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Proof step 51 from proof inv-rename-new-keep-parent (previous step)

fs0[ri0[dentrykey(m, str)]] = dentrynode(key0, m0), fs0[ri0[inodekey(m)]] = inodenode(key1, md0, true, m4, m5, m6), 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-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m0) ∈ ri0, dentrykey(m, str) ∈ ri0, 1 ≤ m6, boolvar2 → 1 ≤ m5, ¬ fs0[ri0[inodekey(m0)]].directory ∧ ¬ boolvar2 ∧ m1 = fs0[ri0[inodekey(m0)]].nlink ∧ m2 = fs0[ri0[inodekey(m0)]].nsubdirs ∨ fs0[ri0[inodekey(m0)]].directory ∧ boolvar2 ∧ m1 = fs0[ri0[inodekey(m0)]].nlink ∧ m2 = fs0[ri0[inodekey(m0)]].nsubdirs ∧ m3 = fs0[ri0[inodekey(m0)]].size, m4 ≠ 0 ∨ m = ROOT_INO ⊦ adr1 = adr2, adr1 = adr3, adr2 = adr3, m = 0, m6 = 0, ubifs-cons (fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m, str0), m0)][adr3, inodenode(inodekey(m), md, true, m4, m5, m6)], (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3], ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), adr2 ∈ ri0 -- dentrykey(m, str), adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, dentrykey(m, str0) ∈ ri0, inodekey(m) ∈ ro, adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 52:
fs0[ri0[inodekey(m)]] = inodenode(key1, md0, true, m4, m5, m6), fs0[ri0[dentrykey(m, str)]] = dentrynode(key0, m0), 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-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), dentrykey(m, str) ∈ ri0, inodekey(m0) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, 1 ≤ m6, boolvar2 → 1 ≤ m5, m4 ≠ 0 ∨ m = ROOT_INO, ¬ fs0[ri0[inodekey(m0)]].directory ∧ ¬ boolvar2 ∧ m1 = fs0[ri0[inodekey(m0)]].nlink ∧ m2 = fs0[ri0[inodekey(m0)]].nsubdirs ∨ fs0[ri0[inodekey(m0)]].directory ∧ boolvar2 ∧ m1 = fs0[ri0[inodekey(m0)]].nlink ∧ m2 = fs0[ri0[inodekey(m0)]].nsubdirs ∧ m3 = fs0[ri0[inodekey(m0)]].size ⊦ adr1 = adr3, adr1 = adr2, adr2 = adr3, m = 0, m6 = 0, adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2], inodekey(m) ∈ ro, dentrykey(m, str0) ∈ ri0, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str), ( ( 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) ∈ ro ∧ ¬ inodekey(fs0[ri0[key]].ino) ∈ ro ∧ 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 = inodekey(m) ∨ key = dentrykey(m, str0) ∨ key ≠ dentrykey(m, str) ∧ key ∈ ri0 → ( (inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) = adr3 ∨ (inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) = adr2 ∨ (inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) = adr1 ∨ (inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ∈ fs0) ∧ (adr3 = (inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = (inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str0), m0) ;(adr1 = (inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key])))] ) ) ) .key = key ∧ ( key.inode? → (adr3 = (inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = (inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str0), m0) ;(adr1 = (inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key])))] ) ) ) .inode? ∧ key.ino ≠ 0) ∧ ( key.dentry? → (adr3 = (inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = (inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str0), m0) ;(adr1 = (inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key])))] ) ) ) .dentry? ∧ inodekey(key.ino) ∈ ri0 ∧ ( (adr3 = (inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = (inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str0), m0) ;(adr1 = (inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key])))] ) ) ) .ino = m ∨ inodekey ((adr3 = (inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = (inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str0), m0) ;(adr1 = (inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key])))] ) ) ) .ino) ∈ ri0) ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey ((adr3 = (inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = (inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str0), m0) ;(adr1 = (inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key])))] ) ) ) .ino) ∈ ro ∧ (adr3 = (m = key.ino ⊃ adr3;ri0[inodekey(key.ino)]) ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = (m = key.ino ⊃ adr3;ri0[inodekey(key.ino)]) ⊃ dentrynode(dentrykey(m, str0), m0) ;(adr1 = (m = key.ino ⊃ adr3;ri0[inodekey(key.ino)]) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])] ) ) ) .directory) ∧ ( key.data? → (adr3 = (inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = (inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str0), m0) ;(adr1 = (inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key])))] ) ) ) .data? ∧ inodekey(key.ino) ∈ ri0 ∧ ¬ (adr3 = (m = key.ino ⊃ adr3;ri0[inodekey(key.ino)]) ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = (m = key.ino ⊃ adr3;ri0[inodekey(key.ino)]) ⊃ dentrynode(dentrykey(m, str0), m0) ;(adr1 = (m = key.ino ⊃ adr3;ri0[inodekey(key.ino)]) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(m = key.ino ⊃ adr3;ri0[inodekey(key.ino)])] ) ) ) .directory ∧ # (adr3 = (inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = (inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str0), m0) ;(adr1 = (inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key])))] ) ) ) .data = VFS_PAGE_SIZE)) ∧ ( ( 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 ∈ log0 ∨ adr = adr1 ∨ adr = adr2 ∨ adr = adr3 → (adr = adr3 ∨ adr = adr2 ∨ adr = adr1 ∨ adr ∈ fs0) ∧ ( (adr3 = adr ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str0), m0);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) .inode? → (adr3 = adr ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str0), m0);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) .key .inode? ∧ (adr3 = adr ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str0), m0);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) .key .ino ≠ 0) ∧ ( (adr3 = adr ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str0), m0);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) .dentry? → (adr3 = adr ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str0), m0);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) .key .dentry?) ∧ ( (adr3 = adr ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str0), m0);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) .data? → (adr3 = adr ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str0), m0);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) .key .data?) ∧ ( (adr3 = adr ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str0), m0);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) .trunc? → (adr3 = adr ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str0), m0);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) .key .inode?))

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-ri: ⊦ ri[key0, adr][key1] = (key0 = key1 ⊃ adr;ri[key1]);%at-del-ri: ⊦ (ri -- key0)[key1] = (key0 = key1 ⊃ (∅)[key0];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)% ⊦ adr ∈ fs[adr1, nd] ↔ adr = adr1 ∨ adr ∈ fs; (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 ∧ ¬ adr2 ∈ fs ∧ adr0 ≠ adr1 ∧ adr0 ≠ adr2 ∧ adr1 ≠ adr2 → ¬ dups(log + adr0 ' + adr1 ' + adr2 '); (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)% ⊦ ks.inodes? → ¬ dentrykey(ino, str) ∈ ks; (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)% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)% ⊦ inodekey(m) ≠ dentrykey(m0, str); (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)