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Proof step 32 from proof inv-writepage (previous step)

# buf = VFS_PAGE_SIZE, (adr1 = (datakey(m, pageno) = key ⊃ adr1;ri[key]) ⊃ datanode(datakey(m, pageno), buf);fs0[(datakey(m, pageno) = key ⊃ adr1;ri[key])]).key = key, key.dentry?, fo.inodes?, ro.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(fi), ri-inj(ri), ubifs-cons(fs0, ri, ro, fi, fo, log0), inodekey(m) ∈ ri, key ∈ ri → ri[key] ∈ fs0 ∧ fs0[ri[key]].key = key ∧ (key.inode? → fs0[ri[key]].inode? ∧ key.ino ≠ 0) ∧ ( key.dentry? → fs0[ri[key]].dentry? ∧ inodekey(key.ino) ∈ ri ∧ inodekey(fs0[ri[key]].ino) ∈ ri ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey(fs0[ri[key]].ino) ∈ ro ∧ fs0[ri[inodekey(key.ino)]].directory) ∧ (key.data? → fs0[ri[key]].data? ∧ inodekey(key.ino) ∈ ri ∧ ¬ fs0[ri[inodekey(key.ino)]].directory ∧ # fs0[ri[key]].data = VFS_PAGE_SIZE), key = datakey(m, pageno) ∨ key ∈ ri ⊦ fs0[ri[inodekey(m)]].directory, adr1 ∈ fs0, (adr1 = (datakey(m, pageno) = key ⊃ adr1;ri[key]) ⊃ datanode(datakey(m, pageno), buf);fs0[(datakey(m, pageno) = key ⊃ adr1;ri[key])]).dentry? ∧ inodekey(key.ino) ∈ ri ∧ inodekey ((adr1 = (datakey(m, pageno) = key ⊃ adr1;ri[key]) ⊃ datanode(datakey(m, pageno), buf);fs0[(datakey(m, pageno) = key ⊃ adr1;ri[key])]).ino) ∈ ri ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey ((adr1 = (datakey(m, pageno) = key ⊃ adr1;ri[key]) ⊃ datanode(datakey(m, pageno), buf);fs0[(datakey(m, pageno) = key ⊃ adr1;ri[key])]).ino) ∈ ro ∧ (adr1 = ri[inodekey(key.ino)] ⊃ datanode(datakey(m, pageno), buf);fs0[ri[inodekey(key.ino)]]).directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 33:
# buf = VFS_PAGE_SIZE, fs0[ri[dentrykey(ino, str)]].key = dentrykey(ino, str), fs0[ri[dentrykey(ino, str)]].dentry?, fs0[ri[inodekey(ino)]].directory, fo.inodes?, ro.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(fi), ri-inj(ri), ubifs-cons(fs0, ri, ro, fi, fo, log0), inodekey(m) ∈ ri, dentrykey(ino, str) ∈ ri, ri[dentrykey(ino, str)] ∈ fs0, inodekey(fs0[ri[dentrykey(ino, str)]].ino) ∈ ri, inodekey(ino) ∈ ri ⊦ fs0[ri[inodekey(m)]].directory, (adr1 = ri[inodekey(ino)] ⊃ datanode(datakey(m, pageno), buf);fs0[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).data?; (s)% ⊦ dentrykey(m, str).ino = m; (s)% ⊦ dentrykey(m, str).dentry?; (s)% ⊦ ¬ dentrykey(m, str).inode?; (s)% ⊦ datakey(m, m0) ≠ dentrykey(m1, str); (s)