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Proof step 112 from proof inv-rename-new-reparent (previous step)

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), key.data?, 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], fs0[ri0[key]].data? ∧ ¬ (adr4 = (m = key.ino ⊃ adr3;ri0[inodekey(key.ino)]) ⊃ inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ;(adr3 = (m = key.ino ⊃ adr3;ri0[inodekey(key.ino)]) ⊃ inodenode(inodekey(m), md, true, m2, n0, m1) ;(adr2 = (m = key.ino ⊃ adr3;ri0[inodekey(key.ino)]) ⊃ dentrynode(dentrykey(m0, str0), m3) ;(adr1 = (m = key.ino ⊃ adr3;ri0[inodekey(key.ino)]) ⊃ dentrynode(dentrykey(m, str), 0);fs0[(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])]) ) ) ) .directory ∧ # fs0[ri0[key]].data = VFS_PAGE_SIZE

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 113:
fs0[ri0[datakey(ino, n)]].key = datakey(ino, n), 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), fs0[ri0[datakey(ino, n)]].data?, (adr4 = (m = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m0), md0, true, m6, m7 + (boolvar2 ⊃ 1;0), m8 + 1) ;(adr3 = (m = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m), md, true, m2, n0, m1) ;(adr2 = (m = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m0, str0), m3) ;(adr1 = (m = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m, str), 0);fs0[(m = ino ⊃ adr3;ri0[inodekey(ino)])]) ) ) ) .directory, 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[datakey(ino, n)] ∈ fs0, datakey(ino, n) ∈ 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(ino) ∈ ri0, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar0 ∧ boolvar2 ∧ m4 = m10, m6 ≠ 0 ∨ m0 = ROOT_INO, m2 ≠ 0 ∨ m = ROOT_INO ⊦ adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, ino = 0, m = 0, m0 = 0, m0 = m, m0 = ino, fs0[ri0[inodekey(ino)]].directory, 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]

Rule argument

Additional information

Used simplifier rules: elim-data: ⊦ key.data? ↔ (∃ ino, n. key = datakey(ino, n));%data-ubifs-cons: ⊦ datakey(ino, n) ∈ ri ∧ ri[datakey(ino, n)] ∈ fs ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[datakey(ino, n)]].data?;%ubifs-file-in: ⊦ datakey(ino, n) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → inodekey(ino) ∈ ri; (forward) from specification aubifs-inv%ubifs-file-notdir: ⊦ datakey(ino, n) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → ¬ fs[ri[inodekey(ino)]].directory; (forward) from specification aubifs-inv% ⊦ ¬ datakey(m, m0).inode?; (s)% ⊦ ¬ datakey(m, m0).dentry?; (s)%⊦ datakey(m, n) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → # fs[ri[datakey(m, n)]].data = VFS_PAGE_SIZE; (s)% ⊦ datakey(m, m0).data?; (s)% ⊦ datakey(m, m0) ≠ dentrykey(m1, str); (s)% ⊦ inodekey(m) ≠ datakey(m0, m1); (s)% ⊦ datakey(m, m0).ino = m; (s)