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Proof step 215 from proof inv-rename-new-reparent (previous step)

n0 + (boolvar2 ⊃ 1;0) = fs0[ri0[inodekey(m)]].nsubdirs, m1 + 1 = fs0[ri0[inodekey(m)]].size, fs0[ri0[inodekey(m3)]] = inodenode(key0, md1, boolvar0, m5, m9, m10), fs0[ri0[dentrykey(m, str)]] = dentrynode(key1, m3), adr = adr2, fs = fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m3)] [adr3, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m1) ] [adr4, inodenode (inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs + (boolvar2 ⊃ 1;0), fs0[ri0[inodekey(m0)]].size + 1) ], key = dentrykey(m0, str0), log = (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', ri = ri0 -- dentrykey(m, str), fs0[ri0[inodekey(m0)]].directory, fs0[ri0[inodekey(m)]].directory, fs0[ri0[inodekey(m)]].inode?, 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-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m)] ∈ fs0, ri0[inodekey(m0)] ∈ fs0, inodekey(m) ∈ ri0, ri0[inodekey(m3)] ∈ fs0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m0) ∈ ri0, inodekey(m3) ∈ ri0, dentrykey(m, str) ∈ ri0, ¬ adr ∈ ri → adr ∈ fs → adr ∈ fs, fs0[ri0[inodekey(m0)]].trunc? ∨ fs0[ri0[inodekey(m0)]].inode?, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar0 ∧ boolvar2 ∧ m4 = m10, fs0[ri0[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO, fs0[ri0[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, m0 = m, adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m0) ∈ ro, dentrykey(m0, str0) ∈ ri0, inodekey(m) ∈ ro, ¬ adr ∈ ri ∧ adr ∈ fs ∧ key-cons(key, fs[adr])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 216:
m1 + 1 = fs0[ri0[inodekey(m)]].size, n0 + (boolvar2 ⊃ 1;0) = fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[dentrykey(m, str)]] = dentrynode(key1, m3), fs0[ri0[inodekey(m3)]] = inodenode(key0, md1, boolvar0, m5, m9, m10), fs0[ri0[inodekey(m)]].directory, fs0[ri0[inodekey(m0)]].directory, fs0[ri0[inodekey(m0)]].inode?, fs0[ri0[inodekey(m)]].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-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), dentrykey(m, str) ∈ ri0, inodekey(m3) ∈ ri0, inodekey(m0) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, ri0[inodekey(m3)] ∈ fs0, inodekey(m) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str), fs0[ri0[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, fs0[ri0[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar0 ∧ boolvar2 ∧ m4 = m10 ⊦ adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, m0 = m, inodekey(m) ∈ ro, dentrykey(m0, str0) ∈ ri0, inodekey(m0) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0

Rule argument

Additional information

Used simplifier rules: at-fs: ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]);% ⊦ dentrynode(key, m).key = key; (s)% ⊦ dentrynode(key, m).dentry?; (s)%⊦ key-cons(dentrykey(ino, str), nd) ↔ nd.dentry? ∧ nd.key = dentrykey(ino, str); (s)% ⊦ adr ≠ adr0 → fs[adr0, nd][adr] = fs[adr]; (s)% ⊦ adr ∈ fs[adr1, nd] ↔ adr = adr1 ∨ adr ∈ fs; (s)% ⊦ adr ≠ adr0 → (adr ∈ fs[adr0, nd] ↔ adr ∈ fs); (s)