[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 291 from proof inv-truncate (previous step)

fs0[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO ↔ inodekey(m) ∈ ro, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, fs = fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, n)] [adr3, fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data, zero, m2 % VFS_PAGE_SIZE, n0) ], inode = mkinode(m, md, false, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2), nd = fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data, zero, m2 % VFS_PAGE_SIZE, n0), nd0 = inodenode(inodekey(m), md, false, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, n), m2 % VFS_PAGE_SIZE ≠ 0, adr1 ≠ adr2, adr1 ≠ adr3, adr2 ≠ adr3, m ≠ 0, fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data?, fs0[ri[inodekey(m)]].inode?, ro.inodes?, fo.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), node-cons ((fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data, zero, m2 % VFS_PAGE_SIZE, n0)).key, fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data, zero, m2 % VFS_PAGE_SIZE, n0)), orphans-cons(fs0, ri, ro), replay-cons-strong(fs0, ri, ro, fi, fo, log0), ri-cons(ri, fs0), ri-inj(ri), ri-inj(fi), ubifs-cons(fs0, ri, ro, fi, fo, log0), inodekey(m) ∈ ri, ri[inodekey(m)] ∈ fs0, datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri, ri[datakey(m, m2 / VFS_PAGE_SIZE)] ∈ fs0, m2 ≤ n, ¬ fs0[ri[inodekey(m)]].directory, ¬ buf-opt.some?, ¬ adr3 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr1 ∈ fs0 ⊦ ⟪aubifs_core_index_store#(datakey(m, m2 / VFS_PAGE_SIZE), adr3, fi, ro, fo, fs, ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar0; ri); log := ((log0 + adr1 ') + adr2 ') + adr3 '; aubifs_core_index_store#(inodekey(m), adr2, fi, ro, fo, fs, log, boolvar0; ri); aubifs_core_index_truncate#(inodekey(m), m2, fi, ro, fo, fs, log, boolvar0; ri); boolvar1 := true; inode := mkinode(inode.ino, nd0.meta, nd0.directory, nd0.nlink, nd0.nsubdirs, nd0.size); if boolvar1 then buf-opt := some(nd.data)⟫ (ubifs-cons(fs, ri, ro, fi, fo, log) ∧ replay-cons-strong(fs, ri, ro, fi, fo, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 292:
boolvar ↔ boolvar0, fs0[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO ↔ inodekey(m) ∈ ro, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, adr = adr3, fs = fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, n)] [adr3, fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data, zero, m2 % VFS_PAGE_SIZE, n0) ], inode = mkinode(m, md, false, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2), key = datakey(m, m2 / VFS_PAGE_SIZE), log = ((log0 + adr1 ') + adr2 ') + adr3 ', nd = fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data, zero, m2 % VFS_PAGE_SIZE, n0), nd0 = inodenode(inodekey(m), md, false, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, n), fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data?, fs0[ri[inodekey(m)]].inode?, fo.inodes?, ro.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), node-cons ((fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data, zero, m2 % VFS_PAGE_SIZE, n0)).key, fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data, zero, m2 % VFS_PAGE_SIZE, n0)), orphans-cons(fs0, ri, ro), replay-cons-strong(fs0, ri, ro, fi, fo, log0), ri-cons(ri, fs0), ri-inj(fi), ri-inj(ri), ubifs-cons(fs0, ri, ro, fi, fo, log0), ri[datakey(m, m2 / VFS_PAGE_SIZE)] ∈ fs0, datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri, ri[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri, m2 ≤ n ⊦ ⟪if ¬ adr ∈ ri ∧ adr ∈ fs ∧ key-cons(key, fs[adr]) then ri[key] := adr else abort; log := ((log0 + adr1 ') + adr2 ') + adr3 '; aubifs_core_index_store#(inodekey(m), adr2, fi, ro, fo, fs, log, boolvar0; ri); aubifs_core_index_truncate#(inodekey(m), m2, fi, ro, fo, fs, log, boolvar0; ri); boolvar1 := true; inode := mkinode(inode.ino, nd0.meta, nd0.directory, nd0.nlink, nd0.nsubdirs, nd0.size); if boolvar1 then buf-opt := some(nd.data)⟫ (ubifs-cons(fs, ri, ro, fi, fo, log) ∧ replay-cons-strong(fs, ri, ro, fi, fo, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro)), m2 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, m = 0, fs0[ri[inodekey(m)]].directory, buf-opt.some?, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0

Rule argument

pos: right 1

Additional information

Used simplifier rules: aubifs_core_index_store#(KEY, ADR, FI, RO, FO, FS, LOG, CSYNCED; RI) {if ¬ ADR ∈ RI ∧ ADR ∈ FS ∧ key-cons(KEY, FS[ADR]) then RI[KEY] := ADR else abort };% ⊦ VFS_PAGE_SIZE ≠ 0; (s)