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Proof step 69 from proof inv-mkdir (previous step)

fs1[ri1[key]].key = key, key.dentry?, fs1[ri1[inodekey(m)]].directory, fs1[ri1[inodekey(m)]].inode?, fo.inodes?, ro.inodes?, file-node-cons(fs1, ri1), log-cons(log0, fs1), orphans-cons(fs1, ri1, ro), replay-cons-strong(fs1, ri1, ro, fi, fo, log0), ri-inj(fi), ri-inj(ri1), ubifs-cons(fs1, ri1, ro, fi, fo, log0), ri1[key] ∈ fs1, ri1[inodekey(m)] ∈ fs1, inodekey(m) ∈ ri1, key ∈ ri1, inodekey(key.ino) ∈ ri1, key.data? → fs1[ri1[key]].data? ∧ ¬ fs1[ri1[inodekey(key.ino)]].directory ∧ # fs1[ri1[key]].data = VFS_PAGE_SIZE, key.dentry? → fs1[ri1[key]].dentry? ∧ inodekey(fs1[ri1[key]].ino) ∈ ri1 ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey(fs1[ri1[key]].ino) ∈ ro ∧ fs1[ri1[inodekey(key.ino)]].directory, key.inode? → fs1[ri1[key]].inode?, fs1[ri1[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ key.ino = 0, 0 = m, adr1 = adr3, adr1 = adr2, adr2 = adr3, inodekey(m) = key, n = 0, inodekey(m) ∈ ro, dentrykey(m, str) ∈ ri1, inodekey(n) ∈ fo, inodekey(n) ∈ ri1, adr1 ∈ fs1, adr2 ∈ fs1, adr3 ∈ fs1, fs1[ri1[key]].dentry? ∧ (fs1[ri1[key]].ino = n ∨ inodekey(fs1[ri1[key]].ino) ∈ ri1) ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey(fs1[ri1[key]].ino) ∈ ro ∧ (adr3 = (m = key.ino ⊃ adr1;ri1[inodekey(key.ino)]) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (m = key.ino ⊃ adr1;ri1[inodekey(key.ino)]) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (m = key.ino ⊃ adr1;ri1[inodekey(key.ino)]) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(m = key.ino ⊃ adr1;ri1[inodekey(key.ino)])] ) ) ) .directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 70:
fs1[ri1[dentrykey(ino, str0)]].key = dentrykey(ino, str0), fs1[ri1[dentrykey(ino, str0)]].dentry?, fs1[ri1[inodekey(m)]].directory, fs1[ri1[inodekey(ino)]].directory, fs1[ri1[inodekey(m)]].inode?, fo.inodes?, ro.inodes?, file-node-cons(fs1, ri1), log-cons(log0, fs1), orphans-cons(fs1, ri1, ro), replay-cons-strong(fs1, ri1, ro, fi, fo, log0), ri-inj(fi), ri-inj(ri1), ubifs-cons(fs1, ri1, ro, fi, fo, log0), ri1[dentrykey(ino, str0)] ∈ fs1, ri1[inodekey(m)] ∈ fs1, inodekey(m) ∈ ri1, dentrykey(ino, str0) ∈ ri1, inodekey(fs1[ri1[dentrykey(ino, str0)]].ino) ∈ ri1, inodekey(ino) ∈ ri1, fs1[ri1[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ 0 = m, adr1 = adr3, adr1 = adr2, adr2 = adr3, ino = 0, n = 0, (adr3 = (m = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (m = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ dentrynode(dentrykey(m, str), n) ;(adr1 = (m = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs + 1, fs1[ri1[inodekey(m)]].size + 1) ;fs1[(m = ino ⊃ adr1;ri1[inodekey(ino)])] ) ) ) .directory, inodekey(m) ∈ ro, dentrykey(m, str) ∈ ri1, inodekey(n) ∈ fo, inodekey(n) ∈ ri1, adr1 ∈ fs1, adr2 ∈ fs1, adr3 ∈ fs1, inodekey(fs1[ri1[dentrykey(ino, str0)]].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)