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Proof step 69 from proof inv-rename-new-keep-parent (previous step)

(adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m0);fs0[(dentrykey(m, str0) = key ⊃ adr2;ri0[key])]).key = key, 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, key ∈ ri0 → ri0[key] ∈ fs0 ∧ fs0[ri0[key]].key = key ∧ (key.inode? → fs0[ri0[key]].inode?) ∧ ( 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), ¬ fs0[ri0[inodekey(m0)]].directory ∧ ¬ boolvar2 ∨ fs0[ri0[inodekey(m0)]].directory ∧ boolvar2 ∧ m3 = fs0[ri0[inodekey(m0)]].size, m4 ≠ 0 ∨ m = ROOT_INO, key = dentrykey(m, str0) ∨ key ∈ ri0 ⊦ key.ino = 0, (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) = adr1, (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) = adr3, adr1 = adr2, adr1 = adr3, adr2 = adr3, key = dentrykey(m, str), key = inodekey(m), 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], ((dentrykey(m, str0) = key ⊃ adr2;ri0[key]) = adr2 ∨ (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ∈ fs0) ∧ ( key.inode? → (adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m0);fs0[(dentrykey(m, str0) = key ⊃ adr2;ri0[key])]).inode?) ∧ ( key.dentry? → (adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m0);fs0[(dentrykey(m, str0) = key ⊃ adr2;ri0[key])]) .dentry? ∧ inodekey(key.ino) ∈ ri0 ∧ ( (adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m0);fs0[(dentrykey(m, str0) = key ⊃ adr2;ri0[key])]) .ino = m ∨ inodekey ((adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m0) ;fs0[(dentrykey(m, str0) = key ⊃ adr2;ri0[key])] ) .ino) ∈ ri0) ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey ((adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m0);fs0[(dentrykey(m, str0) = key ⊃ adr2;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? → (adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m0);fs0[(dentrykey(m, str0) = key ⊃ adr2;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 ∧ # (adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m0);fs0[(dentrykey(m, str0) = key ⊃ adr2;ri0[key])]) .data = VFS_PAGE_SIZE)

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Proof step 70:
(adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m0);fs0[(dentrykey(m, str0) = key ⊃ adr2;ri0[key])]).key = key, 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, key ∈ ri0 → ri0[key] ∈ fs0 ∧ fs0[ri0[key]].key = key ∧ (key.inode? → fs0[ri0[key]].inode?) ∧ ( 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), boolvar2 → 1 ≤ m5, key = dentrykey(m, str0) ∨ key ∈ ri0, m4 ≠ 0 ∨ m = ROOT_INO, ¬ fs0[ri0[inodekey(m0)]].directory ∧ ¬ boolvar2 ∨ fs0[ri0[inodekey(m0)]].directory ∧ boolvar2 ∧ m3 = fs0[ri0[inodekey(m0)]].size ⊦ key.ino = 0, (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) = adr3, ri0[key] = adr1, adr1 = adr3, adr1 = adr2, adr2 = adr3, dentrykey(m, str0) = key, key = inodekey(m), key = dentrykey(m, str), 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), ((dentrykey(m, str0) = key ⊃ adr2;ri0[key]) = adr2 ∨ (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ∈ fs0) ∧ ( key.inode? → (adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m0);fs0[(dentrykey(m, str0) = key ⊃ adr2;ri0[key])]).inode?) ∧ ( key.dentry? → (adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m0);fs0[(dentrykey(m, str0) = key ⊃ adr2;ri0[key])]) .dentry? ∧ inodekey(key.ino) ∈ ri0 ∧ ( (adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m0);fs0[(dentrykey(m, str0) = key ⊃ adr2;ri0[key])]) .ino = m ∨ inodekey ((adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m0) ;fs0[(dentrykey(m, str0) = key ⊃ adr2;ri0[key])] ) .ino) ∈ ri0) ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey ((adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m0);fs0[(dentrykey(m, str0) = key ⊃ adr2;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? → (adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m0);fs0[(dentrykey(m, str0) = key ⊃ adr2;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 ∧ # (adr2 = (dentrykey(m, str0) = key ⊃ adr2;ri0[key]) ⊃ dentrynode(dentrykey(m, str0), m0);fs0[(dentrykey(m, str0) = key ⊃ adr2;ri0[key])]) .data = VFS_PAGE_SIZE)

Rule argument

pos: right 2

Additional information

Used simplifier rules: ubifs-cons-dentry-target-not-in-orphans: ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) ∧ dentrykey(ino, str) ∈ ri ∧ fs[ri[dentrykey(ino, str)]] = dentrynode(key, m) → ¬ inodekey(m) ∈ ro;% ⊦ dentrynode(key, m).key = key; (s)% ⊦ dentrykey(m, str) = dentrykey(m0, str0) ↔ m = m0 ∧ str = str0; (ws)% ⊦ inodekey(m) ≠ dentrykey(m0, str); (s)% ⊦ dentrykey(m, str).ino = m; (s)% ⊦ ¬ dentrykey(m, str).inode?; (s)% ⊦ dentrykey(m, str).dentry?; (s)% ⊦ dentrynode(key, m).dentry?; (s)% ⊦ dentrynode(key, m).ino = m; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).directory ↔ boolvar; (s)% ⊦ ¬ dentrykey(m, str).data?; (s)