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Proof step 344 from proof inv-truncate (previous step)

m = 0 ∧ m0 ≠ ROOT_INO ↔ inodekey(m0) ∈ ro, VFS_PAGE_SIZE = n0 + m4 % VFS_PAGE_SIZE, fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]] = datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf0), fs0[ri0[inodekey(m0)]] = inodenode(key1, md, false, m, m1, m2), key0.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-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), inodekey(m0) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, datakey(m0, m4 / VFS_PAGE_SIZE) ∈ ri0, ri0[datakey(m0, m4 / VFS_PAGE_SIZE)] ∈ fs0, ri0[key0] ∈ fs0, key0 ∈ ri0, m4 ≤ n1, ro ⊆ dom ri0, key0.data? → fs0[ri0[key0]].data? ∧ inodekey(key0.ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(key0.ino)]].directory ∧ # fs0[ri0[key0]].data = VFS_PAGE_SIZE, key0.dentry? → fs0[ri0[key0]].dentry? ∧ inodekey(key0.ino) ∈ ri0 ∧ inodekey(fs0[ri0[key0]].ino) ∈ ri0 ∧ ¬ inodekey(key0.ino) ∈ ro ∧ ¬ inodekey(fs0[ri0[key0]].ino) ∈ ro ∧ fs0[ri0[inodekey(key0.ino)]].directory, key0.inode? → fs0[ri0[key0]].inode? ∧ key0.ino ≠ 0, ¬ key0.data? ∨ key0.ino ≠ m0 ∨ ¬ m4 ≤ key0.part * VFS_PAGE_SIZE ⊦ m4 % VFS_PAGE_SIZE = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, inodekey(m0) = key0, m0 = 0, buf-opt.some?, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr3 ∈ ri0, (adr3 = (key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;(adr2 = (key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ inodenode(inodekey(m0), md0, false, m, m1, n1) ;(adr1 = (key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ truncnode(inodekey(m0), m4) ;fs0[(key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0]))] ) ) ) .data? ∧ inodekey(key0.ino) ∈ ri0 ∧ ¬ (adr3 = (m0 = key0.ino ⊃ adr2;ri0[inodekey(key0.ino)]) ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;(adr2 = (m0 = key0.ino ⊃ adr2;ri0[inodekey(key0.ino)]) ⊃ inodenode(inodekey(m0), md0, false, m, m1, n1) ;(adr1 = (m0 = key0.ino ⊃ adr2;ri0[inodekey(key0.ino)]) ⊃ truncnode(inodekey(m0), m4);fs0[(m0 = key0.ino ⊃ adr2;ri0[inodekey(key0.ino)])]) ) ) .directory ∧ # (adr3 = (key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;(adr2 = (key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ inodenode(inodekey(m0), md0, false, m, m1, n1) ;(adr1 = (key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0])) ⊃ truncnode(inodekey(m0), m4) ;fs0[(key0.ino = m0 ∧ m4 ≤ key0.part * VFS_PAGE_SIZE ⊃ (∅)[key0];(datakey(m0, m4 / VFS_PAGE_SIZE) = key0 ⊃ adr3;ri0[key0]))] ) ) ) .data = VFS_PAGE_SIZE

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 345:
m = 0 ∧ m0 ≠ ROOT_INO ↔ inodekey(m0) ∈ ro, VFS_PAGE_SIZE = n0 + m4 % VFS_PAGE_SIZE, fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]] = datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf0), fs0[ri0[inodekey(m0)]] = inodenode(key1, md, false, m, m1, m2), fs0[ri0[datakey(ino, n)]].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-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), inodekey(m0) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, datakey(m0, m4 / VFS_PAGE_SIZE) ∈ ri0, ri0[datakey(m0, m4 / VFS_PAGE_SIZE)] ∈ fs0, ri0[datakey(ino, n)] ∈ fs0, datakey(ino, n) ∈ ri0, inodekey(ino) ∈ ri0, m4 ≤ n1, ro ⊆ dom ri0, ino ≠ m0 ∨ ¬ m4 ≤ n * VFS_PAGE_SIZE ⊦ m4 % VFS_PAGE_SIZE = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, m0 = 0, fs0[ri0[inodekey(ino)]].directory, buf-opt.some?, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr3 ∈ ri0, (adr3 = (ino = m0 ∧ m4 ≤ n * VFS_PAGE_SIZE ⊃ (∅)[datakey(m0, n)];(datakey(m0, m4 / VFS_PAGE_SIZE) = datakey(ino, n) ⊃ adr3;ri0[datakey(ino, n)])) ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;(adr2 = (ino = m0 ∧ m4 ≤ n * VFS_PAGE_SIZE ⊃ (∅)[datakey(m0, n)];(datakey(m0, m4 / VFS_PAGE_SIZE) = datakey(ino, n) ⊃ adr3;ri0[datakey(ino, n)])) ⊃ inodenode(inodekey(m0), md0, false, m, m1, n1) ;( adr1 = (ino = m0 ∧ m4 ≤ n * VFS_PAGE_SIZE ⊃ (∅)[datakey(m0, n)];(datakey(m0, m4 / VFS_PAGE_SIZE) = datakey(ino, n) ⊃ adr3;ri0[datakey(ino, n)])) ⊃ truncnode(inodekey(m0), m4) ;fs0[(ino = m0 ∧ m4 ≤ n * VFS_PAGE_SIZE ⊃ (∅)[datakey(m0, n)];(datakey(m0, m4 / VFS_PAGE_SIZE) = datakey(ino, n) ⊃ adr3;ri0[datakey(ino, n)]))] ) ) ) .data? ∧ ¬ (adr3 = (m0 = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;(adr2 = (m0 = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m0), md0, false, m, m1, n1) ;(adr1 = (m0 = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ truncnode(inodekey(m0), m4);fs0[(m0 = ino ⊃ adr2;ri0[inodekey(ino)])]) ) ) .directory ∧ # ( adr3 = (ino = m0 ∧ m4 ≤ n * VFS_PAGE_SIZE ⊃ (∅)[datakey(m0, n)];(datakey(m0, m4 / VFS_PAGE_SIZE) = datakey(ino, n) ⊃ adr3;ri0[datakey(ino, n)])) ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;( adr2 = (ino = m0 ∧ m4 ≤ n * VFS_PAGE_SIZE ⊃ (∅)[datakey(m0, n)];(datakey(m0, m4 / VFS_PAGE_SIZE) = datakey(ino, n) ⊃ adr3;ri0[datakey(ino, n)])) ⊃ inodenode(inodekey(m0), md0, false, m, m1, n1) ;( adr1 = (ino = m0 ∧ m4 ≤ n * VFS_PAGE_SIZE ⊃ (∅)[datakey(m0, n)];(datakey(m0, m4 / VFS_PAGE_SIZE) = datakey(ino, n) ⊃ adr3;ri0[datakey(ino, n)])) ⊃ truncnode(inodekey(m0), m4) ;fs0 [(ino = m0 ∧ m4 ≤ n * VFS_PAGE_SIZE ⊃ (∅)[datakey(m0, n)];(datakey(m0, m4 / VFS_PAGE_SIZE) = datakey(ino, n) ⊃ adr3;ri0[datakey(ino, n)])) ] ) ) ) .data = VFS_PAGE_SIZE

Rule argument

Additional information

Used simplifier rules: elim-data: ⊦ key.data? ↔ (∃ ino, n. key = datakey(ino, n));%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).part = m0; (s)% ⊦ ¬ 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).ino = m; (s)% ⊦ datakey(m, m0).data?; (s)% ⊦ inodekey(m) ≠ datakey(m0, m1); (s)