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Proof step 43 from proof inv-write-inode (previous step)

fs0[ri[key]].key = key, fs0[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO ↔ inodekey(m) ∈ ro, key.dentry?, fs0[ri[inodekey(m)]].inode?, ro.inodes?, fo.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, ro), replay-cons-strong(fs0, ri, ro, fi, fo, log0), ri-inj(ri), ri-inj(fi), ubifs-cons(fs0, ri, ro, fi, fo, log0), inodekey(m) ∈ ri, ri[inodekey(m)] ∈ fs0, ri[key] ∈ fs0, key ∈ ri, inodekey(key.ino) ∈ ri, key.data? → fs0[ri[key]].data? ∧ ¬ fs0[ri[inodekey(key.ino)]].directory ∧ # fs0[ri[key]].data = VFS_PAGE_SIZE, key.dentry? → fs0[ri[key]].dentry? ∧ inodekey(fs0[ri[key]].ino) ∈ ri ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey(fs0[ri[key]].ino) ∈ ro ∧ fs0[ri[inodekey(key.ino)]].directory, key.inode? → fs0[ri[key]].inode?, ¬ fs0[ri[inodekey(m)]].directory ∧ ¬ boolvar0 ∨ fs0[ri[inodekey(m)]].directory ∧ boolvar0 ∧ m2 = fs0[ri[inodekey(m)]].size ⊦ key.ino = 0, 0 = m, inodekey(m) = key, adr1 ∈ fs0, fs0[ri[key]].dentry? ∧ inodekey(fs0[ri[key]].ino) ∈ ri ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey(fs0[ri[key]].ino) ∈ ro ∧ (adr1 = (m = key.ino ⊃ adr1;ri[inodekey(key.ino)]) ⊃ inodenode(inodekey(m), md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2) ;fs0[(m = key.ino ⊃ adr1;ri[inodekey(key.ino)])] ) .directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 44:
fs0[ri[dentrykey(ino, str)]].key = dentrykey(ino, str), fs0[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO ↔ inodekey(m) ∈ ro, fs0[ri[dentrykey(ino, str)]].dentry?, fs0[ri[inodekey(ino)]].directory, fs0[ri[inodekey(m)]].inode?, ro.inodes?, fo.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, ro), replay-cons-strong(fs0, ri, ro, fi, fo, log0), ri-inj(ri), ri-inj(fi), ubifs-cons(fs0, ri, ro, fi, fo, log0), inodekey(m) ∈ ri, ri[inodekey(m)] ∈ fs0, ri[dentrykey(ino, str)] ∈ fs0, dentrykey(ino, str) ∈ ri, inodekey(fs0[ri[dentrykey(ino, str)]].ino) ∈ ri, inodekey(ino) ∈ ri, ¬ fs0[ri[inodekey(m)]].directory ∧ ¬ boolvar0 ∨ fs0[ri[inodekey(m)]].directory ∧ boolvar0 ∧ m2 = fs0[ri[inodekey(m)]].size ⊦ 0 = m, ino = 0, (adr1 = (m = ino ⊃ adr1;ri[inodekey(ino)]) ⊃ inodenode(inodekey(m), md, boolvar0, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, m2) ;fs0[(m = ino ⊃ adr1;ri[inodekey(ino)])] ) .directory, adr1 ∈ fs0, inodekey(fs0[ri[dentrykey(ino, str)]].ino) ∈ ro, inodekey(ino) ∈ ro

Rule argument

Additional information

Used simplifier rules: elim-dentry: ⊦ key.dentry? ↔ (∃ ino, str. key = dentrykey(ino, str));%dentry-ubifs-cons: ⊦ dentrykey(ino, str) ∈ ri ∧ ri[dentrykey(ino, str)] ∈ fs ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[dentrykey(ino, str)]].dentry?;%ubifs-parent-in: ⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → inodekey(ino) ∈ ri; (forward) from specification aubifs-inv% ⊦ ¬ dentrykey(m, str).inode?; (s)% ⊦ dentrykey(m, str).dentry?; (s)% ⊦ ¬ dentrykey(m, str).data?; (s)% ⊦ inodekey(m) ≠ dentrykey(m0, str); (s)% ⊦ dentrykey(m, str).ino = m; (s)