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Proof step 52 from proof inv-rename-new-keep-parent (previous step)

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?))

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 53:
fs0[ri0[dentrykey(m, str)]] = dentrynode(key0, m0), fs0[ri0[inodekey(m)]] = inodenode(key1, md0, true, m4, m5, m6), m1 = fs0[ri0[inodekey(m0)]].nlink, 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, 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], ( ( 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

fma: m1 = fs0[ri0[inodekey(m0)]].nlink

Additional information

Used formulas: m1 = fs0[ri0[inodekey(m0)]].nlink