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Proof step 303 from proof inv-truncate (previous step)

fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data, zero, m4 % VFS_PAGE_SIZE, n0) = datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf), boolvar ↔ boolvar0, fs0[ri0[inodekey(m0)]].nlink = 0 ∧ m0 ≠ ROOT_INO ↔ inodekey(m0) ∈ ro, VFS_PAGE_SIZE = n0 + m4 % VFS_PAGE_SIZE, adr = adr2, fs = fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n)] [adr3, fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data, zero, m4 % VFS_PAGE_SIZE, n0) ], key = inodekey(m0), log = ((log0 + adr1 ') + adr2 ') + adr3 ', ri = ri1[key, adr], ri1 = ri0[datakey(m0, m4 / VFS_PAGE_SIZE), adr3], fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data?, fs0[ri0[inodekey(m0)]].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), inodekey(m0) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, datakey(m0, m4 / VFS_PAGE_SIZE) ∈ ri0, ri0[datakey(m0, m4 / VFS_PAGE_SIZE)] ∈ fs0, m4 % VFS_PAGE_SIZE + n0 ≤ # fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data, m4 ≤ n ⊦ ⟪aubifs_core_index_truncate# (inodekey(m0), m4, fi, ro, fo, fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n) ] [adr3, fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data, zero, m4 % VFS_PAGE_SIZE, n0) ], ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar0 ; ri); boolvar1 := true; inode := mkinode (m0, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n).meta, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n).directory, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n).nlink, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n).nsubdirs, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n).size); if boolvar1 then buf-opt := some(buf)⟫ ( ubifs-cons (fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n) ] [adr3, fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data, zero, m4 % VFS_PAGE_SIZE, n0) ], ri, ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ replay-cons-strong (fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n) ] [adr3, fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data, zero, m4 % VFS_PAGE_SIZE, n0) ], ri, ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ file-node-cons (fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n) ] [adr3, fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data, zero, m4 % VFS_PAGE_SIZE, n0) ], ri) ∧ orphans-cons (fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n) ] [adr3, fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data, zero, m4 % VFS_PAGE_SIZE, n0) ], ri, ro)), m4 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, m0 = 0, fs0[ri0[inodekey(m0)]].directory, buf-opt.some?, adr3 ∈ ri0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 304:
fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data, zero, m4 % VFS_PAGE_SIZE, n0) = datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf), fs0[ri0[inodekey(m0)]].nlink = 0 ∧ m0 ≠ ROOT_INO ↔ inodekey(m0) ∈ ro, VFS_PAGE_SIZE = n0 + m4 % VFS_PAGE_SIZE, ri = ri0[datakey(m0, m4 / VFS_PAGE_SIZE), adr3][inodekey(m0), adr2], m4 % VFS_PAGE_SIZE ≠ 0, adr1 ≠ adr2, adr1 ≠ adr3, adr2 ≠ adr3, m0 ≠ 0, fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data?, fs0[ri0[inodekey(m0)]].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), inodekey(m0) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, datakey(m0, m4 / VFS_PAGE_SIZE) ∈ ri0, ri0[datakey(m0, m4 / VFS_PAGE_SIZE)] ∈ fs0, m4 ≤ n, ¬ fs0[ri0[inodekey(m0)]].directory, ¬ buf-opt.some?, ¬ adr3 ∈ ri0, ¬ adr3 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr1 ∈ fs0 ⊦ ⟪aubifs_core_index_truncate# (inodekey(m0), m4, fi, ro, fo, fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n) ] [adr3, fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data, zero, m4 % VFS_PAGE_SIZE, n0) ], ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar0 ; ri); boolvar1 := true; inode := mkinode (m0, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n).meta, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n).directory, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n).nlink, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n).nsubdirs, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n).size); if boolvar1 then buf-opt := some(buf)⟫ ( ubifs-cons (fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n) ] [adr3, fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data, zero, m4 % VFS_PAGE_SIZE, n0) ], ri, ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ replay-cons-strong (fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n) ] [adr3, fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data, zero, m4 % VFS_PAGE_SIZE, n0) ], ri, ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ file-node-cons (fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n) ] [adr3, fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data, zero, m4 % VFS_PAGE_SIZE, n0) ], ri) ∧ orphans-cons (fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n) ] [adr3, fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data, zero, m4 % VFS_PAGE_SIZE, n0) ], ri, ro))

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m; (s)%c: ⊦ m + n = n + m; from specification nat-basic%⊦ datakey(m, n) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → # fs[ri[datakey(m, n)]].data = VFS_PAGE_SIZE; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)