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Proof step 730 from proof inv-truncate (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 731:
fs0[ri0[inodekey(m0)]].nlink = 0 ∧ m0 ≠ ROOT_INO ↔ inodekey(m0) ∈ ro, mkinode(m0, md, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, m4) = mkinode(m, md0, boolvar0, m1, m2, m3), ri = ri0[inodekey(m0), adr2], 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), ri0[inodekey(m0)] ∈ fs0, inodekey(m0) ∈ ri0, buf-opt.some? → # buf-opt.buf = VFS_PAGE_SIZE ⊦ ⟪aubifs_core_index_truncate# (inodekey(m0), min(n, m4), fi, ro, fo, fs0[adr1, truncnode(inodekey(m0), min(n, m4))] [adr2, inodenode(inodekey(m0), md, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n) ], (log0 + adr1 ') + adr2 ', boolvar ; ri); boolvar1 := false; inode := mkinode (m, inodenode(inodekey(m0), md, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n).meta, inodenode(inodekey(m0), md, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n).directory, inodenode(inodekey(m0), md, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n).nlink, inodenode(inodekey(m0), md, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n).nsubdirs, inodenode(inodekey(m0), md, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n).size); if boolvar1 then buf-opt := some(inodenode(inodekey(m0), md, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n).data)⟫ ( ubifs-cons (fs0[adr1, truncnode(inodekey(m0), min(n, m4))] [adr2, inodenode(inodekey(m0), md, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n) ], ri, ro, fi, fo, (log0 + adr1 ') + adr2 ') ∧ replay-cons-strong (fs0[adr1, truncnode(inodekey(m0), min(n, m4))] [adr2, inodenode(inodekey(m0), md, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n) ], ri, ro, fi, fo, (log0 + adr1 ') + adr2 ') ∧ file-node-cons (fs0[adr1, truncnode(inodekey(m0), min(n, m4))] [adr2, inodenode(inodekey(m0), md, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n) ], ri) ∧ orphans-cons (fs0[adr1, truncnode(inodekey(m0), min(n, m4))] [adr2, inodenode(inodekey(m0), md, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n) ], ri, ro)), adr1 = adr2, m0 = 0, fs0[ri0[inodekey(m0)]].directory, adr1 ∈ fs0, adr2 ∈ fs0, m4 ≤ n ∧ m4 % VFS_PAGE_SIZE ≠ 0

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 (m0, md, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, m4), m, md0, boolvar0, m1, m2, m3]

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 (m0, md, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, m4), m, md0, boolvar0, m1, m2, m3