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Proof step 40 from proof inv-truncate (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, boolvar0 ↔ boolvar, fs0[ri[inodekey(m0)]].nlink = 0 ∧ m0 ≠ ROOT_INO ↔ inodekey(m0) ∈ ro, VFS_PAGE_SIZE = n0 + m4 % VFS_PAGE_SIZE, adr = adr3, adr0 = adr2, adr4 = adr1, adr6 = adr5, err = ESUCCESS, fs = fs0[adr4, nd1][adr0, nd0][adr, nd], inode = mkinode(m0, md, false, fs0[ri[inodekey(m0)]].nlink, fs0[ri[inodekey(m0)]].nsubdirs, m4), log = ((log0 + adr4) + adr0) + adr, nd = datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf-opt.buf).data, zero, m4 % VFS_PAGE_SIZE, n0)), nd0 = inodenode(inodekey(m0), md, false, fs0[ri[inodekey(m0)]].nlink, fs0[ri[inodekey(m0)]].nsubdirs, n), nd1 = truncnode(inodekey(m0), m4), datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf-opt.buf).data?, fs0[ri[inodekey(m0)]].inode?, ro.inodes?, fo.inodes?, buf-opt.some?, file-node-cons(fs0, ri), log-cons(log0, fs0), new(adr1 ' + (adr2 ' + adr3), fs0), orphans-cons(fs0, ri, ro), replay-cons-strong(fs0, ri, ro, fi, fo, log0), ri-inj(ri), ri-inj(fi), ubifs-cons(fs0, ri, ro, fi, fo, log0), ri[inodekey(m0)] ∈ fs0, inodekey(m0) ∈ ri, m4 % VFS_PAGE_SIZE + n0 ≤ # datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf-opt.buf).data, m4 ≤ n ⊦ ⟪aubifs_core_index_store#(datakey(m0, m4 / VFS_PAGE_SIZE), adr, fi, ro, fo, fs, log, boolvar0; ri); if err = ESUCCESS then {aubifs_core_index_store#(inodekey(m0), adr0, fi, ro, fo, fs, log, boolvar0; ri); aubifs_core_index_truncate#(inodekey(m0), m4, 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-opt0 := some (datanode (datakey(m0, m4 / VFS_PAGE_SIZE), fill(datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf-opt.buf).data, zero, m4 % VFS_PAGE_SIZE, n0)) .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)), m4 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0, fs0[ri[inodekey(m0)]].directory, dups(adr1 ' + adr2 ' + adr3 ')

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 41:
# buf-opt.buf = VFS_PAGE_SIZE, fs0[ri[inodekey(m0)]].nlink = 0 ∧ m0 ≠ ROOT_INO ↔ inodekey(m0) ∈ ro, VFS_PAGE_SIZE = n0 + m4 % VFS_PAGE_SIZE, fs = fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md, false, fs0[ri[inodekey(m0)]].nlink, fs0[ri[inodekey(m0)]].nsubdirs, n)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m4 % VFS_PAGE_SIZE, n0)) ], inode = mkinode(m0, md, false, fs0[ri[inodekey(m0)]].nlink, fs0[ri[inodekey(m0)]].nsubdirs, m4), nd0 = inodenode(inodekey(m0), md, false, fs0[ri[inodekey(m0)]].nlink, fs0[ri[inodekey(m0)]].nsubdirs, n), m4 % VFS_PAGE_SIZE ≠ 0, adr1 ≠ adr3, adr1 ≠ adr2, adr2 ≠ adr3, fs0[ri[inodekey(m0)]].inode?, ro.inodes?, fo.inodes?, buf-opt.some?, file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, ro), replay-cons-strong(fs0, ri, ro, fi, fo, log0), ri-inj(ri), ri-inj(fi), ubifs-cons(fs0, ri, ro, fi, fo, log0), ri[inodekey(m0)] ∈ fs0, inodekey(m0) ∈ ri, m4 ≤ n, ¬ fs0[ri[inodekey(m0)]].directory, ¬ adr1 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr3 ∈ fs0 ⊦ ⟪aubifs_core_index_store#(datakey(m0, m4 / VFS_PAGE_SIZE), adr3, fi, ro, fo, fs, ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar0; ri); log := ((log0 + adr1 ') + adr2 ') + adr3 '; aubifs_core_index_store#(inodekey(m0), adr2, fi, ro, fo, fs, log, boolvar0; ri); aubifs_core_index_truncate#(inodekey(m0), m4, 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-opt0 := some (datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf-opt.buf).data, zero, m4 % VFS_PAGE_SIZE, n0)) .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))

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m; (s)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ adr ∈ adr0 ' ↔ adr = adr0; (s)% ⊦ adr ∈ adr0 ' + ax ↔ adr = adr0 ∨ adr ∈ ax; (s)% ⊦ dups(adr ' + adr0 ') ↔ adr = adr0; (s)% ⊦ dups(adr ' + ax) ↔ dups(ax) ∨ adr ∈ ax; (ws)% ⊦ datanode(key, buf).data?; (s)% ⊦ new(adr ', fs) ↔ ¬ adr ∈ fs; (s)% ⊦ new(adr ' + log, fs) ↔ ¬ adr ∈ fs ∧ new(log, fs); (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ ax + adr = ax + adr '; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)% ⊦ datanode(key, buf).data = buf; (s)