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Proof step 97 from proof inv-rename-new-reparent (previous step)

fs0[ri0[key]].key = key, fs0[ri0[dentrykey(m, str)]] = dentrynode(key1, m3), fs0[ri0[inodekey(m3)]] = inodenode(key0, md1, boolvar0, m5, m9, m10), fs0[ri0[inodekey(m0)]] = inodenode(key2, md3, true, m6, m7, m8), 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), inodekey(key.ino) ∈ ri0, dentrykey(m, str) ∈ ri0, inodekey(m3) ∈ ri0, inodekey(m0) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, ri0[inodekey(m3)] ∈ fs0, inodekey(m) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, key ∈ ri0, ri0[key] ∈ fs0, key.inode? → fs0[ri0[key]].inode?, key.dentry? → fs0[ri0[key]].dentry? ∧ 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? ∧ ¬ fs0[ri0[inodekey(key.ino)]].directory ∧ # fs0[ri0[key]].data = VFS_PAGE_SIZE, m2 ≠ 0 ∨ m = ROOT_INO, m6 ≠ 0 ∨ m0 = ROOT_INO, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar0 ∧ boolvar2 ∧ m4 = m10 ⊦ key.ino = 0, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, key = dentrykey(m, str), key = inodekey(m), key = inodekey(m0), m = 0, m0 = m, m0 = 0, adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2], inodekey(m) ∈ ro, dentrykey(m0, str0) ∈ ri0, inodekey(m0) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str), adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3], ( key.dentry? → fs0[ri0[key]].dentry? ∧ inodekey(fs0[ri0[key]].ino) ∈ ri0 ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey(fs0[ri0[key]].ino) ∈ ro ∧ (adr4 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ;(adr3 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m), md, true, m2, n0, m1) ;(adr2 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m0, str0), m3) ;(adr1 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)]))] ) ) ) ) .directory) ∧ ( key.data? → fs0[ri0[key]].data? ∧ ¬ (adr4 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ;(adr3 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m), md, true, m2, n0, m1) ;(adr2 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m0, str0), m3) ;(adr1 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)]))] ) ) ) ) .directory ∧ # fs0[ri0[key]].data = VFS_PAGE_SIZE)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 98:
fs0[ri0[key]].key = key, fs0[ri0[inodekey(m0)]] = inodenode(key2, md3, true, m6, m7, m8), fs0[ri0[inodekey(m3)]] = inodenode(key0, md1, boolvar0, m5, m9, m10), fs0[ri0[dentrykey(m, str)]] = dentrynode(key1, m3), 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), ri0[key] ∈ fs0, key ∈ ri0, ri0[inodekey(m)] ∈ fs0, ri0[inodekey(m0)] ∈ fs0, inodekey(m) ∈ ri0, ri0[inodekey(m3)] ∈ fs0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m0) ∈ ri0, inodekey(m3) ∈ ri0, dentrykey(m, str) ∈ ri0, inodekey(key.ino) ∈ ri0, key.data? → fs0[ri0[key]].data? ∧ ¬ fs0[ri0[inodekey(key.ino)]].directory ∧ # fs0[ri0[key]].data = VFS_PAGE_SIZE, key.dentry? → fs0[ri0[key]].dentry? ∧ 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?, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar0 ∧ boolvar2 ∧ m4 = m10, m6 ≠ 0 ∨ m0 = ROOT_INO, m2 ≠ 0 ∨ m = ROOT_INO ⊦ key.ino = 0, adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, key = inodekey(m0), key = inodekey(m), key = dentrykey(m, str), m = 0, m0 = 0, m0 = m, m0 = key.ino, adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3], adr2 ∈ ri0 -- dentrykey(m, str), adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m0) ∈ ro, dentrykey(m0, str0) ∈ ri0, inodekey(m) ∈ ro, adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2], ( key.dentry? → fs0[ri0[key]].dentry? ∧ inodekey(fs0[ri0[key]].ino) ∈ ri0 ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey(fs0[ri0[key]].ino) ∈ ro ∧ (adr4 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ;(adr3 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m), md, true, m2, n0, m1) ;(adr2 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m0, str0), m3) ;(adr1 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)]))] ) ) ) ) .directory) ∧ ( key.data? → fs0[ri0[key]].data? ∧ ¬ (adr4 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ;(adr3 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m), md, true, m2, n0, m1) ;(adr2 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m0, str0), m3) ;(adr1 = (m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(m0 = key.ino ⊃ adr4;(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)]))] ) ) ) ) .directory ∧ # fs0[ri0[key]].data = VFS_PAGE_SIZE)

Rule argument

fma: m0 = key.ino

Additional information

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