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Proof step 572 from proof inv-truncate (previous step)

fs0[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO ↔ inodekey(m) ∈ ro, adr = adr4, adr0 = adr3, err = ESUCCESS, fs = fs0[adr1, nd0][adr2, nd], inode = mkinode(m, md, false, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2), log = (log0 + adr1) + adr2, nd = nd1, nd0 = truncnode(inodekey(m), m2), nd1 = inodenode(inodekey(m), md, false, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, n), fs0[ri[inodekey(m)]].inode?, ro.inodes?, fo.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), new(adr1 ' + adr2 ', fs0), node-cons(nd0.key, nd0), node-cons(nd.key, nd), 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, m2 ≤ n ⊦ ⟪aubifs_core_index_store#(inodekey(m), adr2, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_truncate#(inodekey(m), m2, fi, ro, fo, fs, log, boolvar; ri); boolvar1 := false; inode := mkinode(inode.ino, nd1.meta, nd1.directory, nd1.nlink, nd1.nsubdirs, nd1.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, fs0[ri[inodekey(m)]].directory, buf-opt.some?, dups(adr1 ' + adr2 '), datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 573:
fs0[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO ↔ inodekey(m) ∈ ro, fs = fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, n)], inode = mkinode(m, md, false, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2), nd1 = inodenode(inodekey(m), md, false, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, n), m2 % VFS_PAGE_SIZE ≠ 0, adr1 ≠ adr2, m ≠ 0, fs0[ri[inodekey(m)]].inode?, fo.inodes?, ro.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), 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[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri, m2 ≤ n, ¬ fs0[ri[inodekey(m)]].directory, ¬ buf-opt.some?, ¬ adr2 ∈ fs0, ¬ adr1 ∈ fs0, ¬ datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri ⊦ ⟪aubifs_core_index_store#(inodekey(m), adr2, fi, ro, fo, fs, (log0 + adr1 ') + adr2 ', boolvar; ri); aubifs_core_index_truncate#(inodekey(m), m2, fi, ro, fo, fs, (log0 + adr1 ') + adr2 ', boolvar; ri); boolvar1 := false; inode := mkinode(inode.ino, nd1.meta, nd1.directory, nd1.nlink, nd1.nsubdirs, nd1.size); if boolvar1 then buf-opt := some(nd1.data)⟫ ( ubifs-cons(fs, ri, ro, fi, fo, (log0 + adr1 ') + adr2 ') ∧ replay-cons-strong(fs, ri, ro, fi, fo, (log0 + adr1 ') + adr2 ') ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro))

Rule argument

Additional information

Used simplifier rules: ⊦ ax + adr = ax + adr '; (s)% ⊦ dups(adr ' + adr0 ') ↔ adr = adr0; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ new(adr ', fs) ↔ ¬ adr ∈ fs; (s)% ⊦ new(adr ' + log, fs) ↔ ¬ adr ∈ fs ∧ new(log, fs); (s)% ⊦ node-cons(key0, truncnode(key1, n)) ↔ key0.inode?; (s)% ⊦ truncnode(key, m).key = key; (s)% ⊦ inodekey(m).ino = m; (s)% ⊦ inodekey(m).inode?; (s)%⊦ node-cons(key0, inodenode(key1, md, boolvar, n, n0, m)) ↔ key0.inode? ∧ key0.ino ≠ 0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).key = key; (s)