key.ino)]].directory ∧ # fs0[ri0[key]].data = VFS_PAGE_SIZE, 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.inode? → fs0[ri0[key]].inode? ∧ key.ino ≠ 0, m1 ≠ 0 ∨ m = ROOT_INO, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar0 ∧ boolvar2 ∧ m6 = m10 ⊦ 0 = m, 0 = m8, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, inodekey(m8) = key, inodekey(m) = key, m0 = 0, m4 = 0, m8 = ROOT_INO, inodekey(m) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str0), (adr4 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), 0);fs0[(dentrykey(m, str0) = key ⊃ adr2;ri0[key])]) ) ) ) .data? ∧ inodekey(key.ino) ∈ ri0 ∧ ¬ (adr4 = (m8 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (m8 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (m8 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (m8 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m, str0), 0) ;fs0[(m8 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)]))] ) ) ) ) .directory ∧ # (adr4 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), 0);fs0[(dentrykey(m, str0) = key ⊃ adr2;ri0[key])]) ) ) ) .data = VFS_PAGE_SIZE

Rule argument

pos: right 20

Additional information

Used simplifier rules: elim-inode: ⊦ key.inode? ↔ (∃ ino. key = inodekey(ino));%inode-ubifs-cons: ⊦ inodekey(ino) ∈ ri ∧ ri[inodekey(ino)] ∈ fs ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].inode?;% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)% ⊦ ¬ inodekey(m).data?; (s)% ⊦ ¬ inodekey(m).dentry?; (s)% ⊦ inodekey(m).inode?; (s)% ⊦ inodekey(m).ino = m; (s)% ⊦ inodekey(m) ≠ dentrykey(m0, str); (s)