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Proof step 590 from proof inv-truncate (previous step)

fs0[ri0[inodekey(m0)]].nlink = 0 ∧ m0 ≠ ROOT_INO ↔ inodekey(m0) ∈ ro, 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), ri0[inodekey(m0)] ∈ fs0, inodekey(m0) ∈ ri0, m4 ≤ n0 ⊦ m4 % VFS_PAGE_SIZE = 0, adr1 = adr2, m0 = 0, fs0[ri0[inodekey(m0)]].directory, buf-opt.some?, ubifs-cons (fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ], ri0[inodekey(m0), adr2] \ datakeys(inodekey(m0), m4, ri0[inodekey(m0), adr2]), ro, fi, fo, (log0 + adr1 ') + adr2 '), datakey(m0, m4 / VFS_PAGE_SIZE) ∈ ri0, adr1 ∈ fs0, adr2 ∈ fs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ubifs-cons-reduce: ⊦ ubifs-cons(fs0, ri0, ro0, fi0, fo0, log0) → ( ubifs-cons(fs1, ri1, ro1, fi1, fo1, log1) ↔ ¬ inodekey(0) ∈ ri1 ∧ (ro0.inodes? → ro1.inodes?) ∧ (fo0.inodes? → fo1.inodes?) ∧ (ro0 ⊆ dom ri0 → (∀ key. key ∈ ro1 → key ∈ ri1)) ∧ (fo0 ⊆ dom fi0 → (∀ key. key ∈ fo1 → key ∈ fi1)) ∧ (¬ dups(log0) → ¬ dups(log1)) ∧ (∀ key. ( key ∈ ri0 → ri0[key] ∈ fs0 ∧ fs0[ri0[key]].key = key ∧ (key.inode? → fs0[ri0[key]].inode? ∧ key.ino ≠ 0) ∧ ( key.dentry? → fs0[ri0[key]].dentry? ∧ inodekey(key.ino) ∈ ri0 ∧ inodekey(fs0[ri0[key]].ino) ∈ ri0 ∧ ¬ inodekey(key.ino) ∈ ro0 ∧ ¬ inodekey(fs0[ri0[key]].ino) ∈ ro0 ∧ fs0[ri0[inodekey(key.ino)]].directory) ∧ ( key.data? → fs0[ri0[key]].data? ∧ inodekey(key.ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(key.ino)]].directory ∧ # fs0[ri0[key]].data = VFS_PAGE_SIZE)) → key ∈ ri1 → ri1[key] ∈ fs1 ∧ fs1[ri1[key]].key = key ∧ (key.inode? → fs1[ri1[key]].inode? ∧ key.ino ≠ 0) ∧ ( key.dentry? → fs1[ri1[key]].dentry? ∧ inodekey(key.ino) ∈ ri1 ∧ inodekey(fs1[ri1[key]].ino) ∈ ri1 ∧ ¬ inodekey(key.ino) ∈ ro1 ∧ ¬ inodekey(fs1[ri1[key]].ino) ∈ ro1 ∧ fs1[ri1[inodekey(key.ino)]].directory) ∧ ( key.data? → fs1[ri1[key]].data? ∧ inodekey(key.ino) ∈ ri1 ∧ ¬ fs1[ri1[inodekey(key.ino)]].directory ∧ # fs1[ri1[key]].data = VFS_PAGE_SIZE)) ∧ (∀ adr. ( adr ∈ log0 → adr ∈ fs0 ∧ ( fs0[adr].inode? → fs0[adr].key.inode? ∧ fs0[adr].key.ino ≠ 0) ∧ (fs0[adr].dentry? → fs0[adr].key.dentry?) ∧ (fs0[adr].data? → fs0[adr].key.data?) ∧ (fs0[adr].trunc? → fs0[adr].key.inode?)) → adr ∈ log1 → adr ∈ fs1 ∧ ( fs1[adr].inode? → fs1[adr].key.inode? ∧ fs1[adr].key.ino ≠ 0) ∧ (fs1[adr].dentry? → fs1[adr].key.dentry?) ∧ (fs1[adr].data? → fs1[adr].key.data?) ∧ (fs1[adr].trunc? → fs1[adr].key.inode?)));%in-ri: ⊦ key0 ∈ ri[key1, adr] ↔ key0 = key1 ∨ key0 ∈ ri;%at-diff-ri: ⊦ (ri \ ks)[key] = (key ∈ ks ⊃ (∅)[key];ri[key]);%at-ri: ⊦ ri[key0, adr][key1] = (key0 = key1 ⊃ adr;ri[key1]);%at-fs: ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]);% ⊦ adr ∈ adr0 ' ↔ adr = adr0; (s)% ⊦ adr ∈ adr0 ' + ax ↔ adr = adr0 ∨ adr ∈ ax; (s)% ⊦ adr ∈ ax + ax0 ↔ adr ∈ ax ∨ adr ∈ ax0; (s)% ⊦ ¬ inodekey(m).data?; (s)% ⊦ key.dentry? → ¬ key.data?; (s)% ⊦ key.inode? → ¬ key.data?; (s)% ⊦ adr ∈ fs[adr1, nd] ↔ adr = adr1 ∨ adr ∈ fs; (s)% ⊦ ri-cons(ri, fs) ∧ key ∈ ri → fs[ri[key]].key = key; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]%⊦ ubifs-cons(fs, ri, ro, fi, fo, log) ∧ ¬ adr0 ∈ fs ∧ ¬ adr1 ∈ fs ∧ adr0 ≠ adr1 → ¬ dups(log + adr0 ' + adr1 '); (s)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → ¬ dups(log); (s)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) ∧ key ∈ fo → key ∈ fi; (ss)% ⊦ inodekey(m).ino = m; (s)% ⊦ inodekey(m).inode?; (s)%⊦ key ∈ datakeys(key0, ri) ↔ key ∈ ri ∧ key.data? ∧ key0.inode? ∧ key.ino = key0.ino; (s)% ⊦ datakeys(key, ri[inodekey(ino), adr]) = datakeys(key, ri); (s)%⊦ key ∈ datakeys(key0, n, ri) ↔ key ∈ datakeys(key0, ri) ∧ n ≤ key.part * VFS_PAGE_SIZE; (s)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) ∧ key ∈ ro → key ∈ ri; (ss)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → ¬ inodekey(0) ∈ ri; (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)% ⊦ key ∈ ri \ ks ↔ key ∈ ri ∧ ¬ key ∈ ks; (ls)