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Proof step 577 from proof inv-truncate (previous step)

fs0[ri0[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO ↔ inodekey(m) ∈ ro, ri = ri0[inodekey(m), adr2], m2 % VFS_PAGE_SIZE ≠ 0, adr1 ≠ adr2, m ≠ 0, fs0[ri0[inodekey(m)]].inode?, fo.inodes?, ro.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(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, m2 ≤ n, ¬ fs0[ri0[inodekey(m)]].directory, ¬ buf-opt.some?, ¬ datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri0, ¬ adr1 ∈ fs0, ¬ adr2 ∈ fs0 ⊦ ⟪aubifs_core_index_truncate# (inodekey(m), m2, fi, ro, fo, fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n)], (log0 + adr1 ') + adr2 ', boolvar ; ri); boolvar1 := false; inode := mkinode (mkinode(m, md, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, m2).ino, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n).meta, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n).directory, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n).nlink, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n).nsubdirs, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n).size); if boolvar1 then buf-opt := some(inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n).data)⟫ ( ubifs-cons (fs0[adr1, truncnode(inodekey(m), m2)] [adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n) ], ri, ro, fi, fo, (log0 + adr1 ') + adr2 ') ∧ replay-cons-strong (fs0[adr1, truncnode(inodekey(m), m2)] [adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n) ], ri, ro, fi, fo, (log0 + adr1 ') + adr2 ') ∧ file-node-cons (fs0[adr1, truncnode(inodekey(m), m2)] [adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n) ], ri) ∧ orphans-cons (fs0[adr1, truncnode(inodekey(m), m2)] [adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n) ], ri, ro))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 578:
fs0[ri0[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO ↔ inodekey(m) ∈ ro, mkinode(m, md, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, m2) = mkinode(m0, md0, boolvar0, m1, m3, m4), ri = ri0[inodekey(m), adr2], fs0[ri0[inodekey(m)]].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(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, m2 ≤ n ⊦ ⟪aubifs_core_index_truncate# (inodekey(m), m2, fi, ro, fo, fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n)], (log0 + adr1 ') + adr2 ', boolvar ; ri); boolvar1 := false; inode := mkinode (m0, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n).meta, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n).directory, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n).nlink, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n).nsubdirs, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n).size); if boolvar1 then buf-opt := some(inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n).data)⟫ ( ubifs-cons (fs0[adr1, truncnode(inodekey(m), m2)] [adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n) ], ri, ro, fi, fo, (log0 + adr1 ') + adr2 ') ∧ replay-cons-strong (fs0[adr1, truncnode(inodekey(m), m2)] [adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n) ], ri, ro, fi, fo, (log0 + adr1 ') + adr2 ') ∧ file-node-cons (fs0[adr1, truncnode(inodekey(m), m2)] [adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n) ], ri) ∧ orphans-cons (fs0[adr1, truncnode(inodekey(m), m2)] [adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n) ], ri, ro)), m2 % VFS_PAGE_SIZE = 0, adr1 = adr2, m = 0, fs0[ri0[inodekey(m)]].directory, buf-opt.some?, datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri0, adr1 ∈ fs0, adr2 ∈ fs0

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [mkinode (m, md, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, m2), m0, md0, boolvar0, m1, m3, m4]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: mkinode (m, md, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, m2), m0, md0, boolvar0, m1, m3, m4